diff --git "a/new_globjson/processed_ncert_class12_physics-2.json" "b/new_globjson/processed_ncert_class12_physics-2.json" new file mode 100644--- /dev/null +++ "b/new_globjson/processed_ncert_class12_physics-2.json" @@ -0,0 +1,21197 @@ +[ + { + "Chapter": "9", + "sentence_range": "1-4", + "Text": "Chapter Nine\nRAY OPTICS\nAND OPTICAL\nINSTRUMENTS\n9 1 INTRODUCTION\nNature has endowed the human eye (retina) with the sensitivity to detect\nelectromagnetic waves within a small range of the electromagnetic\nspectrum Electromagnetic radiation belonging to this region of the\nspectrum (wavelength of about 400 nm to 750 nm) is called light It is\nmainly through light and the sense of vision that we know and interpret\nthe world around us" + }, + { + "Chapter": "9", + "sentence_range": "2-5", + "Text": "1 INTRODUCTION\nNature has endowed the human eye (retina) with the sensitivity to detect\nelectromagnetic waves within a small range of the electromagnetic\nspectrum Electromagnetic radiation belonging to this region of the\nspectrum (wavelength of about 400 nm to 750 nm) is called light It is\nmainly through light and the sense of vision that we know and interpret\nthe world around us There are two things that we can intuitively mention about light from\ncommon experience" + }, + { + "Chapter": "9", + "sentence_range": "3-6", + "Text": "Electromagnetic radiation belonging to this region of the\nspectrum (wavelength of about 400 nm to 750 nm) is called light It is\nmainly through light and the sense of vision that we know and interpret\nthe world around us There are two things that we can intuitively mention about light from\ncommon experience First, that it travels with enormous speed and second,\nthat it travels in a straight line" + }, + { + "Chapter": "9", + "sentence_range": "4-7", + "Text": "It is\nmainly through light and the sense of vision that we know and interpret\nthe world around us There are two things that we can intuitively mention about light from\ncommon experience First, that it travels with enormous speed and second,\nthat it travels in a straight line It took some time for people to realise that\nthe speed of light is finite and measurable" + }, + { + "Chapter": "9", + "sentence_range": "5-8", + "Text": "There are two things that we can intuitively mention about light from\ncommon experience First, that it travels with enormous speed and second,\nthat it travels in a straight line It took some time for people to realise that\nthe speed of light is finite and measurable Its presently accepted value\nin vacuum is c = 2" + }, + { + "Chapter": "9", + "sentence_range": "6-9", + "Text": "First, that it travels with enormous speed and second,\nthat it travels in a straight line It took some time for people to realise that\nthe speed of light is finite and measurable Its presently accepted value\nin vacuum is c = 2 99792458 \u00d7 108 m s\u20131" + }, + { + "Chapter": "9", + "sentence_range": "7-10", + "Text": "It took some time for people to realise that\nthe speed of light is finite and measurable Its presently accepted value\nin vacuum is c = 2 99792458 \u00d7 108 m s\u20131 For many purposes, it suffices\nto take c = 3 \u00d7 108 m s\u20131" + }, + { + "Chapter": "9", + "sentence_range": "8-11", + "Text": "Its presently accepted value\nin vacuum is c = 2 99792458 \u00d7 108 m s\u20131 For many purposes, it suffices\nto take c = 3 \u00d7 108 m s\u20131 The speed of light in vacuum is the highest\nspeed attainable in nature" + }, + { + "Chapter": "9", + "sentence_range": "9-12", + "Text": "99792458 \u00d7 108 m s\u20131 For many purposes, it suffices\nto take c = 3 \u00d7 108 m s\u20131 The speed of light in vacuum is the highest\nspeed attainable in nature The intuitive notion that light travels in a straight line seems to\ncontradict what we have learnt in Chapter 8, that light is an\nelectromagnetic wave of wavelength belonging to the visible part of the\nspectrum" + }, + { + "Chapter": "9", + "sentence_range": "10-13", + "Text": "For many purposes, it suffices\nto take c = 3 \u00d7 108 m s\u20131 The speed of light in vacuum is the highest\nspeed attainable in nature The intuitive notion that light travels in a straight line seems to\ncontradict what we have learnt in Chapter 8, that light is an\nelectromagnetic wave of wavelength belonging to the visible part of the\nspectrum How to reconcile the two facts" + }, + { + "Chapter": "9", + "sentence_range": "11-14", + "Text": "The speed of light in vacuum is the highest\nspeed attainable in nature The intuitive notion that light travels in a straight line seems to\ncontradict what we have learnt in Chapter 8, that light is an\nelectromagnetic wave of wavelength belonging to the visible part of the\nspectrum How to reconcile the two facts The answer is that the\nwavelength of light is very small compared to the size of ordinary objects\nthat we encounter commonly (generally of the order of a few cm or larger)" + }, + { + "Chapter": "9", + "sentence_range": "12-15", + "Text": "The intuitive notion that light travels in a straight line seems to\ncontradict what we have learnt in Chapter 8, that light is an\nelectromagnetic wave of wavelength belonging to the visible part of the\nspectrum How to reconcile the two facts The answer is that the\nwavelength of light is very small compared to the size of ordinary objects\nthat we encounter commonly (generally of the order of a few cm or larger) In this situation, as you will learn in Chapter 10, a light wave can be\nconsidered to travel from one point to another, along a straight line joining\nRationalised 2023-24\nPhysics\n222\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "13-16", + "Text": "How to reconcile the two facts The answer is that the\nwavelength of light is very small compared to the size of ordinary objects\nthat we encounter commonly (generally of the order of a few cm or larger) In this situation, as you will learn in Chapter 10, a light wave can be\nconsidered to travel from one point to another, along a straight line joining\nRationalised 2023-24\nPhysics\n222\nFIGURE 9 1 The incident ray, reflected ray\nand the normal to the reflecting surface lie\nin the same plane" + }, + { + "Chapter": "9", + "sentence_range": "14-17", + "Text": "The answer is that the\nwavelength of light is very small compared to the size of ordinary objects\nthat we encounter commonly (generally of the order of a few cm or larger) In this situation, as you will learn in Chapter 10, a light wave can be\nconsidered to travel from one point to another, along a straight line joining\nRationalised 2023-24\nPhysics\n222\nFIGURE 9 1 The incident ray, reflected ray\nand the normal to the reflecting surface lie\nin the same plane FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "15-18", + "Text": "In this situation, as you will learn in Chapter 10, a light wave can be\nconsidered to travel from one point to another, along a straight line joining\nRationalised 2023-24\nPhysics\n222\nFIGURE 9 1 The incident ray, reflected ray\nand the normal to the reflecting surface lie\nin the same plane FIGURE 9 2 The Cartesian Sign Convention" + }, + { + "Chapter": "9", + "sentence_range": "16-19", + "Text": "1 The incident ray, reflected ray\nand the normal to the reflecting surface lie\nin the same plane FIGURE 9 2 The Cartesian Sign Convention them" + }, + { + "Chapter": "9", + "sentence_range": "17-20", + "Text": "FIGURE 9 2 The Cartesian Sign Convention them The path is called a ray of light, and a bundle of such rays\nconstitutes a beam of light" + }, + { + "Chapter": "9", + "sentence_range": "18-21", + "Text": "2 The Cartesian Sign Convention them The path is called a ray of light, and a bundle of such rays\nconstitutes a beam of light In this chapter, we consider the phenomena of reflection, refraction\nand dispersion of light, using the ray picture of light" + }, + { + "Chapter": "9", + "sentence_range": "19-22", + "Text": "them The path is called a ray of light, and a bundle of such rays\nconstitutes a beam of light In this chapter, we consider the phenomena of reflection, refraction\nand dispersion of light, using the ray picture of light Using the basic\nlaws of reflection and refraction, we shall study the image formation by\nplane and spherical reflecting and refracting surfaces" + }, + { + "Chapter": "9", + "sentence_range": "20-23", + "Text": "The path is called a ray of light, and a bundle of such rays\nconstitutes a beam of light In this chapter, we consider the phenomena of reflection, refraction\nand dispersion of light, using the ray picture of light Using the basic\nlaws of reflection and refraction, we shall study the image formation by\nplane and spherical reflecting and refracting surfaces We then go on to\ndescribe the construction and working of some important optical\ninstruments, including the human eye" + }, + { + "Chapter": "9", + "sentence_range": "21-24", + "Text": "In this chapter, we consider the phenomena of reflection, refraction\nand dispersion of light, using the ray picture of light Using the basic\nlaws of reflection and refraction, we shall study the image formation by\nplane and spherical reflecting and refracting surfaces We then go on to\ndescribe the construction and working of some important optical\ninstruments, including the human eye 9" + }, + { + "Chapter": "9", + "sentence_range": "22-25", + "Text": "Using the basic\nlaws of reflection and refraction, we shall study the image formation by\nplane and spherical reflecting and refracting surfaces We then go on to\ndescribe the construction and working of some important optical\ninstruments, including the human eye 9 2 REFLECTION OF LIGHT BY SPHERICAL MIRRORS\nWe are familiar with the laws of reflection" + }, + { + "Chapter": "9", + "sentence_range": "23-26", + "Text": "We then go on to\ndescribe the construction and working of some important optical\ninstruments, including the human eye 9 2 REFLECTION OF LIGHT BY SPHERICAL MIRRORS\nWe are familiar with the laws of reflection The\nangle of reflection (i" + }, + { + "Chapter": "9", + "sentence_range": "24-27", + "Text": "9 2 REFLECTION OF LIGHT BY SPHERICAL MIRRORS\nWe are familiar with the laws of reflection The\nangle of reflection (i e" + }, + { + "Chapter": "9", + "sentence_range": "25-28", + "Text": "2 REFLECTION OF LIGHT BY SPHERICAL MIRRORS\nWe are familiar with the laws of reflection The\nangle of reflection (i e , the angle between reflected\nray and the normal to the reflecting surface or\nthe mirror) equals the angle of incidence (angle\nbetween incident ray and the normal)" + }, + { + "Chapter": "9", + "sentence_range": "26-29", + "Text": "The\nangle of reflection (i e , the angle between reflected\nray and the normal to the reflecting surface or\nthe mirror) equals the angle of incidence (angle\nbetween incident ray and the normal) Also that\nthe incident ray, reflected ray and the normal to\nthe reflecting surface at the point of incidence lie\nin the same plane (Fig" + }, + { + "Chapter": "9", + "sentence_range": "27-30", + "Text": "e , the angle between reflected\nray and the normal to the reflecting surface or\nthe mirror) equals the angle of incidence (angle\nbetween incident ray and the normal) Also that\nthe incident ray, reflected ray and the normal to\nthe reflecting surface at the point of incidence lie\nin the same plane (Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "28-31", + "Text": ", the angle between reflected\nray and the normal to the reflecting surface or\nthe mirror) equals the angle of incidence (angle\nbetween incident ray and the normal) Also that\nthe incident ray, reflected ray and the normal to\nthe reflecting surface at the point of incidence lie\nin the same plane (Fig 9 1)" + }, + { + "Chapter": "9", + "sentence_range": "29-32", + "Text": "Also that\nthe incident ray, reflected ray and the normal to\nthe reflecting surface at the point of incidence lie\nin the same plane (Fig 9 1) These laws are valid\nat each point on any reflecting surface whether\nplane or curved" + }, + { + "Chapter": "9", + "sentence_range": "30-33", + "Text": "9 1) These laws are valid\nat each point on any reflecting surface whether\nplane or curved However, we shall restrict our\ndiscussion to the special case of curved surfaces,\nthat is, spherical surfaces" + }, + { + "Chapter": "9", + "sentence_range": "31-34", + "Text": "1) These laws are valid\nat each point on any reflecting surface whether\nplane or curved However, we shall restrict our\ndiscussion to the special case of curved surfaces,\nthat is, spherical surfaces The normal in this case\nis to be taken as normal to the tangent to surface\nat the point of incidence" + }, + { + "Chapter": "9", + "sentence_range": "32-35", + "Text": "These laws are valid\nat each point on any reflecting surface whether\nplane or curved However, we shall restrict our\ndiscussion to the special case of curved surfaces,\nthat is, spherical surfaces The normal in this case\nis to be taken as normal to the tangent to surface\nat the point of incidence That is, the normal is\nalong the radius, the line joining the centre of curvature of the mirror to\nthe point of incidence" + }, + { + "Chapter": "9", + "sentence_range": "33-36", + "Text": "However, we shall restrict our\ndiscussion to the special case of curved surfaces,\nthat is, spherical surfaces The normal in this case\nis to be taken as normal to the tangent to surface\nat the point of incidence That is, the normal is\nalong the radius, the line joining the centre of curvature of the mirror to\nthe point of incidence We have already studied that the geometric centre of a spherical mirror\nis called its pole while that of a spherical lens is called its optical centre" + }, + { + "Chapter": "9", + "sentence_range": "34-37", + "Text": "The normal in this case\nis to be taken as normal to the tangent to surface\nat the point of incidence That is, the normal is\nalong the radius, the line joining the centre of curvature of the mirror to\nthe point of incidence We have already studied that the geometric centre of a spherical mirror\nis called its pole while that of a spherical lens is called its optical centre The line joining the pole and the centre of curvature of the spherical\nmirror is known as the principal axis" + }, + { + "Chapter": "9", + "sentence_range": "35-38", + "Text": "That is, the normal is\nalong the radius, the line joining the centre of curvature of the mirror to\nthe point of incidence We have already studied that the geometric centre of a spherical mirror\nis called its pole while that of a spherical lens is called its optical centre The line joining the pole and the centre of curvature of the spherical\nmirror is known as the principal axis In the case of spherical lenses, the\nprincipal axis is the line joining the optical centre with its principal focus\nas you will see later" + }, + { + "Chapter": "9", + "sentence_range": "36-39", + "Text": "We have already studied that the geometric centre of a spherical mirror\nis called its pole while that of a spherical lens is called its optical centre The line joining the pole and the centre of curvature of the spherical\nmirror is known as the principal axis In the case of spherical lenses, the\nprincipal axis is the line joining the optical centre with its principal focus\nas you will see later 9" + }, + { + "Chapter": "9", + "sentence_range": "37-40", + "Text": "The line joining the pole and the centre of curvature of the spherical\nmirror is known as the principal axis In the case of spherical lenses, the\nprincipal axis is the line joining the optical centre with its principal focus\nas you will see later 9 2" + }, + { + "Chapter": "9", + "sentence_range": "38-41", + "Text": "In the case of spherical lenses, the\nprincipal axis is the line joining the optical centre with its principal focus\nas you will see later 9 2 1 Sign convention\nTo derive the relevant formulae for\nreflection by spherical mirrors and\nrefraction by spherical lenses, we must\nfirst adopt a sign convention for\nmeasuring distances" + }, + { + "Chapter": "9", + "sentence_range": "39-42", + "Text": "9 2 1 Sign convention\nTo derive the relevant formulae for\nreflection by spherical mirrors and\nrefraction by spherical lenses, we must\nfirst adopt a sign convention for\nmeasuring distances In this book, we\nshall follow the Cartesian sign\nconvention" + }, + { + "Chapter": "9", + "sentence_range": "40-43", + "Text": "2 1 Sign convention\nTo derive the relevant formulae for\nreflection by spherical mirrors and\nrefraction by spherical lenses, we must\nfirst adopt a sign convention for\nmeasuring distances In this book, we\nshall follow the Cartesian sign\nconvention According to this\nconvention, all distances are measured\nfrom the pole of the mirror or the optical\ncentre of the lens" + }, + { + "Chapter": "9", + "sentence_range": "41-44", + "Text": "1 Sign convention\nTo derive the relevant formulae for\nreflection by spherical mirrors and\nrefraction by spherical lenses, we must\nfirst adopt a sign convention for\nmeasuring distances In this book, we\nshall follow the Cartesian sign\nconvention According to this\nconvention, all distances are measured\nfrom the pole of the mirror or the optical\ncentre of the lens The distances\nmeasured in the same direction as the\nincident light are taken as positive and\nthose measured in the direction\nopposite to the direction of incident light are taken as negative (Fig" + }, + { + "Chapter": "9", + "sentence_range": "42-45", + "Text": "In this book, we\nshall follow the Cartesian sign\nconvention According to this\nconvention, all distances are measured\nfrom the pole of the mirror or the optical\ncentre of the lens The distances\nmeasured in the same direction as the\nincident light are taken as positive and\nthose measured in the direction\nopposite to the direction of incident light are taken as negative (Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "43-46", + "Text": "According to this\nconvention, all distances are measured\nfrom the pole of the mirror or the optical\ncentre of the lens The distances\nmeasured in the same direction as the\nincident light are taken as positive and\nthose measured in the direction\nopposite to the direction of incident light are taken as negative (Fig 9 2)" + }, + { + "Chapter": "9", + "sentence_range": "44-47", + "Text": "The distances\nmeasured in the same direction as the\nincident light are taken as positive and\nthose measured in the direction\nopposite to the direction of incident light are taken as negative (Fig 9 2) The heights measured upwards with respect to x-axis and normal to the\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n223\nprincipal axis (x-axis) of the mirror/lens are taken as positive (Fig" + }, + { + "Chapter": "9", + "sentence_range": "45-48", + "Text": "9 2) The heights measured upwards with respect to x-axis and normal to the\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n223\nprincipal axis (x-axis) of the mirror/lens are taken as positive (Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "46-49", + "Text": "2) The heights measured upwards with respect to x-axis and normal to the\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n223\nprincipal axis (x-axis) of the mirror/lens are taken as positive (Fig 9 2)" + }, + { + "Chapter": "9", + "sentence_range": "47-50", + "Text": "The heights measured upwards with respect to x-axis and normal to the\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n223\nprincipal axis (x-axis) of the mirror/lens are taken as positive (Fig 9 2) The heights measured downwards are taken as negative" + }, + { + "Chapter": "9", + "sentence_range": "48-51", + "Text": "9 2) The heights measured downwards are taken as negative With a common accepted convention, it turns out that a single formula\nfor spherical mirrors and a single formula for spherical lenses can handle\nall different cases" + }, + { + "Chapter": "9", + "sentence_range": "49-52", + "Text": "2) The heights measured downwards are taken as negative With a common accepted convention, it turns out that a single formula\nfor spherical mirrors and a single formula for spherical lenses can handle\nall different cases 9" + }, + { + "Chapter": "9", + "sentence_range": "50-53", + "Text": "The heights measured downwards are taken as negative With a common accepted convention, it turns out that a single formula\nfor spherical mirrors and a single formula for spherical lenses can handle\nall different cases 9 2" + }, + { + "Chapter": "9", + "sentence_range": "51-54", + "Text": "With a common accepted convention, it turns out that a single formula\nfor spherical mirrors and a single formula for spherical lenses can handle\nall different cases 9 2 2 Focal length of spherical mirrors\nFigure 9" + }, + { + "Chapter": "9", + "sentence_range": "52-55", + "Text": "9 2 2 Focal length of spherical mirrors\nFigure 9 3 shows what happens when a parallel beam of light is incident\non (a) a concave mirror, and (b) a convex mirror" + }, + { + "Chapter": "9", + "sentence_range": "53-56", + "Text": "2 2 Focal length of spherical mirrors\nFigure 9 3 shows what happens when a parallel beam of light is incident\non (a) a concave mirror, and (b) a convex mirror We assume that the rays\nare paraxial, i" + }, + { + "Chapter": "9", + "sentence_range": "54-57", + "Text": "2 Focal length of spherical mirrors\nFigure 9 3 shows what happens when a parallel beam of light is incident\non (a) a concave mirror, and (b) a convex mirror We assume that the rays\nare paraxial, i e" + }, + { + "Chapter": "9", + "sentence_range": "55-58", + "Text": "3 shows what happens when a parallel beam of light is incident\non (a) a concave mirror, and (b) a convex mirror We assume that the rays\nare paraxial, i e , they are incident at points close to the pole P of the mirror\nand make small angles with the principal axis" + }, + { + "Chapter": "9", + "sentence_range": "56-59", + "Text": "We assume that the rays\nare paraxial, i e , they are incident at points close to the pole P of the mirror\nand make small angles with the principal axis The reflected rays converge\nat a point F on the principal axis of a concave mirror [Fig" + }, + { + "Chapter": "9", + "sentence_range": "57-60", + "Text": "e , they are incident at points close to the pole P of the mirror\nand make small angles with the principal axis The reflected rays converge\nat a point F on the principal axis of a concave mirror [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "58-61", + "Text": ", they are incident at points close to the pole P of the mirror\nand make small angles with the principal axis The reflected rays converge\nat a point F on the principal axis of a concave mirror [Fig 9 3(a)]" + }, + { + "Chapter": "9", + "sentence_range": "59-62", + "Text": "The reflected rays converge\nat a point F on the principal axis of a concave mirror [Fig 9 3(a)] For a convex mirror, the reflected rays appear to diverge from a point F\non its principal axis [Fig" + }, + { + "Chapter": "9", + "sentence_range": "60-63", + "Text": "9 3(a)] For a convex mirror, the reflected rays appear to diverge from a point F\non its principal axis [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "61-64", + "Text": "3(a)] For a convex mirror, the reflected rays appear to diverge from a point F\non its principal axis [Fig 9 3(b)]" + }, + { + "Chapter": "9", + "sentence_range": "62-65", + "Text": "For a convex mirror, the reflected rays appear to diverge from a point F\non its principal axis [Fig 9 3(b)] The point F is called the principal focus\nof the mirror" + }, + { + "Chapter": "9", + "sentence_range": "63-66", + "Text": "9 3(b)] The point F is called the principal focus\nof the mirror If the parallel paraxial beam of light were incident, making\nsome angle with the principal axis, the reflected rays would converge (or\nappear to diverge) from a point in a plane through F normal to the principal\naxis" + }, + { + "Chapter": "9", + "sentence_range": "64-67", + "Text": "3(b)] The point F is called the principal focus\nof the mirror If the parallel paraxial beam of light were incident, making\nsome angle with the principal axis, the reflected rays would converge (or\nappear to diverge) from a point in a plane through F normal to the principal\naxis This is called the focal plane of the mirror [Fig" + }, + { + "Chapter": "9", + "sentence_range": "65-68", + "Text": "The point F is called the principal focus\nof the mirror If the parallel paraxial beam of light were incident, making\nsome angle with the principal axis, the reflected rays would converge (or\nappear to diverge) from a point in a plane through F normal to the principal\naxis This is called the focal plane of the mirror [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "66-69", + "Text": "If the parallel paraxial beam of light were incident, making\nsome angle with the principal axis, the reflected rays would converge (or\nappear to diverge) from a point in a plane through F normal to the principal\naxis This is called the focal plane of the mirror [Fig 9 3(c)]" + }, + { + "Chapter": "9", + "sentence_range": "67-70", + "Text": "This is called the focal plane of the mirror [Fig 9 3(c)] FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "68-71", + "Text": "9 3(c)] FIGURE 9 3 Focus of a concave and convex mirror" + }, + { + "Chapter": "9", + "sentence_range": "69-72", + "Text": "3(c)] FIGURE 9 3 Focus of a concave and convex mirror The distance between the focus F and the pole P of the mirror is called\nthe focal length of the mirror, denoted by f" + }, + { + "Chapter": "9", + "sentence_range": "70-73", + "Text": "FIGURE 9 3 Focus of a concave and convex mirror The distance between the focus F and the pole P of the mirror is called\nthe focal length of the mirror, denoted by f We now show that f = R/2,\nwhere R is the radius of curvature of the mirror" + }, + { + "Chapter": "9", + "sentence_range": "71-74", + "Text": "3 Focus of a concave and convex mirror The distance between the focus F and the pole P of the mirror is called\nthe focal length of the mirror, denoted by f We now show that f = R/2,\nwhere R is the radius of curvature of the mirror The geometry of reflection\nof an incident ray is shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "72-75", + "Text": "The distance between the focus F and the pole P of the mirror is called\nthe focal length of the mirror, denoted by f We now show that f = R/2,\nwhere R is the radius of curvature of the mirror The geometry of reflection\nof an incident ray is shown in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "73-76", + "Text": "We now show that f = R/2,\nwhere R is the radius of curvature of the mirror The geometry of reflection\nof an incident ray is shown in Fig 9 4" + }, + { + "Chapter": "9", + "sentence_range": "74-77", + "Text": "The geometry of reflection\nof an incident ray is shown in Fig 9 4 Let C be the centre of curvature of the mirror" + }, + { + "Chapter": "9", + "sentence_range": "75-78", + "Text": "9 4 Let C be the centre of curvature of the mirror Consider a ray parallel\nto the principal axis striking the mirror at M" + }, + { + "Chapter": "9", + "sentence_range": "76-79", + "Text": "4 Let C be the centre of curvature of the mirror Consider a ray parallel\nto the principal axis striking the mirror at M Then CM will be\nperpendicular to the mirror at M" + }, + { + "Chapter": "9", + "sentence_range": "77-80", + "Text": "Let C be the centre of curvature of the mirror Consider a ray parallel\nto the principal axis striking the mirror at M Then CM will be\nperpendicular to the mirror at M Let q be the angle of incidence, and MD\nRationalised 2023-24\nPhysics\n224\nbe the perpendicular from M on the principal axis" + }, + { + "Chapter": "9", + "sentence_range": "78-81", + "Text": "Consider a ray parallel\nto the principal axis striking the mirror at M Then CM will be\nperpendicular to the mirror at M Let q be the angle of incidence, and MD\nRationalised 2023-24\nPhysics\n224\nbe the perpendicular from M on the principal axis Then,\n\u00d0MCP = q and \u00d0MFP = 2q\nNow,\ntanq =\nMD\nCD and tan 2q = \nMD\nFD\n(9" + }, + { + "Chapter": "9", + "sentence_range": "79-82", + "Text": "Then CM will be\nperpendicular to the mirror at M Let q be the angle of incidence, and MD\nRationalised 2023-24\nPhysics\n224\nbe the perpendicular from M on the principal axis Then,\n\u00d0MCP = q and \u00d0MFP = 2q\nNow,\ntanq =\nMD\nCD and tan 2q = \nMD\nFD\n(9 1)\nFor small q, which is true for paraxial rays, tanq \u00bb q,\ntan 2q \u00bb 2q" + }, + { + "Chapter": "9", + "sentence_range": "80-83", + "Text": "Let q be the angle of incidence, and MD\nRationalised 2023-24\nPhysics\n224\nbe the perpendicular from M on the principal axis Then,\n\u00d0MCP = q and \u00d0MFP = 2q\nNow,\ntanq =\nMD\nCD and tan 2q = \nMD\nFD\n(9 1)\nFor small q, which is true for paraxial rays, tanq \u00bb q,\ntan 2q \u00bb 2q Therefore, Eq" + }, + { + "Chapter": "9", + "sentence_range": "81-84", + "Text": "Then,\n\u00d0MCP = q and \u00d0MFP = 2q\nNow,\ntanq =\nMD\nCD and tan 2q = \nMD\nFD\n(9 1)\nFor small q, which is true for paraxial rays, tanq \u00bb q,\ntan 2q \u00bb 2q Therefore, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "82-85", + "Text": "1)\nFor small q, which is true for paraxial rays, tanq \u00bb q,\ntan 2q \u00bb 2q Therefore, Eq (9 1) gives\nMD\nFD = 2 \nMD\nCD\nor, FD = \nCD\n2\n(9" + }, + { + "Chapter": "9", + "sentence_range": "83-86", + "Text": "Therefore, Eq (9 1) gives\nMD\nFD = 2 \nMD\nCD\nor, FD = \nCD\n2\n(9 2)\nNow, for small q, the point D is very close to the point P" + }, + { + "Chapter": "9", + "sentence_range": "84-87", + "Text": "(9 1) gives\nMD\nFD = 2 \nMD\nCD\nor, FD = \nCD\n2\n(9 2)\nNow, for small q, the point D is very close to the point P Therefore, FD = f and CD = R" + }, + { + "Chapter": "9", + "sentence_range": "85-88", + "Text": "1) gives\nMD\nFD = 2 \nMD\nCD\nor, FD = \nCD\n2\n(9 2)\nNow, for small q, the point D is very close to the point P Therefore, FD = f and CD = R Equation (9" + }, + { + "Chapter": "9", + "sentence_range": "86-89", + "Text": "2)\nNow, for small q, the point D is very close to the point P Therefore, FD = f and CD = R Equation (9 2) then gives\nf = R/2\n(9" + }, + { + "Chapter": "9", + "sentence_range": "87-90", + "Text": "Therefore, FD = f and CD = R Equation (9 2) then gives\nf = R/2\n(9 3)\n9" + }, + { + "Chapter": "9", + "sentence_range": "88-91", + "Text": "Equation (9 2) then gives\nf = R/2\n(9 3)\n9 2" + }, + { + "Chapter": "9", + "sentence_range": "89-92", + "Text": "2) then gives\nf = R/2\n(9 3)\n9 2 3 The mirror equation\nIf rays emanating from a point actually meet at another point\nafter reflection and/or refraction, that point is called the image\nof the first point" + }, + { + "Chapter": "9", + "sentence_range": "90-93", + "Text": "3)\n9 2 3 The mirror equation\nIf rays emanating from a point actually meet at another point\nafter reflection and/or refraction, that point is called the image\nof the first point The image is real if the rays actually converge\nto the point; it is virtual if the rays do not actually meet but\nappear to diverge from the point when produced\nbackwards" + }, + { + "Chapter": "9", + "sentence_range": "91-94", + "Text": "2 3 The mirror equation\nIf rays emanating from a point actually meet at another point\nafter reflection and/or refraction, that point is called the image\nof the first point The image is real if the rays actually converge\nto the point; it is virtual if the rays do not actually meet but\nappear to diverge from the point when produced\nbackwards An image is thus a point-to-point\ncorrespondence with the object established through\nreflection and/or refraction" + }, + { + "Chapter": "9", + "sentence_range": "92-95", + "Text": "3 The mirror equation\nIf rays emanating from a point actually meet at another point\nafter reflection and/or refraction, that point is called the image\nof the first point The image is real if the rays actually converge\nto the point; it is virtual if the rays do not actually meet but\nappear to diverge from the point when produced\nbackwards An image is thus a point-to-point\ncorrespondence with the object established through\nreflection and/or refraction In principle, we can take any two rays emanating\nfrom a point on an object, trace their paths, find their\npoint of intersection and thus, obtain the image of\nthe point due to reflection at a spherical mirror" + }, + { + "Chapter": "9", + "sentence_range": "93-96", + "Text": "The image is real if the rays actually converge\nto the point; it is virtual if the rays do not actually meet but\nappear to diverge from the point when produced\nbackwards An image is thus a point-to-point\ncorrespondence with the object established through\nreflection and/or refraction In principle, we can take any two rays emanating\nfrom a point on an object, trace their paths, find their\npoint of intersection and thus, obtain the image of\nthe point due to reflection at a spherical mirror In\npractice, however, it is convenient to choose any two\nof the following rays:\n(i)\nThe ray from the point which is parallel to the\nprincipal axis" + }, + { + "Chapter": "9", + "sentence_range": "94-97", + "Text": "An image is thus a point-to-point\ncorrespondence with the object established through\nreflection and/or refraction In principle, we can take any two rays emanating\nfrom a point on an object, trace their paths, find their\npoint of intersection and thus, obtain the image of\nthe point due to reflection at a spherical mirror In\npractice, however, it is convenient to choose any two\nof the following rays:\n(i)\nThe ray from the point which is parallel to the\nprincipal axis The reflected ray goes through\nthe focus of the mirror" + }, + { + "Chapter": "9", + "sentence_range": "95-98", + "Text": "In principle, we can take any two rays emanating\nfrom a point on an object, trace their paths, find their\npoint of intersection and thus, obtain the image of\nthe point due to reflection at a spherical mirror In\npractice, however, it is convenient to choose any two\nof the following rays:\n(i)\nThe ray from the point which is parallel to the\nprincipal axis The reflected ray goes through\nthe focus of the mirror (ii)\nThe ray passing through the centre of\ncurvature of a concave mirror or appearing to\npass through it for a convex mirror" + }, + { + "Chapter": "9", + "sentence_range": "96-99", + "Text": "In\npractice, however, it is convenient to choose any two\nof the following rays:\n(i)\nThe ray from the point which is parallel to the\nprincipal axis The reflected ray goes through\nthe focus of the mirror (ii)\nThe ray passing through the centre of\ncurvature of a concave mirror or appearing to\npass through it for a convex mirror The\nreflected ray simply retraces the path" + }, + { + "Chapter": "9", + "sentence_range": "97-100", + "Text": "The reflected ray goes through\nthe focus of the mirror (ii)\nThe ray passing through the centre of\ncurvature of a concave mirror or appearing to\npass through it for a convex mirror The\nreflected ray simply retraces the path (iii) The ray passing through (or directed towards) the focus of the concave\nmirror or appearing to pass through (or directed towards) the focus\nof a convex mirror" + }, + { + "Chapter": "9", + "sentence_range": "98-101", + "Text": "(ii)\nThe ray passing through the centre of\ncurvature of a concave mirror or appearing to\npass through it for a convex mirror The\nreflected ray simply retraces the path (iii) The ray passing through (or directed towards) the focus of the concave\nmirror or appearing to pass through (or directed towards) the focus\nof a convex mirror The reflected ray is parallel to the principal axis" + }, + { + "Chapter": "9", + "sentence_range": "99-102", + "Text": "The\nreflected ray simply retraces the path (iii) The ray passing through (or directed towards) the focus of the concave\nmirror or appearing to pass through (or directed towards) the focus\nof a convex mirror The reflected ray is parallel to the principal axis (iv) The ray incident at any angle at the pole" + }, + { + "Chapter": "9", + "sentence_range": "100-103", + "Text": "(iii) The ray passing through (or directed towards) the focus of the concave\nmirror or appearing to pass through (or directed towards) the focus\nof a convex mirror The reflected ray is parallel to the principal axis (iv) The ray incident at any angle at the pole The reflected ray follows\nlaws of reflection" + }, + { + "Chapter": "9", + "sentence_range": "101-104", + "Text": "The reflected ray is parallel to the principal axis (iv) The ray incident at any angle at the pole The reflected ray follows\nlaws of reflection Figure 9" + }, + { + "Chapter": "9", + "sentence_range": "102-105", + "Text": "(iv) The ray incident at any angle at the pole The reflected ray follows\nlaws of reflection Figure 9 5 shows the ray diagram considering three rays" + }, + { + "Chapter": "9", + "sentence_range": "103-106", + "Text": "The reflected ray follows\nlaws of reflection Figure 9 5 shows the ray diagram considering three rays It shows\nthe image A\u00a2B\u00a2 (in this case, real) of an object AB formed by a concave\nmirror" + }, + { + "Chapter": "9", + "sentence_range": "104-107", + "Text": "Figure 9 5 shows the ray diagram considering three rays It shows\nthe image A\u00a2B\u00a2 (in this case, real) of an object AB formed by a concave\nmirror It does not mean that only three rays emanate from the point A" + }, + { + "Chapter": "9", + "sentence_range": "105-108", + "Text": "5 shows the ray diagram considering three rays It shows\nthe image A\u00a2B\u00a2 (in this case, real) of an object AB formed by a concave\nmirror It does not mean that only three rays emanate from the point A An infinite number of rays emanate from any source, in all directions" + }, + { + "Chapter": "9", + "sentence_range": "106-109", + "Text": "It shows\nthe image A\u00a2B\u00a2 (in this case, real) of an object AB formed by a concave\nmirror It does not mean that only three rays emanate from the point A An infinite number of rays emanate from any source, in all directions Thus, point A\u00a2 is image point of A if every ray originating at point A and\nfalling on the concave mirror after reflection passes through the point A\u00a2" + }, + { + "Chapter": "9", + "sentence_range": "107-110", + "Text": "It does not mean that only three rays emanate from the point A An infinite number of rays emanate from any source, in all directions Thus, point A\u00a2 is image point of A if every ray originating at point A and\nfalling on the concave mirror after reflection passes through the point A\u00a2 FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "108-111", + "Text": "An infinite number of rays emanate from any source, in all directions Thus, point A\u00a2 is image point of A if every ray originating at point A and\nfalling on the concave mirror after reflection passes through the point A\u00a2 FIGURE 9 4 Geometry of\nreflection of an incident ray on\n(a) concave spherical mirror,\nand (b) convex spherical mirror" + }, + { + "Chapter": "9", + "sentence_range": "109-112", + "Text": "Thus, point A\u00a2 is image point of A if every ray originating at point A and\nfalling on the concave mirror after reflection passes through the point A\u00a2 FIGURE 9 4 Geometry of\nreflection of an incident ray on\n(a) concave spherical mirror,\nand (b) convex spherical mirror FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "110-113", + "Text": "FIGURE 9 4 Geometry of\nreflection of an incident ray on\n(a) concave spherical mirror,\nand (b) convex spherical mirror FIGURE 9 5 Ray diagram for image\nformation by a concave mirror" + }, + { + "Chapter": "9", + "sentence_range": "111-114", + "Text": "4 Geometry of\nreflection of an incident ray on\n(a) concave spherical mirror,\nand (b) convex spherical mirror FIGURE 9 5 Ray diagram for image\nformation by a concave mirror Rationalised 2023-24\nRay Optics and\nOptical Instruments\n225\nWe now derive the mirror equation or the relation between the object\ndistance (u), image distance (v) and the focal length ( f )" + }, + { + "Chapter": "9", + "sentence_range": "112-115", + "Text": "FIGURE 9 5 Ray diagram for image\nformation by a concave mirror Rationalised 2023-24\nRay Optics and\nOptical Instruments\n225\nWe now derive the mirror equation or the relation between the object\ndistance (u), image distance (v) and the focal length ( f ) From Fig" + }, + { + "Chapter": "9", + "sentence_range": "113-116", + "Text": "5 Ray diagram for image\nformation by a concave mirror Rationalised 2023-24\nRay Optics and\nOptical Instruments\n225\nWe now derive the mirror equation or the relation between the object\ndistance (u), image distance (v) and the focal length ( f ) From Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "114-117", + "Text": "Rationalised 2023-24\nRay Optics and\nOptical Instruments\n225\nWe now derive the mirror equation or the relation between the object\ndistance (u), image distance (v) and the focal length ( f ) From Fig 9 5, the two right-angled triangles A\u00a2B\u00a2F and MPF are\nsimilar" + }, + { + "Chapter": "9", + "sentence_range": "115-118", + "Text": "From Fig 9 5, the two right-angled triangles A\u00a2B\u00a2F and MPF are\nsimilar (For paraxial rays, MP can be considered to be a straight line\nperpendicular to CP" + }, + { + "Chapter": "9", + "sentence_range": "116-119", + "Text": "9 5, the two right-angled triangles A\u00a2B\u00a2F and MPF are\nsimilar (For paraxial rays, MP can be considered to be a straight line\nperpendicular to CP ) Therefore,\nB A\nB F\nPM\nFP\n\u2032\n\u2032\n\u2032\n=\nor \nB A\nB F\nBA\nFP\n\u2032\n\u2032\n\u2032\n=\n (\u2235PM = AB)\n(9" + }, + { + "Chapter": "9", + "sentence_range": "117-120", + "Text": "5, the two right-angled triangles A\u00a2B\u00a2F and MPF are\nsimilar (For paraxial rays, MP can be considered to be a straight line\nperpendicular to CP ) Therefore,\nB A\nB F\nPM\nFP\n\u2032\n\u2032\n\u2032\n=\nor \nB A\nB F\nBA\nFP\n\u2032\n\u2032\n\u2032\n=\n (\u2235PM = AB)\n(9 4)\nSince \u00d0 APB = \u00d0 A\u00a2PB\u00a2, the right angled triangles A\u00a2B\u00a2P and ABP are\nalso similar" + }, + { + "Chapter": "9", + "sentence_range": "118-121", + "Text": "(For paraxial rays, MP can be considered to be a straight line\nperpendicular to CP ) Therefore,\nB A\nB F\nPM\nFP\n\u2032\n\u2032\n\u2032\n=\nor \nB A\nB F\nBA\nFP\n\u2032\n\u2032\n\u2032\n=\n (\u2235PM = AB)\n(9 4)\nSince \u00d0 APB = \u00d0 A\u00a2PB\u00a2, the right angled triangles A\u00a2B\u00a2P and ABP are\nalso similar Therefore,\nB A\nB P\nB A\nB P\n\u2032\n\u2032\n\u2032\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "119-122", + "Text": ") Therefore,\nB A\nB F\nPM\nFP\n\u2032\n\u2032\n\u2032\n=\nor \nB A\nB F\nBA\nFP\n\u2032\n\u2032\n\u2032\n=\n (\u2235PM = AB)\n(9 4)\nSince \u00d0 APB = \u00d0 A\u00a2PB\u00a2, the right angled triangles A\u00a2B\u00a2P and ABP are\nalso similar Therefore,\nB A\nB P\nB A\nB P\n\u2032\n\u2032\n\u2032\n=\n(9 5)\nComparing Eqs" + }, + { + "Chapter": "9", + "sentence_range": "120-123", + "Text": "4)\nSince \u00d0 APB = \u00d0 A\u00a2PB\u00a2, the right angled triangles A\u00a2B\u00a2P and ABP are\nalso similar Therefore,\nB A\nB P\nB A\nB P\n\u2032\n\u2032\n\u2032\n=\n(9 5)\nComparing Eqs (9" + }, + { + "Chapter": "9", + "sentence_range": "121-124", + "Text": "Therefore,\nB A\nB P\nB A\nB P\n\u2032\n\u2032\n\u2032\n=\n(9 5)\nComparing Eqs (9 4) and (9" + }, + { + "Chapter": "9", + "sentence_range": "122-125", + "Text": "5)\nComparing Eqs (9 4) and (9 5), we get\nB P \u2013 FP\nB F\nB P\nFP\nFP\nBP\n\u2032\n\u2032\n\u2032\n=\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "123-126", + "Text": "(9 4) and (9 5), we get\nB P \u2013 FP\nB F\nB P\nFP\nFP\nBP\n\u2032\n\u2032\n\u2032\n=\n=\n(9 6)\nEquation (9" + }, + { + "Chapter": "9", + "sentence_range": "124-127", + "Text": "4) and (9 5), we get\nB P \u2013 FP\nB F\nB P\nFP\nFP\nBP\n\u2032\n\u2032\n\u2032\n=\n=\n(9 6)\nEquation (9 6) is a relation involving magnitude of distances" + }, + { + "Chapter": "9", + "sentence_range": "125-128", + "Text": "5), we get\nB P \u2013 FP\nB F\nB P\nFP\nFP\nBP\n\u2032\n\u2032\n\u2032\n=\n=\n(9 6)\nEquation (9 6) is a relation involving magnitude of distances We now\napply the sign convention" + }, + { + "Chapter": "9", + "sentence_range": "126-129", + "Text": "6)\nEquation (9 6) is a relation involving magnitude of distances We now\napply the sign convention We note that light travels from the object to\nthe mirror MPN" + }, + { + "Chapter": "9", + "sentence_range": "127-130", + "Text": "6) is a relation involving magnitude of distances We now\napply the sign convention We note that light travels from the object to\nthe mirror MPN Hence this is taken as the positive direction" + }, + { + "Chapter": "9", + "sentence_range": "128-131", + "Text": "We now\napply the sign convention We note that light travels from the object to\nthe mirror MPN Hence this is taken as the positive direction To reach\nthe object AB, image A\u00a2B\u00a2 as well as the focus F from the pole P, we have\nto travel opposite to the direction of incident light" + }, + { + "Chapter": "9", + "sentence_range": "129-132", + "Text": "We note that light travels from the object to\nthe mirror MPN Hence this is taken as the positive direction To reach\nthe object AB, image A\u00a2B\u00a2 as well as the focus F from the pole P, we have\nto travel opposite to the direction of incident light Hence, all the three\nwill have negative signs" + }, + { + "Chapter": "9", + "sentence_range": "130-133", + "Text": "Hence this is taken as the positive direction To reach\nthe object AB, image A\u00a2B\u00a2 as well as the focus F from the pole P, we have\nto travel opposite to the direction of incident light Hence, all the three\nwill have negative signs Thus,\nB\u00a2 P = \u2013v, FP = \u2013f, BP = \u2013u\nUsing these in Eq" + }, + { + "Chapter": "9", + "sentence_range": "131-134", + "Text": "To reach\nthe object AB, image A\u00a2B\u00a2 as well as the focus F from the pole P, we have\nto travel opposite to the direction of incident light Hence, all the three\nwill have negative signs Thus,\nB\u00a2 P = \u2013v, FP = \u2013f, BP = \u2013u\nUsing these in Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "132-135", + "Text": "Hence, all the three\nwill have negative signs Thus,\nB\u00a2 P = \u2013v, FP = \u2013f, BP = \u2013u\nUsing these in Eq (9 6), we get\n\u2013\n\u2013\nv\u2013\nf\nv\nf\nu\n+\n= \u2013\nor\nv\u2013\nf\nv\nf\nu\n=\n v\nf\nuv\n=\n+\n1\nDividing it by v, we get\n \n1\n1\n1\nv\nu\nf\n+\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "133-136", + "Text": "Thus,\nB\u00a2 P = \u2013v, FP = \u2013f, BP = \u2013u\nUsing these in Eq (9 6), we get\n\u2013\n\u2013\nv\u2013\nf\nv\nf\nu\n+\n= \u2013\nor\nv\u2013\nf\nv\nf\nu\n=\n v\nf\nuv\n=\n+\n1\nDividing it by v, we get\n \n1\n1\n1\nv\nu\nf\n+\n=\n(9 7)\nThis relation is known as the mirror equation" + }, + { + "Chapter": "9", + "sentence_range": "134-137", + "Text": "(9 6), we get\n\u2013\n\u2013\nv\u2013\nf\nv\nf\nu\n+\n= \u2013\nor\nv\u2013\nf\nv\nf\nu\n=\n v\nf\nuv\n=\n+\n1\nDividing it by v, we get\n \n1\n1\n1\nv\nu\nf\n+\n=\n(9 7)\nThis relation is known as the mirror equation The size of the image relative to the size of the object is another\nimportant quantity to consider" + }, + { + "Chapter": "9", + "sentence_range": "135-138", + "Text": "6), we get\n\u2013\n\u2013\nv\u2013\nf\nv\nf\nu\n+\n= \u2013\nor\nv\u2013\nf\nv\nf\nu\n=\n v\nf\nuv\n=\n+\n1\nDividing it by v, we get\n \n1\n1\n1\nv\nu\nf\n+\n=\n(9 7)\nThis relation is known as the mirror equation The size of the image relative to the size of the object is another\nimportant quantity to consider We define linear magnification (m) as the\nratio of the height of the image (h\u00a2) to the height of the object (h):\nm = \nh\nh\n\u2032\n(9" + }, + { + "Chapter": "9", + "sentence_range": "136-139", + "Text": "7)\nThis relation is known as the mirror equation The size of the image relative to the size of the object is another\nimportant quantity to consider We define linear magnification (m) as the\nratio of the height of the image (h\u00a2) to the height of the object (h):\nm = \nh\nh\n\u2032\n(9 8)\nh and h\u00a2 will be taken positive or negative in accordance with the accepted\nsign convention" + }, + { + "Chapter": "9", + "sentence_range": "137-140", + "Text": "The size of the image relative to the size of the object is another\nimportant quantity to consider We define linear magnification (m) as the\nratio of the height of the image (h\u00a2) to the height of the object (h):\nm = \nh\nh\n\u2032\n(9 8)\nh and h\u00a2 will be taken positive or negative in accordance with the accepted\nsign convention In triangles A\u00a2B\u00a2P and ABP, we have,\nB A\nB P\nBA\nBP\n\u2032\n\u2032\n\u2032\n=\nWith the sign convention, this becomes\nRationalised 2023-24\nPhysics\n226\n\u2013\n\u2013\nh\nv\nh\nu\n\u2032 = \u2013\nso that\nm = \n\u2013\nh\nv\nh\nu\n\u2032 =\n(9" + }, + { + "Chapter": "9", + "sentence_range": "138-141", + "Text": "We define linear magnification (m) as the\nratio of the height of the image (h\u00a2) to the height of the object (h):\nm = \nh\nh\n\u2032\n(9 8)\nh and h\u00a2 will be taken positive or negative in accordance with the accepted\nsign convention In triangles A\u00a2B\u00a2P and ABP, we have,\nB A\nB P\nBA\nBP\n\u2032\n\u2032\n\u2032\n=\nWith the sign convention, this becomes\nRationalised 2023-24\nPhysics\n226\n\u2013\n\u2013\nh\nv\nh\nu\n\u2032 = \u2013\nso that\nm = \n\u2013\nh\nv\nh\nu\n\u2032 =\n(9 9)\nWe have derived here the mirror equation, Eq" + }, + { + "Chapter": "9", + "sentence_range": "139-142", + "Text": "8)\nh and h\u00a2 will be taken positive or negative in accordance with the accepted\nsign convention In triangles A\u00a2B\u00a2P and ABP, we have,\nB A\nB P\nBA\nBP\n\u2032\n\u2032\n\u2032\n=\nWith the sign convention, this becomes\nRationalised 2023-24\nPhysics\n226\n\u2013\n\u2013\nh\nv\nh\nu\n\u2032 = \u2013\nso that\nm = \n\u2013\nh\nv\nh\nu\n\u2032 =\n(9 9)\nWe have derived here the mirror equation, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "140-143", + "Text": "In triangles A\u00a2B\u00a2P and ABP, we have,\nB A\nB P\nBA\nBP\n\u2032\n\u2032\n\u2032\n=\nWith the sign convention, this becomes\nRationalised 2023-24\nPhysics\n226\n\u2013\n\u2013\nh\nv\nh\nu\n\u2032 = \u2013\nso that\nm = \n\u2013\nh\nv\nh\nu\n\u2032 =\n(9 9)\nWe have derived here the mirror equation, Eq (9 7), and the\nmagnification formula, Eq" + }, + { + "Chapter": "9", + "sentence_range": "141-144", + "Text": "9)\nWe have derived here the mirror equation, Eq (9 7), and the\nmagnification formula, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "142-145", + "Text": "(9 7), and the\nmagnification formula, Eq (9 9), for the case of real, inverted image formed\nby a concave mirror" + }, + { + "Chapter": "9", + "sentence_range": "143-146", + "Text": "7), and the\nmagnification formula, Eq (9 9), for the case of real, inverted image formed\nby a concave mirror With the proper use of sign convention, these are,\nin fact, valid for all the cases of reflection by a spherical mirror (concave\nor convex) whether the image formed is real or virtual" + }, + { + "Chapter": "9", + "sentence_range": "144-147", + "Text": "(9 9), for the case of real, inverted image formed\nby a concave mirror With the proper use of sign convention, these are,\nin fact, valid for all the cases of reflection by a spherical mirror (concave\nor convex) whether the image formed is real or virtual Figure 9" + }, + { + "Chapter": "9", + "sentence_range": "145-148", + "Text": "9), for the case of real, inverted image formed\nby a concave mirror With the proper use of sign convention, these are,\nin fact, valid for all the cases of reflection by a spherical mirror (concave\nor convex) whether the image formed is real or virtual Figure 9 6 shows\nthe ray diagrams for virtual image formed by a concave and convex mirror" + }, + { + "Chapter": "9", + "sentence_range": "146-149", + "Text": "With the proper use of sign convention, these are,\nin fact, valid for all the cases of reflection by a spherical mirror (concave\nor convex) whether the image formed is real or virtual Figure 9 6 shows\nthe ray diagrams for virtual image formed by a concave and convex mirror You should verify that Eqs" + }, + { + "Chapter": "9", + "sentence_range": "147-150", + "Text": "Figure 9 6 shows\nthe ray diagrams for virtual image formed by a concave and convex mirror You should verify that Eqs (9" + }, + { + "Chapter": "9", + "sentence_range": "148-151", + "Text": "6 shows\nthe ray diagrams for virtual image formed by a concave and convex mirror You should verify that Eqs (9 7) and (9" + }, + { + "Chapter": "9", + "sentence_range": "149-152", + "Text": "You should verify that Eqs (9 7) and (9 9) are valid for these cases as\nwell" + }, + { + "Chapter": "9", + "sentence_range": "150-153", + "Text": "(9 7) and (9 9) are valid for these cases as\nwell FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "151-154", + "Text": "7) and (9 9) are valid for these cases as\nwell FIGURE 9 6 Image formation by (a) a concave mirror with object between\nP and F, and (b) a convex mirror" + }, + { + "Chapter": "9", + "sentence_range": "152-155", + "Text": "9) are valid for these cases as\nwell FIGURE 9 6 Image formation by (a) a concave mirror with object between\nP and F, and (b) a convex mirror EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "153-156", + "Text": "FIGURE 9 6 Image formation by (a) a concave mirror with object between\nP and F, and (b) a convex mirror EXAMPLE 9 1\nExample 9" + }, + { + "Chapter": "9", + "sentence_range": "154-157", + "Text": "6 Image formation by (a) a concave mirror with object between\nP and F, and (b) a convex mirror EXAMPLE 9 1\nExample 9 1 Suppose that the lower half of the concave mirror\u2019s\nreflecting surface in Fig" + }, + { + "Chapter": "9", + "sentence_range": "155-158", + "Text": "EXAMPLE 9 1\nExample 9 1 Suppose that the lower half of the concave mirror\u2019s\nreflecting surface in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "156-159", + "Text": "1\nExample 9 1 Suppose that the lower half of the concave mirror\u2019s\nreflecting surface in Fig 9 6 is covered with an opaque (non-reflective)\nmaterial" + }, + { + "Chapter": "9", + "sentence_range": "157-160", + "Text": "1 Suppose that the lower half of the concave mirror\u2019s\nreflecting surface in Fig 9 6 is covered with an opaque (non-reflective)\nmaterial What effect will this have on the image of an object placed\nin front of the mirror" + }, + { + "Chapter": "9", + "sentence_range": "158-161", + "Text": "9 6 is covered with an opaque (non-reflective)\nmaterial What effect will this have on the image of an object placed\nin front of the mirror Solution You may think that the image will now show only half of the\nobject, but taking the laws of reflection to be true for all points of the\nremaining part of the mirror, the image will be that of the whole object" + }, + { + "Chapter": "9", + "sentence_range": "159-162", + "Text": "6 is covered with an opaque (non-reflective)\nmaterial What effect will this have on the image of an object placed\nin front of the mirror Solution You may think that the image will now show only half of the\nobject, but taking the laws of reflection to be true for all points of the\nremaining part of the mirror, the image will be that of the whole object However, as the area of the reflecting surface has been reduced, the\nintensity of the image will be low (in this case, half)" + }, + { + "Chapter": "9", + "sentence_range": "160-163", + "Text": "What effect will this have on the image of an object placed\nin front of the mirror Solution You may think that the image will now show only half of the\nobject, but taking the laws of reflection to be true for all points of the\nremaining part of the mirror, the image will be that of the whole object However, as the area of the reflecting surface has been reduced, the\nintensity of the image will be low (in this case, half) Example 9" + }, + { + "Chapter": "9", + "sentence_range": "161-164", + "Text": "Solution You may think that the image will now show only half of the\nobject, but taking the laws of reflection to be true for all points of the\nremaining part of the mirror, the image will be that of the whole object However, as the area of the reflecting surface has been reduced, the\nintensity of the image will be low (in this case, half) Example 9 2 A mobile phone lies along the principal axis of a concave\nmirror, as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "162-165", + "Text": "However, as the area of the reflecting surface has been reduced, the\nintensity of the image will be low (in this case, half) Example 9 2 A mobile phone lies along the principal axis of a concave\nmirror, as shown in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "163-166", + "Text": "Example 9 2 A mobile phone lies along the principal axis of a concave\nmirror, as shown in Fig 9 7" + }, + { + "Chapter": "9", + "sentence_range": "164-167", + "Text": "2 A mobile phone lies along the principal axis of a concave\nmirror, as shown in Fig 9 7 Show by suitable diagram, the formation\nof its image" + }, + { + "Chapter": "9", + "sentence_range": "165-168", + "Text": "9 7 Show by suitable diagram, the formation\nof its image Explain why the magnification is not uniform" + }, + { + "Chapter": "9", + "sentence_range": "166-169", + "Text": "7 Show by suitable diagram, the formation\nof its image Explain why the magnification is not uniform Will the\ndistortion of image depend on the location of the phone with respect\nto the mirror" + }, + { + "Chapter": "9", + "sentence_range": "167-170", + "Text": "Show by suitable diagram, the formation\nof its image Explain why the magnification is not uniform Will the\ndistortion of image depend on the location of the phone with respect\nto the mirror FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "168-171", + "Text": "Explain why the magnification is not uniform Will the\ndistortion of image depend on the location of the phone with respect\nto the mirror FIGURE 9 7\n EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "169-172", + "Text": "Will the\ndistortion of image depend on the location of the phone with respect\nto the mirror FIGURE 9 7\n EXAMPLE 9 2\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n227\n EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "170-173", + "Text": "FIGURE 9 7\n EXAMPLE 9 2\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n227\n EXAMPLE 9 3\n EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "171-174", + "Text": "7\n EXAMPLE 9 2\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n227\n EXAMPLE 9 3\n EXAMPLE 9 4\nSolution\nThe ray diagram for the formation of the image of the phone is shown\nin Fig" + }, + { + "Chapter": "9", + "sentence_range": "172-175", + "Text": "2\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n227\n EXAMPLE 9 3\n EXAMPLE 9 4\nSolution\nThe ray diagram for the formation of the image of the phone is shown\nin Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "173-176", + "Text": "3\n EXAMPLE 9 4\nSolution\nThe ray diagram for the formation of the image of the phone is shown\nin Fig 9 7" + }, + { + "Chapter": "9", + "sentence_range": "174-177", + "Text": "4\nSolution\nThe ray diagram for the formation of the image of the phone is shown\nin Fig 9 7 The image of the part which is on the plane perpendicular\nto principal axis will be on the same plane" + }, + { + "Chapter": "9", + "sentence_range": "175-178", + "Text": "9 7 The image of the part which is on the plane perpendicular\nto principal axis will be on the same plane It will be of the same size,\ni" + }, + { + "Chapter": "9", + "sentence_range": "176-179", + "Text": "7 The image of the part which is on the plane perpendicular\nto principal axis will be on the same plane It will be of the same size,\ni e" + }, + { + "Chapter": "9", + "sentence_range": "177-180", + "Text": "The image of the part which is on the plane perpendicular\nto principal axis will be on the same plane It will be of the same size,\ni e , B\u00a2C = BC" + }, + { + "Chapter": "9", + "sentence_range": "178-181", + "Text": "It will be of the same size,\ni e , B\u00a2C = BC You can yourself realise why the image is distorted" + }, + { + "Chapter": "9", + "sentence_range": "179-182", + "Text": "e , B\u00a2C = BC You can yourself realise why the image is distorted Example 9" + }, + { + "Chapter": "9", + "sentence_range": "180-183", + "Text": ", B\u00a2C = BC You can yourself realise why the image is distorted Example 9 3\nAn object is placed at (i) 10 cm, (ii) 5 cm in front of a\nconcave mirror of radius of curvature 15 cm" + }, + { + "Chapter": "9", + "sentence_range": "181-184", + "Text": "You can yourself realise why the image is distorted Example 9 3\nAn object is placed at (i) 10 cm, (ii) 5 cm in front of a\nconcave mirror of radius of curvature 15 cm Find the position, nature,\nand magnification of the image in each case" + }, + { + "Chapter": "9", + "sentence_range": "182-185", + "Text": "Example 9 3\nAn object is placed at (i) 10 cm, (ii) 5 cm in front of a\nconcave mirror of radius of curvature 15 cm Find the position, nature,\nand magnification of the image in each case Solution\nThe focal length f = \u201315/2 cm = \u20137" + }, + { + "Chapter": "9", + "sentence_range": "183-186", + "Text": "3\nAn object is placed at (i) 10 cm, (ii) 5 cm in front of a\nconcave mirror of radius of curvature 15 cm Find the position, nature,\nand magnification of the image in each case Solution\nThe focal length f = \u201315/2 cm = \u20137 5 cm\n(i) The object distance u = \u201310 cm" + }, + { + "Chapter": "9", + "sentence_range": "184-187", + "Text": "Find the position, nature,\nand magnification of the image in each case Solution\nThe focal length f = \u201315/2 cm = \u20137 5 cm\n(i) The object distance u = \u201310 cm Then Eq" + }, + { + "Chapter": "9", + "sentence_range": "185-188", + "Text": "Solution\nThe focal length f = \u201315/2 cm = \u20137 5 cm\n(i) The object distance u = \u201310 cm Then Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "186-189", + "Text": "5 cm\n(i) The object distance u = \u201310 cm Then Eq (9 7) gives\n\u2013\n\u2013" + }, + { + "Chapter": "9", + "sentence_range": "187-190", + "Text": "Then Eq (9 7) gives\n\u2013\n\u2013 1\n1\n1\n10\n7 5\nv +\n=\nor" + }, + { + "Chapter": "9", + "sentence_range": "188-191", + "Text": "(9 7) gives\n\u2013\n\u2013 1\n1\n1\n10\n7 5\nv +\n=\nor 10\n7 5\n2 5\nv\n\u2212\u00d7\n=\n = \u2013 30 cm\nThe image is 30 cm from the mirror on the same side as the object" + }, + { + "Chapter": "9", + "sentence_range": "189-192", + "Text": "7) gives\n\u2013\n\u2013 1\n1\n1\n10\n7 5\nv +\n=\nor 10\n7 5\n2 5\nv\n\u2212\u00d7\n=\n = \u2013 30 cm\nThe image is 30 cm from the mirror on the same side as the object Also, magnification m = \n( 30)\n\u2013\n\u2013\n\u2013 3\n( 10)\nv\nu\n\u2212\n=\n=\n\u2212\nThe image is magnified, real and inverted" + }, + { + "Chapter": "9", + "sentence_range": "190-193", + "Text": "1\n1\n1\n10\n7 5\nv +\n=\nor 10\n7 5\n2 5\nv\n\u2212\u00d7\n=\n = \u2013 30 cm\nThe image is 30 cm from the mirror on the same side as the object Also, magnification m = \n( 30)\n\u2013\n\u2013\n\u2013 3\n( 10)\nv\nu\n\u2212\n=\n=\n\u2212\nThe image is magnified, real and inverted (ii) The object distance u = \u20135 cm" + }, + { + "Chapter": "9", + "sentence_range": "191-194", + "Text": "10\n7 5\n2 5\nv\n\u2212\u00d7\n=\n = \u2013 30 cm\nThe image is 30 cm from the mirror on the same side as the object Also, magnification m = \n( 30)\n\u2013\n\u2013\n\u2013 3\n( 10)\nv\nu\n\u2212\n=\n=\n\u2212\nThe image is magnified, real and inverted (ii) The object distance u = \u20135 cm Then from Eq" + }, + { + "Chapter": "9", + "sentence_range": "192-195", + "Text": "Also, magnification m = \n( 30)\n\u2013\n\u2013\n\u2013 3\n( 10)\nv\nu\n\u2212\n=\n=\n\u2212\nThe image is magnified, real and inverted (ii) The object distance u = \u20135 cm Then from Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "193-196", + "Text": "(ii) The object distance u = \u20135 cm Then from Eq (9 7),\n1\n1\n1\n5\n7" + }, + { + "Chapter": "9", + "sentence_range": "194-197", + "Text": "Then from Eq (9 7),\n1\n1\n1\n5\n7 5\nv +\n=\n\u2212\n\u2212\nor \n(\n)" + }, + { + "Chapter": "9", + "sentence_range": "195-198", + "Text": "(9 7),\n1\n1\n1\n5\n7 5\nv +\n=\n\u2212\n\u2212\nor \n(\n) \u2013\n5\n7 5\n15 cm\n7 5\n5\nv\n\u00d7\n=\n=\nThis image is formed at 15 cm behind the mirror" + }, + { + "Chapter": "9", + "sentence_range": "196-199", + "Text": "7),\n1\n1\n1\n5\n7 5\nv +\n=\n\u2212\n\u2212\nor \n(\n) \u2013\n5\n7 5\n15 cm\n7 5\n5\nv\n\u00d7\n=\n=\nThis image is formed at 15 cm behind the mirror It is a virtual image" + }, + { + "Chapter": "9", + "sentence_range": "197-200", + "Text": "5\nv +\n=\n\u2212\n\u2212\nor \n(\n) \u2013\n5\n7 5\n15 cm\n7 5\n5\nv\n\u00d7\n=\n=\nThis image is formed at 15 cm behind the mirror It is a virtual image Magnification m = \n15\n\u2013\n\u2013\n3\n( 5)\nv\nu =\n=\n\u2212\nThe image is magnified, virtual and erect" + }, + { + "Chapter": "9", + "sentence_range": "198-201", + "Text": "\u2013\n5\n7 5\n15 cm\n7 5\n5\nv\n\u00d7\n=\n=\nThis image is formed at 15 cm behind the mirror It is a virtual image Magnification m = \n15\n\u2013\n\u2013\n3\n( 5)\nv\nu =\n=\n\u2212\nThe image is magnified, virtual and erect Example 9" + }, + { + "Chapter": "9", + "sentence_range": "199-202", + "Text": "It is a virtual image Magnification m = \n15\n\u2013\n\u2013\n3\n( 5)\nv\nu =\n=\n\u2212\nThe image is magnified, virtual and erect Example 9 4 Suppose while sitting in a parked car, you notice a\njogger approaching towards you in the side view mirror of R = 2 m" + }, + { + "Chapter": "9", + "sentence_range": "200-203", + "Text": "Magnification m = \n15\n\u2013\n\u2013\n3\n( 5)\nv\nu =\n=\n\u2212\nThe image is magnified, virtual and erect Example 9 4 Suppose while sitting in a parked car, you notice a\njogger approaching towards you in the side view mirror of R = 2 m If\nthe jogger is running at a speed of 5 m s\u20131, how fast the image of the\njogger appear to move when the jogger is (a) 39 m, (b) 29 m, (c) 19 m,\nand (d) 9 m away" + }, + { + "Chapter": "9", + "sentence_range": "201-204", + "Text": "Example 9 4 Suppose while sitting in a parked car, you notice a\njogger approaching towards you in the side view mirror of R = 2 m If\nthe jogger is running at a speed of 5 m s\u20131, how fast the image of the\njogger appear to move when the jogger is (a) 39 m, (b) 29 m, (c) 19 m,\nand (d) 9 m away Solution\nFrom the mirror equation, Eq" + }, + { + "Chapter": "9", + "sentence_range": "202-205", + "Text": "4 Suppose while sitting in a parked car, you notice a\njogger approaching towards you in the side view mirror of R = 2 m If\nthe jogger is running at a speed of 5 m s\u20131, how fast the image of the\njogger appear to move when the jogger is (a) 39 m, (b) 29 m, (c) 19 m,\nand (d) 9 m away Solution\nFrom the mirror equation, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "203-206", + "Text": "If\nthe jogger is running at a speed of 5 m s\u20131, how fast the image of the\njogger appear to move when the jogger is (a) 39 m, (b) 29 m, (c) 19 m,\nand (d) 9 m away Solution\nFrom the mirror equation, Eq (9 7), we get\nfu\nv\nu\nf\n=\n\u2212\nFor convex mirror, since R = 2 m, f = 1 m" + }, + { + "Chapter": "9", + "sentence_range": "204-207", + "Text": "Solution\nFrom the mirror equation, Eq (9 7), we get\nfu\nv\nu\nf\n=\n\u2212\nFor convex mirror, since R = 2 m, f = 1 m Then\nfor u = \u201339 m, \n( 39)\n1\n39 m\n39\n1\n40\nv\n\u2212\n\u00d7\n=\n=\n\u2212\n\u2212\nSince the jogger moves at a constant speed of 5 m s\u20131, after 1 s the\nposition of the image v (for u = \u201339 + 5 = \u201334) is (34/35 )m" + }, + { + "Chapter": "9", + "sentence_range": "205-208", + "Text": "(9 7), we get\nfu\nv\nu\nf\n=\n\u2212\nFor convex mirror, since R = 2 m, f = 1 m Then\nfor u = \u201339 m, \n( 39)\n1\n39 m\n39\n1\n40\nv\n\u2212\n\u00d7\n=\n=\n\u2212\n\u2212\nSince the jogger moves at a constant speed of 5 m s\u20131, after 1 s the\nposition of the image v (for u = \u201339 + 5 = \u201334) is (34/35 )m EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "206-209", + "Text": "7), we get\nfu\nv\nu\nf\n=\n\u2212\nFor convex mirror, since R = 2 m, f = 1 m Then\nfor u = \u201339 m, \n( 39)\n1\n39 m\n39\n1\n40\nv\n\u2212\n\u00d7\n=\n=\n\u2212\n\u2212\nSince the jogger moves at a constant speed of 5 m s\u20131, after 1 s the\nposition of the image v (for u = \u201339 + 5 = \u201334) is (34/35 )m EXAMPLE 9 2\nRationalised 2023-24\nPhysics\n228\n EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "207-210", + "Text": "Then\nfor u = \u201339 m, \n( 39)\n1\n39 m\n39\n1\n40\nv\n\u2212\n\u00d7\n=\n=\n\u2212\n\u2212\nSince the jogger moves at a constant speed of 5 m s\u20131, after 1 s the\nposition of the image v (for u = \u201339 + 5 = \u201334) is (34/35 )m EXAMPLE 9 2\nRationalised 2023-24\nPhysics\n228\n EXAMPLE 9 4\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "208-211", + "Text": "EXAMPLE 9 2\nRationalised 2023-24\nPhysics\n228\n EXAMPLE 9 4\nFIGURE 9 8 Refraction and reflection of light" + }, + { + "Chapter": "9", + "sentence_range": "209-212", + "Text": "2\nRationalised 2023-24\nPhysics\n228\n EXAMPLE 9 4\nFIGURE 9 8 Refraction and reflection of light The shift in the position of image in 1 s is\n1365\n1360\n39\n34\n5\n1\nm\n40\n35\n1400\n1400\n280\n\u2212\n\u2212\n=\n=\n=\nTherefore, the average speed of the image when the jogger is between\n39 m and 34 m from the mirror, is (1/280) m s\u20131\nSimilarly, it can be seen that for u = \u201329 m, \u201319 m and \u20139 m, the\nspeed with which the image appears to move is\n \n\u20131\n\u20131\n\u20131\n1\n1\n1\nm s ,\nm s\nand\nm s ,\n150\n60\n10\n respectively" + }, + { + "Chapter": "9", + "sentence_range": "210-213", + "Text": "4\nFIGURE 9 8 Refraction and reflection of light The shift in the position of image in 1 s is\n1365\n1360\n39\n34\n5\n1\nm\n40\n35\n1400\n1400\n280\n\u2212\n\u2212\n=\n=\n=\nTherefore, the average speed of the image when the jogger is between\n39 m and 34 m from the mirror, is (1/280) m s\u20131\nSimilarly, it can be seen that for u = \u201329 m, \u201319 m and \u20139 m, the\nspeed with which the image appears to move is\n \n\u20131\n\u20131\n\u20131\n1\n1\n1\nm s ,\nm s\nand\nm s ,\n150\n60\n10\n respectively Although the jogger has been moving with a constant speed, the speed\nof his/her image appears to increase substantially as he/she moves\ncloser to the mirror" + }, + { + "Chapter": "9", + "sentence_range": "211-214", + "Text": "8 Refraction and reflection of light The shift in the position of image in 1 s is\n1365\n1360\n39\n34\n5\n1\nm\n40\n35\n1400\n1400\n280\n\u2212\n\u2212\n=\n=\n=\nTherefore, the average speed of the image when the jogger is between\n39 m and 34 m from the mirror, is (1/280) m s\u20131\nSimilarly, it can be seen that for u = \u201329 m, \u201319 m and \u20139 m, the\nspeed with which the image appears to move is\n \n\u20131\n\u20131\n\u20131\n1\n1\n1\nm s ,\nm s\nand\nm s ,\n150\n60\n10\n respectively Although the jogger has been moving with a constant speed, the speed\nof his/her image appears to increase substantially as he/she moves\ncloser to the mirror This phenomenon can be noticed by any person\nsitting in a stationary car or a bus" + }, + { + "Chapter": "9", + "sentence_range": "212-215", + "Text": "The shift in the position of image in 1 s is\n1365\n1360\n39\n34\n5\n1\nm\n40\n35\n1400\n1400\n280\n\u2212\n\u2212\n=\n=\n=\nTherefore, the average speed of the image when the jogger is between\n39 m and 34 m from the mirror, is (1/280) m s\u20131\nSimilarly, it can be seen that for u = \u201329 m, \u201319 m and \u20139 m, the\nspeed with which the image appears to move is\n \n\u20131\n\u20131\n\u20131\n1\n1\n1\nm s ,\nm s\nand\nm s ,\n150\n60\n10\n respectively Although the jogger has been moving with a constant speed, the speed\nof his/her image appears to increase substantially as he/she moves\ncloser to the mirror This phenomenon can be noticed by any person\nsitting in a stationary car or a bus In case of moving vehicles, a\nsimilar phenomenon could be observed if the vehicle in the rear is\nmoving closer with a constant speed" + }, + { + "Chapter": "9", + "sentence_range": "213-216", + "Text": "Although the jogger has been moving with a constant speed, the speed\nof his/her image appears to increase substantially as he/she moves\ncloser to the mirror This phenomenon can be noticed by any person\nsitting in a stationary car or a bus In case of moving vehicles, a\nsimilar phenomenon could be observed if the vehicle in the rear is\nmoving closer with a constant speed 9" + }, + { + "Chapter": "9", + "sentence_range": "214-217", + "Text": "This phenomenon can be noticed by any person\nsitting in a stationary car or a bus In case of moving vehicles, a\nsimilar phenomenon could be observed if the vehicle in the rear is\nmoving closer with a constant speed 9 3 REFRACTION\nWhen a beam of light encounters another transparent medium, a part of\nlight gets reflected back into the first medium while the rest enters the\nother" + }, + { + "Chapter": "9", + "sentence_range": "215-218", + "Text": "In case of moving vehicles, a\nsimilar phenomenon could be observed if the vehicle in the rear is\nmoving closer with a constant speed 9 3 REFRACTION\nWhen a beam of light encounters another transparent medium, a part of\nlight gets reflected back into the first medium while the rest enters the\nother A ray of light represents a beam" + }, + { + "Chapter": "9", + "sentence_range": "216-219", + "Text": "9 3 REFRACTION\nWhen a beam of light encounters another transparent medium, a part of\nlight gets reflected back into the first medium while the rest enters the\nother A ray of light represents a beam The direction of propagation of an\nobliquely incident (0\u00b0< i < 90\u00b0) ray of light that enters the other medium,\nchanges at the interface of the two media" + }, + { + "Chapter": "9", + "sentence_range": "217-220", + "Text": "3 REFRACTION\nWhen a beam of light encounters another transparent medium, a part of\nlight gets reflected back into the first medium while the rest enters the\nother A ray of light represents a beam The direction of propagation of an\nobliquely incident (0\u00b0< i < 90\u00b0) ray of light that enters the other medium,\nchanges at the interface of the two media This phenomenon is called\nrefraction of light" + }, + { + "Chapter": "9", + "sentence_range": "218-221", + "Text": "A ray of light represents a beam The direction of propagation of an\nobliquely incident (0\u00b0< i < 90\u00b0) ray of light that enters the other medium,\nchanges at the interface of the two media This phenomenon is called\nrefraction of light Snell experimentally obtained the following laws\nof refraction:\n(i)\nThe incident ray, the refracted ray and the\nnormal to the interface at the point of\nincidence, all lie in the same plane" + }, + { + "Chapter": "9", + "sentence_range": "219-222", + "Text": "The direction of propagation of an\nobliquely incident (0\u00b0< i < 90\u00b0) ray of light that enters the other medium,\nchanges at the interface of the two media This phenomenon is called\nrefraction of light Snell experimentally obtained the following laws\nof refraction:\n(i)\nThe incident ray, the refracted ray and the\nnormal to the interface at the point of\nincidence, all lie in the same plane (ii) The ratio of the sine of the angle of incidence\nto the sine of angle of refraction is constant" + }, + { + "Chapter": "9", + "sentence_range": "220-223", + "Text": "This phenomenon is called\nrefraction of light Snell experimentally obtained the following laws\nof refraction:\n(i)\nThe incident ray, the refracted ray and the\nnormal to the interface at the point of\nincidence, all lie in the same plane (ii) The ratio of the sine of the angle of incidence\nto the sine of angle of refraction is constant Remember that the angles of incidence (i ) and\nrefraction (r ) are the angles that the incident\nand its refracted ray make with the normal,\nrespectively" + }, + { + "Chapter": "9", + "sentence_range": "221-224", + "Text": "Snell experimentally obtained the following laws\nof refraction:\n(i)\nThe incident ray, the refracted ray and the\nnormal to the interface at the point of\nincidence, all lie in the same plane (ii) The ratio of the sine of the angle of incidence\nto the sine of angle of refraction is constant Remember that the angles of incidence (i ) and\nrefraction (r ) are the angles that the incident\nand its refracted ray make with the normal,\nrespectively We have\n21\nsin\nsin\ni\nr =n\n(9" + }, + { + "Chapter": "9", + "sentence_range": "222-225", + "Text": "(ii) The ratio of the sine of the angle of incidence\nto the sine of angle of refraction is constant Remember that the angles of incidence (i ) and\nrefraction (r ) are the angles that the incident\nand its refracted ray make with the normal,\nrespectively We have\n21\nsin\nsin\ni\nr =n\n(9 10)\nwhere n 21 is a constant, called the refractive\nindex of the second medium with respect to the\nfirst medium" + }, + { + "Chapter": "9", + "sentence_range": "223-226", + "Text": "Remember that the angles of incidence (i ) and\nrefraction (r ) are the angles that the incident\nand its refracted ray make with the normal,\nrespectively We have\n21\nsin\nsin\ni\nr =n\n(9 10)\nwhere n 21 is a constant, called the refractive\nindex of the second medium with respect to the\nfirst medium Equation (9" + }, + { + "Chapter": "9", + "sentence_range": "224-227", + "Text": "We have\n21\nsin\nsin\ni\nr =n\n(9 10)\nwhere n 21 is a constant, called the refractive\nindex of the second medium with respect to the\nfirst medium Equation (9 10) is the well-known\nSnell\u2019s law of refraction" + }, + { + "Chapter": "9", + "sentence_range": "225-228", + "Text": "10)\nwhere n 21 is a constant, called the refractive\nindex of the second medium with respect to the\nfirst medium Equation (9 10) is the well-known\nSnell\u2019s law of refraction We note that n 21 is a\ncharacteristic of the pair of media (and also depends on the wavelength\nof light), but is independent of the angle of incidence" + }, + { + "Chapter": "9", + "sentence_range": "226-229", + "Text": "Equation (9 10) is the well-known\nSnell\u2019s law of refraction We note that n 21 is a\ncharacteristic of the pair of media (and also depends on the wavelength\nof light), but is independent of the angle of incidence From Eq" + }, + { + "Chapter": "9", + "sentence_range": "227-230", + "Text": "10) is the well-known\nSnell\u2019s law of refraction We note that n 21 is a\ncharacteristic of the pair of media (and also depends on the wavelength\nof light), but is independent of the angle of incidence From Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "228-231", + "Text": "We note that n 21 is a\ncharacteristic of the pair of media (and also depends on the wavelength\nof light), but is independent of the angle of incidence From Eq (9 10), if n 21 > 1, r < i, i" + }, + { + "Chapter": "9", + "sentence_range": "229-232", + "Text": "From Eq (9 10), if n 21 > 1, r < i, i e" + }, + { + "Chapter": "9", + "sentence_range": "230-233", + "Text": "(9 10), if n 21 > 1, r < i, i e , the refracted ray bends towards\nthe normal" + }, + { + "Chapter": "9", + "sentence_range": "231-234", + "Text": "10), if n 21 > 1, r < i, i e , the refracted ray bends towards\nthe normal In such a case medium 2 is said to be optically denser (or\ndenser, in short) than medium 1" + }, + { + "Chapter": "9", + "sentence_range": "232-235", + "Text": "e , the refracted ray bends towards\nthe normal In such a case medium 2 is said to be optically denser (or\ndenser, in short) than medium 1 On the other hand, if n 21 <1, r > i, the\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n229\nrefracted ray bends away from the normal" + }, + { + "Chapter": "9", + "sentence_range": "233-236", + "Text": ", the refracted ray bends towards\nthe normal In such a case medium 2 is said to be optically denser (or\ndenser, in short) than medium 1 On the other hand, if n 21 <1, r > i, the\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n229\nrefracted ray bends away from the normal This\nis the case when incident ray in a denser\nmedium refracts into a rarer medium" + }, + { + "Chapter": "9", + "sentence_range": "234-237", + "Text": "In such a case medium 2 is said to be optically denser (or\ndenser, in short) than medium 1 On the other hand, if n 21 <1, r > i, the\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n229\nrefracted ray bends away from the normal This\nis the case when incident ray in a denser\nmedium refracts into a rarer medium Note: Optical density should not be\nconfused with mass density, which is mass\nper unit volume" + }, + { + "Chapter": "9", + "sentence_range": "235-238", + "Text": "On the other hand, if n 21 <1, r > i, the\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n229\nrefracted ray bends away from the normal This\nis the case when incident ray in a denser\nmedium refracts into a rarer medium Note: Optical density should not be\nconfused with mass density, which is mass\nper unit volume It is possible that mass\ndensity of an optically denser medium may\nbe less than that of an optically rarer\nmedium (optical density is the ratio of the\nspeed of light in two media)" + }, + { + "Chapter": "9", + "sentence_range": "236-239", + "Text": "This\nis the case when incident ray in a denser\nmedium refracts into a rarer medium Note: Optical density should not be\nconfused with mass density, which is mass\nper unit volume It is possible that mass\ndensity of an optically denser medium may\nbe less than that of an optically rarer\nmedium (optical density is the ratio of the\nspeed of light in two media) For example,\nturpentine and water" + }, + { + "Chapter": "9", + "sentence_range": "237-240", + "Text": "Note: Optical density should not be\nconfused with mass density, which is mass\nper unit volume It is possible that mass\ndensity of an optically denser medium may\nbe less than that of an optically rarer\nmedium (optical density is the ratio of the\nspeed of light in two media) For example,\nturpentine and water Mass density of\nturpentine is less than that of water but\nits optical density is higher" + }, + { + "Chapter": "9", + "sentence_range": "238-241", + "Text": "It is possible that mass\ndensity of an optically denser medium may\nbe less than that of an optically rarer\nmedium (optical density is the ratio of the\nspeed of light in two media) For example,\nturpentine and water Mass density of\nturpentine is less than that of water but\nits optical density is higher If n 21 is the refractive index of medium 2 with\nrespect to medium 1 and n12 the refractive index\nof medium 1 with respect to medium 2, then it\nshould be clear that\n12\n21\n1\nn\n=n\n(9" + }, + { + "Chapter": "9", + "sentence_range": "239-242", + "Text": "For example,\nturpentine and water Mass density of\nturpentine is less than that of water but\nits optical density is higher If n 21 is the refractive index of medium 2 with\nrespect to medium 1 and n12 the refractive index\nof medium 1 with respect to medium 2, then it\nshould be clear that\n12\n21\n1\nn\n=n\n(9 11)\nIt also follows that if n 32 is the refractive index\nof medium 3 with respect to medium 2 then n 32 =\nn 31 \u00d7 n 12, where n 31 is the refractive index of\nmedium 3 with respect to medium 1" + }, + { + "Chapter": "9", + "sentence_range": "240-243", + "Text": "Mass density of\nturpentine is less than that of water but\nits optical density is higher If n 21 is the refractive index of medium 2 with\nrespect to medium 1 and n12 the refractive index\nof medium 1 with respect to medium 2, then it\nshould be clear that\n12\n21\n1\nn\n=n\n(9 11)\nIt also follows that if n 32 is the refractive index\nof medium 3 with respect to medium 2 then n 32 =\nn 31 \u00d7 n 12, where n 31 is the refractive index of\nmedium 3 with respect to medium 1 Some elementary results based on the laws of\nrefraction follow immediately" + }, + { + "Chapter": "9", + "sentence_range": "241-244", + "Text": "If n 21 is the refractive index of medium 2 with\nrespect to medium 1 and n12 the refractive index\nof medium 1 with respect to medium 2, then it\nshould be clear that\n12\n21\n1\nn\n=n\n(9 11)\nIt also follows that if n 32 is the refractive index\nof medium 3 with respect to medium 2 then n 32 =\nn 31 \u00d7 n 12, where n 31 is the refractive index of\nmedium 3 with respect to medium 1 Some elementary results based on the laws of\nrefraction follow immediately For a rectangular\nslab, refraction takes place at two interfaces (air-\nglass and glass-air)" + }, + { + "Chapter": "9", + "sentence_range": "242-245", + "Text": "11)\nIt also follows that if n 32 is the refractive index\nof medium 3 with respect to medium 2 then n 32 =\nn 31 \u00d7 n 12, where n 31 is the refractive index of\nmedium 3 with respect to medium 1 Some elementary results based on the laws of\nrefraction follow immediately For a rectangular\nslab, refraction takes place at two interfaces (air-\nglass and glass-air) It is easily seen from Fig" + }, + { + "Chapter": "9", + "sentence_range": "243-246", + "Text": "Some elementary results based on the laws of\nrefraction follow immediately For a rectangular\nslab, refraction takes place at two interfaces (air-\nglass and glass-air) It is easily seen from Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "244-247", + "Text": "For a rectangular\nslab, refraction takes place at two interfaces (air-\nglass and glass-air) It is easily seen from Fig 9 9\nthat r2 = i1, i" + }, + { + "Chapter": "9", + "sentence_range": "245-248", + "Text": "It is easily seen from Fig 9 9\nthat r2 = i1, i e" + }, + { + "Chapter": "9", + "sentence_range": "246-249", + "Text": "9 9\nthat r2 = i1, i e , the emergent ray is parallel to the\nincident ray\u2014there is no deviation, but it does\nsuffer lateral displacement/shift with respect to the\nincident ray" + }, + { + "Chapter": "9", + "sentence_range": "247-250", + "Text": "9\nthat r2 = i1, i e , the emergent ray is parallel to the\nincident ray\u2014there is no deviation, but it does\nsuffer lateral displacement/shift with respect to the\nincident ray Another familiar observation is that\nthe bottom of a tank filled with water appears to be\nraised (Fig" + }, + { + "Chapter": "9", + "sentence_range": "248-251", + "Text": "e , the emergent ray is parallel to the\nincident ray\u2014there is no deviation, but it does\nsuffer lateral displacement/shift with respect to the\nincident ray Another familiar observation is that\nthe bottom of a tank filled with water appears to be\nraised (Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "249-252", + "Text": ", the emergent ray is parallel to the\nincident ray\u2014there is no deviation, but it does\nsuffer lateral displacement/shift with respect to the\nincident ray Another familiar observation is that\nthe bottom of a tank filled with water appears to be\nraised (Fig 9 10)" + }, + { + "Chapter": "9", + "sentence_range": "250-253", + "Text": "Another familiar observation is that\nthe bottom of a tank filled with water appears to be\nraised (Fig 9 10) For viewing near the normal direction, it can be shown\nthat the apparent depth (h1) is real depth (h 2) divided by the refractive\nindex of the medium (water)" + }, + { + "Chapter": "9", + "sentence_range": "251-254", + "Text": "9 10) For viewing near the normal direction, it can be shown\nthat the apparent depth (h1) is real depth (h 2) divided by the refractive\nindex of the medium (water) 9" + }, + { + "Chapter": "9", + "sentence_range": "252-255", + "Text": "10) For viewing near the normal direction, it can be shown\nthat the apparent depth (h1) is real depth (h 2) divided by the refractive\nindex of the medium (water) 9 4 TOTAL INTERNAL REFLECTION\nWhen light travels from an optically denser medium to a rarer medium\nat the interface, it is partly reflected back into the same medium and\npartly refracted to the second medium" + }, + { + "Chapter": "9", + "sentence_range": "253-256", + "Text": "For viewing near the normal direction, it can be shown\nthat the apparent depth (h1) is real depth (h 2) divided by the refractive\nindex of the medium (water) 9 4 TOTAL INTERNAL REFLECTION\nWhen light travels from an optically denser medium to a rarer medium\nat the interface, it is partly reflected back into the same medium and\npartly refracted to the second medium This reflection is called the internal\nreflection" + }, + { + "Chapter": "9", + "sentence_range": "254-257", + "Text": "9 4 TOTAL INTERNAL REFLECTION\nWhen light travels from an optically denser medium to a rarer medium\nat the interface, it is partly reflected back into the same medium and\npartly refracted to the second medium This reflection is called the internal\nreflection When a ray of light enters from a denser medium to a rarer medium,\nit bends away from the normal, for example, the ray AO1 B in Fig" + }, + { + "Chapter": "9", + "sentence_range": "255-258", + "Text": "4 TOTAL INTERNAL REFLECTION\nWhen light travels from an optically denser medium to a rarer medium\nat the interface, it is partly reflected back into the same medium and\npartly refracted to the second medium This reflection is called the internal\nreflection When a ray of light enters from a denser medium to a rarer medium,\nit bends away from the normal, for example, the ray AO1 B in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "256-259", + "Text": "This reflection is called the internal\nreflection When a ray of light enters from a denser medium to a rarer medium,\nit bends away from the normal, for example, the ray AO1 B in Fig 9 11" + }, + { + "Chapter": "9", + "sentence_range": "257-260", + "Text": "When a ray of light enters from a denser medium to a rarer medium,\nit bends away from the normal, for example, the ray AO1 B in Fig 9 11 The incident ray AO1 is partially reflected (O1C) and partially transmitted\n(O1B) or refracted, the angle of refraction (r) being larger than the angle of\nincidence (i)" + }, + { + "Chapter": "9", + "sentence_range": "258-261", + "Text": "9 11 The incident ray AO1 is partially reflected (O1C) and partially transmitted\n(O1B) or refracted, the angle of refraction (r) being larger than the angle of\nincidence (i) As the angle of incidence increases, so does the angle of\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "259-262", + "Text": "11 The incident ray AO1 is partially reflected (O1C) and partially transmitted\n(O1B) or refracted, the angle of refraction (r) being larger than the angle of\nincidence (i) As the angle of incidence increases, so does the angle of\nFIGURE 9 10 Apparent depth for\n(a) normal, and (b) oblique viewing" + }, + { + "Chapter": "9", + "sentence_range": "260-263", + "Text": "The incident ray AO1 is partially reflected (O1C) and partially transmitted\n(O1B) or refracted, the angle of refraction (r) being larger than the angle of\nincidence (i) As the angle of incidence increases, so does the angle of\nFIGURE 9 10 Apparent depth for\n(a) normal, and (b) oblique viewing FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "261-264", + "Text": "As the angle of incidence increases, so does the angle of\nFIGURE 9 10 Apparent depth for\n(a) normal, and (b) oblique viewing FIGURE 9 9 Lateral shift of a ray refracted\nthrough a parallel-sided slab" + }, + { + "Chapter": "9", + "sentence_range": "262-265", + "Text": "10 Apparent depth for\n(a) normal, and (b) oblique viewing FIGURE 9 9 Lateral shift of a ray refracted\nthrough a parallel-sided slab Rationalised 2023-24\nPhysics\n230\nrefraction, till for the ray AO3, the angle of\nrefraction is p/2" + }, + { + "Chapter": "9", + "sentence_range": "263-266", + "Text": "FIGURE 9 9 Lateral shift of a ray refracted\nthrough a parallel-sided slab Rationalised 2023-24\nPhysics\n230\nrefraction, till for the ray AO3, the angle of\nrefraction is p/2 The refracted ray is bent\nso much away from the normal that it\ngrazes the surface at the interface between\nthe two media" + }, + { + "Chapter": "9", + "sentence_range": "264-267", + "Text": "9 Lateral shift of a ray refracted\nthrough a parallel-sided slab Rationalised 2023-24\nPhysics\n230\nrefraction, till for the ray AO3, the angle of\nrefraction is p/2 The refracted ray is bent\nso much away from the normal that it\ngrazes the surface at the interface between\nthe two media This is shown by the ray\nAO3 D in Fig" + }, + { + "Chapter": "9", + "sentence_range": "265-268", + "Text": "Rationalised 2023-24\nPhysics\n230\nrefraction, till for the ray AO3, the angle of\nrefraction is p/2 The refracted ray is bent\nso much away from the normal that it\ngrazes the surface at the interface between\nthe two media This is shown by the ray\nAO3 D in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "266-269", + "Text": "The refracted ray is bent\nso much away from the normal that it\ngrazes the surface at the interface between\nthe two media This is shown by the ray\nAO3 D in Fig 9 11" + }, + { + "Chapter": "9", + "sentence_range": "267-270", + "Text": "This is shown by the ray\nAO3 D in Fig 9 11 If the angle of incidence\nis increased still further (e" + }, + { + "Chapter": "9", + "sentence_range": "268-271", + "Text": "9 11 If the angle of incidence\nis increased still further (e g" + }, + { + "Chapter": "9", + "sentence_range": "269-272", + "Text": "11 If the angle of incidence\nis increased still further (e g , the ray AO4),\nrefraction is not possible, and the incident\nray is totally reflected" + }, + { + "Chapter": "9", + "sentence_range": "270-273", + "Text": "If the angle of incidence\nis increased still further (e g , the ray AO4),\nrefraction is not possible, and the incident\nray is totally reflected This is called total\ninternal reflection" + }, + { + "Chapter": "9", + "sentence_range": "271-274", + "Text": "g , the ray AO4),\nrefraction is not possible, and the incident\nray is totally reflected This is called total\ninternal reflection When light gets\nreflected by a surface, normally some\nfraction of it gets transmitted" + }, + { + "Chapter": "9", + "sentence_range": "272-275", + "Text": ", the ray AO4),\nrefraction is not possible, and the incident\nray is totally reflected This is called total\ninternal reflection When light gets\nreflected by a surface, normally some\nfraction of it gets transmitted The\nreflected ray, therefore, is always less\nintense than the incident ray, howsoever\nsmooth the reflecting surface may be" + }, + { + "Chapter": "9", + "sentence_range": "273-276", + "Text": "This is called total\ninternal reflection When light gets\nreflected by a surface, normally some\nfraction of it gets transmitted The\nreflected ray, therefore, is always less\nintense than the incident ray, howsoever\nsmooth the reflecting surface may be In\ntotal internal reflection, on the other hand,\nno transmission of light takes place" + }, + { + "Chapter": "9", + "sentence_range": "274-277", + "Text": "When light gets\nreflected by a surface, normally some\nfraction of it gets transmitted The\nreflected ray, therefore, is always less\nintense than the incident ray, howsoever\nsmooth the reflecting surface may be In\ntotal internal reflection, on the other hand,\nno transmission of light takes place The angle of incidence corresponding to an angle of refraction 90\u00b0,\nsay \u00d0AO3N, is called the critical angle (ic ) for the given pair of media" + }, + { + "Chapter": "9", + "sentence_range": "275-278", + "Text": "The\nreflected ray, therefore, is always less\nintense than the incident ray, howsoever\nsmooth the reflecting surface may be In\ntotal internal reflection, on the other hand,\nno transmission of light takes place The angle of incidence corresponding to an angle of refraction 90\u00b0,\nsay \u00d0AO3N, is called the critical angle (ic ) for the given pair of media We\nsee from Snell\u2019s law [Eq" + }, + { + "Chapter": "9", + "sentence_range": "276-279", + "Text": "In\ntotal internal reflection, on the other hand,\nno transmission of light takes place The angle of incidence corresponding to an angle of refraction 90\u00b0,\nsay \u00d0AO3N, is called the critical angle (ic ) for the given pair of media We\nsee from Snell\u2019s law [Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "277-280", + "Text": "The angle of incidence corresponding to an angle of refraction 90\u00b0,\nsay \u00d0AO3N, is called the critical angle (ic ) for the given pair of media We\nsee from Snell\u2019s law [Eq (9 10)] that if the relative refractive index of the\nrefracting medium is less than one then, since the maximum value of sin\nr is unity, there is an upper limit to the value of sin i for which the law\ncan be satisfied, that is, i = ic such that\nsin ic = n 21\n(9" + }, + { + "Chapter": "9", + "sentence_range": "278-281", + "Text": "We\nsee from Snell\u2019s law [Eq (9 10)] that if the relative refractive index of the\nrefracting medium is less than one then, since the maximum value of sin\nr is unity, there is an upper limit to the value of sin i for which the law\ncan be satisfied, that is, i = ic such that\nsin ic = n 21\n(9 12)\nFor values of i larger than ic, Snell\u2019s law of refraction cannot be\nsatisfied, and hence no refraction is possible" + }, + { + "Chapter": "9", + "sentence_range": "279-282", + "Text": "(9 10)] that if the relative refractive index of the\nrefracting medium is less than one then, since the maximum value of sin\nr is unity, there is an upper limit to the value of sin i for which the law\ncan be satisfied, that is, i = ic such that\nsin ic = n 21\n(9 12)\nFor values of i larger than ic, Snell\u2019s law of refraction cannot be\nsatisfied, and hence no refraction is possible The refractive index of denser medium 1 with respect to rarer medium\n2 will be n12 = 1/sinic" + }, + { + "Chapter": "9", + "sentence_range": "280-283", + "Text": "10)] that if the relative refractive index of the\nrefracting medium is less than one then, since the maximum value of sin\nr is unity, there is an upper limit to the value of sin i for which the law\ncan be satisfied, that is, i = ic such that\nsin ic = n 21\n(9 12)\nFor values of i larger than ic, Snell\u2019s law of refraction cannot be\nsatisfied, and hence no refraction is possible The refractive index of denser medium 1 with respect to rarer medium\n2 will be n12 = 1/sinic Some typical critical angles are listed in Table 9" + }, + { + "Chapter": "9", + "sentence_range": "281-284", + "Text": "12)\nFor values of i larger than ic, Snell\u2019s law of refraction cannot be\nsatisfied, and hence no refraction is possible The refractive index of denser medium 1 with respect to rarer medium\n2 will be n12 = 1/sinic Some typical critical angles are listed in Table 9 1" + }, + { + "Chapter": "9", + "sentence_range": "282-285", + "Text": "The refractive index of denser medium 1 with respect to rarer medium\n2 will be n12 = 1/sinic Some typical critical angles are listed in Table 9 1 FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "283-286", + "Text": "Some typical critical angles are listed in Table 9 1 FIGURE 9 11 Refraction and internal reflection\nof rays from a point A in the denser medium\n(water) incident at different angles at the interface\nwith a rarer medium (air)" + }, + { + "Chapter": "9", + "sentence_range": "284-287", + "Text": "1 FIGURE 9 11 Refraction and internal reflection\nof rays from a point A in the denser medium\n(water) incident at different angles at the interface\nwith a rarer medium (air) A demonstration for total internal reflection\nAll optical phenomena can be demonstrated very easily with the use of a\nlaser torch or pointer, which is easily available nowadays" + }, + { + "Chapter": "9", + "sentence_range": "285-288", + "Text": "FIGURE 9 11 Refraction and internal reflection\nof rays from a point A in the denser medium\n(water) incident at different angles at the interface\nwith a rarer medium (air) A demonstration for total internal reflection\nAll optical phenomena can be demonstrated very easily with the use of a\nlaser torch or pointer, which is easily available nowadays Take a glass\nbeaker with clear water in it" + }, + { + "Chapter": "9", + "sentence_range": "286-289", + "Text": "11 Refraction and internal reflection\nof rays from a point A in the denser medium\n(water) incident at different angles at the interface\nwith a rarer medium (air) A demonstration for total internal reflection\nAll optical phenomena can be demonstrated very easily with the use of a\nlaser torch or pointer, which is easily available nowadays Take a glass\nbeaker with clear water in it Add a few drops of milk or any other\nsuspension to water and stir so that water becomes a little turbid" + }, + { + "Chapter": "9", + "sentence_range": "287-290", + "Text": "A demonstration for total internal reflection\nAll optical phenomena can be demonstrated very easily with the use of a\nlaser torch or pointer, which is easily available nowadays Take a glass\nbeaker with clear water in it Add a few drops of milk or any other\nsuspension to water and stir so that water becomes a little turbid Take\na laser pointer and shine its beam through the turbid water" + }, + { + "Chapter": "9", + "sentence_range": "288-291", + "Text": "Take a glass\nbeaker with clear water in it Add a few drops of milk or any other\nsuspension to water and stir so that water becomes a little turbid Take\na laser pointer and shine its beam through the turbid water You will\nfind that the path of the beam inside the water shines brightly" + }, + { + "Chapter": "9", + "sentence_range": "289-292", + "Text": "Add a few drops of milk or any other\nsuspension to water and stir so that water becomes a little turbid Take\na laser pointer and shine its beam through the turbid water You will\nfind that the path of the beam inside the water shines brightly TABLE 9" + }, + { + "Chapter": "9", + "sentence_range": "290-293", + "Text": "Take\na laser pointer and shine its beam through the turbid water You will\nfind that the path of the beam inside the water shines brightly TABLE 9 1 CRITICAL ANGLE OF SOME TRANSPARENT MEDIA WITH RESPECT TO AIR\nSubstance medium\nRefractive index\nCritical angle\nWater\n1" + }, + { + "Chapter": "9", + "sentence_range": "291-294", + "Text": "You will\nfind that the path of the beam inside the water shines brightly TABLE 9 1 CRITICAL ANGLE OF SOME TRANSPARENT MEDIA WITH RESPECT TO AIR\nSubstance medium\nRefractive index\nCritical angle\nWater\n1 33\n48" + }, + { + "Chapter": "9", + "sentence_range": "292-295", + "Text": "TABLE 9 1 CRITICAL ANGLE OF SOME TRANSPARENT MEDIA WITH RESPECT TO AIR\nSubstance medium\nRefractive index\nCritical angle\nWater\n1 33\n48 75\nCrown glass\n1" + }, + { + "Chapter": "9", + "sentence_range": "293-296", + "Text": "1 CRITICAL ANGLE OF SOME TRANSPARENT MEDIA WITH RESPECT TO AIR\nSubstance medium\nRefractive index\nCritical angle\nWater\n1 33\n48 75\nCrown glass\n1 52\n41" + }, + { + "Chapter": "9", + "sentence_range": "294-297", + "Text": "33\n48 75\nCrown glass\n1 52\n41 14\nDense flint glass\n1" + }, + { + "Chapter": "9", + "sentence_range": "295-298", + "Text": "75\nCrown glass\n1 52\n41 14\nDense flint glass\n1 62\n37" + }, + { + "Chapter": "9", + "sentence_range": "296-299", + "Text": "52\n41 14\nDense flint glass\n1 62\n37 31\nDiamond\n2" + }, + { + "Chapter": "9", + "sentence_range": "297-300", + "Text": "14\nDense flint glass\n1 62\n37 31\nDiamond\n2 42\n24" + }, + { + "Chapter": "9", + "sentence_range": "298-301", + "Text": "62\n37 31\nDiamond\n2 42\n24 41\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n231\nShine the beam from below the beaker such that it strikes at the\nupper water surface at the other end" + }, + { + "Chapter": "9", + "sentence_range": "299-302", + "Text": "31\nDiamond\n2 42\n24 41\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n231\nShine the beam from below the beaker such that it strikes at the\nupper water surface at the other end Do you find that it undergoes partial\nreflection (which is seen as a spot on the table below) and partial refraction\n[which comes out in the air and is seen as a spot on the roof; Fig" + }, + { + "Chapter": "9", + "sentence_range": "300-303", + "Text": "42\n24 41\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n231\nShine the beam from below the beaker such that it strikes at the\nupper water surface at the other end Do you find that it undergoes partial\nreflection (which is seen as a spot on the table below) and partial refraction\n[which comes out in the air and is seen as a spot on the roof; Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "301-304", + "Text": "41\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n231\nShine the beam from below the beaker such that it strikes at the\nupper water surface at the other end Do you find that it undergoes partial\nreflection (which is seen as a spot on the table below) and partial refraction\n[which comes out in the air and is seen as a spot on the roof; Fig 9 12(a)]" + }, + { + "Chapter": "9", + "sentence_range": "302-305", + "Text": "Do you find that it undergoes partial\nreflection (which is seen as a spot on the table below) and partial refraction\n[which comes out in the air and is seen as a spot on the roof; Fig 9 12(a)] Now direct the laser beam from one side of the beaker such that it strikes\nthe upper surface of water more obliquely [Fig" + }, + { + "Chapter": "9", + "sentence_range": "303-306", + "Text": "9 12(a)] Now direct the laser beam from one side of the beaker such that it strikes\nthe upper surface of water more obliquely [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "304-307", + "Text": "12(a)] Now direct the laser beam from one side of the beaker such that it strikes\nthe upper surface of water more obliquely [Fig 9 12(b)]" + }, + { + "Chapter": "9", + "sentence_range": "305-308", + "Text": "Now direct the laser beam from one side of the beaker such that it strikes\nthe upper surface of water more obliquely [Fig 9 12(b)] Adjust the\ndirection of laser beam until you find the angle for which the refraction\nabove the water surface is totally absent and the beam is totally reflected\nback to water" + }, + { + "Chapter": "9", + "sentence_range": "306-309", + "Text": "9 12(b)] Adjust the\ndirection of laser beam until you find the angle for which the refraction\nabove the water surface is totally absent and the beam is totally reflected\nback to water This is total internal reflection at its simplest" + }, + { + "Chapter": "9", + "sentence_range": "307-310", + "Text": "12(b)] Adjust the\ndirection of laser beam until you find the angle for which the refraction\nabove the water surface is totally absent and the beam is totally reflected\nback to water This is total internal reflection at its simplest Pour this water in a long test tube and shine the laser light from top,\nas shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "308-311", + "Text": "Adjust the\ndirection of laser beam until you find the angle for which the refraction\nabove the water surface is totally absent and the beam is totally reflected\nback to water This is total internal reflection at its simplest Pour this water in a long test tube and shine the laser light from top,\nas shown in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "309-312", + "Text": "This is total internal reflection at its simplest Pour this water in a long test tube and shine the laser light from top,\nas shown in Fig 9 12(c)" + }, + { + "Chapter": "9", + "sentence_range": "310-313", + "Text": "Pour this water in a long test tube and shine the laser light from top,\nas shown in Fig 9 12(c) Adjust the direction of the laser beam such that\nit is totally internally reflected every time it strikes the walls of the tube" + }, + { + "Chapter": "9", + "sentence_range": "311-314", + "Text": "9 12(c) Adjust the direction of the laser beam such that\nit is totally internally reflected every time it strikes the walls of the tube This is similar to what happens in optical fibres" + }, + { + "Chapter": "9", + "sentence_range": "312-315", + "Text": "12(c) Adjust the direction of the laser beam such that\nit is totally internally reflected every time it strikes the walls of the tube This is similar to what happens in optical fibres Take care not to look into the laser beam directly and not to point it\nat anybody\u2019s face" + }, + { + "Chapter": "9", + "sentence_range": "313-316", + "Text": "Adjust the direction of the laser beam such that\nit is totally internally reflected every time it strikes the walls of the tube This is similar to what happens in optical fibres Take care not to look into the laser beam directly and not to point it\nat anybody\u2019s face 9" + }, + { + "Chapter": "9", + "sentence_range": "314-317", + "Text": "This is similar to what happens in optical fibres Take care not to look into the laser beam directly and not to point it\nat anybody\u2019s face 9 4" + }, + { + "Chapter": "9", + "sentence_range": "315-318", + "Text": "Take care not to look into the laser beam directly and not to point it\nat anybody\u2019s face 9 4 1 Total internal reflection in nature and\nits technelogical applications\n(i)\nPrism: Prisms designed to bend light by 90\u00b0 or by 180\u00b0 make use of\ntotal internal reflection [Fig" + }, + { + "Chapter": "9", + "sentence_range": "316-319", + "Text": "9 4 1 Total internal reflection in nature and\nits technelogical applications\n(i)\nPrism: Prisms designed to bend light by 90\u00b0 or by 180\u00b0 make use of\ntotal internal reflection [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "317-320", + "Text": "4 1 Total internal reflection in nature and\nits technelogical applications\n(i)\nPrism: Prisms designed to bend light by 90\u00b0 or by 180\u00b0 make use of\ntotal internal reflection [Fig 9 13(a) and (b)]" + }, + { + "Chapter": "9", + "sentence_range": "318-321", + "Text": "1 Total internal reflection in nature and\nits technelogical applications\n(i)\nPrism: Prisms designed to bend light by 90\u00b0 or by 180\u00b0 make use of\ntotal internal reflection [Fig 9 13(a) and (b)] Such a prism is also\nused to invert images without chxanging their size [Fig" + }, + { + "Chapter": "9", + "sentence_range": "319-322", + "Text": "9 13(a) and (b)] Such a prism is also\nused to invert images without chxanging their size [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "320-323", + "Text": "13(a) and (b)] Such a prism is also\nused to invert images without chxanging their size [Fig 9 13(c)]" + }, + { + "Chapter": "9", + "sentence_range": "321-324", + "Text": "Such a prism is also\nused to invert images without chxanging their size [Fig 9 13(c)] In the first two cases, the critical angle ic for the material of the prism\nmust be less than 45\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "322-325", + "Text": "9 13(c)] In the first two cases, the critical angle ic for the material of the prism\nmust be less than 45\u00b0 We see from Table 9" + }, + { + "Chapter": "9", + "sentence_range": "323-326", + "Text": "13(c)] In the first two cases, the critical angle ic for the material of the prism\nmust be less than 45\u00b0 We see from Table 9 1 that this is true for both\ncrown glass and dense flint glass" + }, + { + "Chapter": "9", + "sentence_range": "324-327", + "Text": "In the first two cases, the critical angle ic for the material of the prism\nmust be less than 45\u00b0 We see from Table 9 1 that this is true for both\ncrown glass and dense flint glass (ii) Optical fibres: Nowadays optical fibres are extensively used for\ntransmitting audio and video signals through long distances" + }, + { + "Chapter": "9", + "sentence_range": "325-328", + "Text": "We see from Table 9 1 that this is true for both\ncrown glass and dense flint glass (ii) Optical fibres: Nowadays optical fibres are extensively used for\ntransmitting audio and video signals through long distances Optical\nfibres too make use of the phenomenon of total internal reflection" + }, + { + "Chapter": "9", + "sentence_range": "326-329", + "Text": "1 that this is true for both\ncrown glass and dense flint glass (ii) Optical fibres: Nowadays optical fibres are extensively used for\ntransmitting audio and video signals through long distances Optical\nfibres too make use of the phenomenon of total internal reflection Optical fibres are fabricated with high quality composite glass/quartz\nfibres" + }, + { + "Chapter": "9", + "sentence_range": "327-330", + "Text": "(ii) Optical fibres: Nowadays optical fibres are extensively used for\ntransmitting audio and video signals through long distances Optical\nfibres too make use of the phenomenon of total internal reflection Optical fibres are fabricated with high quality composite glass/quartz\nfibres Each fibre consists of a core and\ncladding" + }, + { + "Chapter": "9", + "sentence_range": "328-331", + "Text": "Optical\nfibres too make use of the phenomenon of total internal reflection Optical fibres are fabricated with high quality composite glass/quartz\nfibres Each fibre consists of a core and\ncladding The refractive index of the\nmaterial of the core is higher than that\nof the cladding" + }, + { + "Chapter": "9", + "sentence_range": "329-332", + "Text": "Optical fibres are fabricated with high quality composite glass/quartz\nfibres Each fibre consists of a core and\ncladding The refractive index of the\nmaterial of the core is higher than that\nof the cladding When a signal in the form of light is\ndirected at one end of the fibre at a suitable\nangle, it undergoes repeated total internal\nreflections along the length of the fibre and\nfinally comes out at the other end (Fig" + }, + { + "Chapter": "9", + "sentence_range": "330-333", + "Text": "Each fibre consists of a core and\ncladding The refractive index of the\nmaterial of the core is higher than that\nof the cladding When a signal in the form of light is\ndirected at one end of the fibre at a suitable\nangle, it undergoes repeated total internal\nreflections along the length of the fibre and\nfinally comes out at the other end (Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "331-334", + "Text": "The refractive index of the\nmaterial of the core is higher than that\nof the cladding When a signal in the form of light is\ndirected at one end of the fibre at a suitable\nangle, it undergoes repeated total internal\nreflections along the length of the fibre and\nfinally comes out at the other end (Fig 9 14)" + }, + { + "Chapter": "9", + "sentence_range": "332-335", + "Text": "When a signal in the form of light is\ndirected at one end of the fibre at a suitable\nangle, it undergoes repeated total internal\nreflections along the length of the fibre and\nfinally comes out at the other end (Fig 9 14) Since light undergoes total internal\nreflection at each stage, there is no\nappreciable loss in the intensity of the light\nsignal" + }, + { + "Chapter": "9", + "sentence_range": "333-336", + "Text": "9 14) Since light undergoes total internal\nreflection at each stage, there is no\nappreciable loss in the intensity of the light\nsignal Optical fibres are fabricated such\nthat light reflected at one side of inner\nsurface strikes the other at an angle larger\nthan the critical angle" + }, + { + "Chapter": "9", + "sentence_range": "334-337", + "Text": "14) Since light undergoes total internal\nreflection at each stage, there is no\nappreciable loss in the intensity of the light\nsignal Optical fibres are fabricated such\nthat light reflected at one side of inner\nsurface strikes the other at an angle larger\nthan the critical angle Even if the fibre is\nbent, light can easily travel along its length" + }, + { + "Chapter": "9", + "sentence_range": "335-338", + "Text": "Since light undergoes total internal\nreflection at each stage, there is no\nappreciable loss in the intensity of the light\nsignal Optical fibres are fabricated such\nthat light reflected at one side of inner\nsurface strikes the other at an angle larger\nthan the critical angle Even if the fibre is\nbent, light can easily travel along its length Thus, an optical fibre can be used to act as\nan optical pipe" + }, + { + "Chapter": "9", + "sentence_range": "336-339", + "Text": "Optical fibres are fabricated such\nthat light reflected at one side of inner\nsurface strikes the other at an angle larger\nthan the critical angle Even if the fibre is\nbent, light can easily travel along its length Thus, an optical fibre can be used to act as\nan optical pipe A bundle of optical fibres can be put to\nseveral uses" + }, + { + "Chapter": "9", + "sentence_range": "337-340", + "Text": "Even if the fibre is\nbent, light can easily travel along its length Thus, an optical fibre can be used to act as\nan optical pipe A bundle of optical fibres can be put to\nseveral uses Optical fibres are extensively\nused for transmitting and receiving\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "338-341", + "Text": "Thus, an optical fibre can be used to act as\nan optical pipe A bundle of optical fibres can be put to\nseveral uses Optical fibres are extensively\nused for transmitting and receiving\nFIGURE 9 12\nObserving total internal\nreflection in water with\na laser beam (refraction\ndue to glass of beaker\nneglected being very\nthin)" + }, + { + "Chapter": "9", + "sentence_range": "339-342", + "Text": "A bundle of optical fibres can be put to\nseveral uses Optical fibres are extensively\nused for transmitting and receiving\nFIGURE 9 12\nObserving total internal\nreflection in water with\na laser beam (refraction\ndue to glass of beaker\nneglected being very\nthin) FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "340-343", + "Text": "Optical fibres are extensively\nused for transmitting and receiving\nFIGURE 9 12\nObserving total internal\nreflection in water with\na laser beam (refraction\ndue to glass of beaker\nneglected being very\nthin) FIGURE 9 13 Prisms designed to bend rays by\n90\u00b0 and 180\u00b0 or to invert image without changing\nits size make use of total internal reflection" + }, + { + "Chapter": "9", + "sentence_range": "341-344", + "Text": "12\nObserving total internal\nreflection in water with\na laser beam (refraction\ndue to glass of beaker\nneglected being very\nthin) FIGURE 9 13 Prisms designed to bend rays by\n90\u00b0 and 180\u00b0 or to invert image without changing\nits size make use of total internal reflection Rationalised 2023-24\nPhysics\n232\nelectrical signals which are converted to light\nby suitable transducers" + }, + { + "Chapter": "9", + "sentence_range": "342-345", + "Text": "FIGURE 9 13 Prisms designed to bend rays by\n90\u00b0 and 180\u00b0 or to invert image without changing\nits size make use of total internal reflection Rationalised 2023-24\nPhysics\n232\nelectrical signals which are converted to light\nby suitable transducers Obviously, optical\nfibres can also be used for transmission of\noptical signals" + }, + { + "Chapter": "9", + "sentence_range": "343-346", + "Text": "13 Prisms designed to bend rays by\n90\u00b0 and 180\u00b0 or to invert image without changing\nits size make use of total internal reflection Rationalised 2023-24\nPhysics\n232\nelectrical signals which are converted to light\nby suitable transducers Obviously, optical\nfibres can also be used for transmission of\noptical signals For example, these are used\nas a \u2018light pipe\u2019 to facilitate visual examination\nof internal organs like esophagus, stomach\nand intestines" + }, + { + "Chapter": "9", + "sentence_range": "344-347", + "Text": "Rationalised 2023-24\nPhysics\n232\nelectrical signals which are converted to light\nby suitable transducers Obviously, optical\nfibres can also be used for transmission of\noptical signals For example, these are used\nas a \u2018light pipe\u2019 to facilitate visual examination\nof internal organs like esophagus, stomach\nand intestines You might have seen a\ncommonly available decorative lamp with fine\nplastic fibres with their free ends forming a\nfountain like structure" + }, + { + "Chapter": "9", + "sentence_range": "345-348", + "Text": "Obviously, optical\nfibres can also be used for transmission of\noptical signals For example, these are used\nas a \u2018light pipe\u2019 to facilitate visual examination\nof internal organs like esophagus, stomach\nand intestines You might have seen a\ncommonly available decorative lamp with fine\nplastic fibres with their free ends forming a\nfountain like structure The other end of the\nfibres is fixed over an electric lamp" + }, + { + "Chapter": "9", + "sentence_range": "346-349", + "Text": "For example, these are used\nas a \u2018light pipe\u2019 to facilitate visual examination\nof internal organs like esophagus, stomach\nand intestines You might have seen a\ncommonly available decorative lamp with fine\nplastic fibres with their free ends forming a\nfountain like structure The other end of the\nfibres is fixed over an electric lamp When the\nlamp is switched on, the light travels from the bottom of each fibre and\nappears at the tip of its free end as a dot of light" + }, + { + "Chapter": "9", + "sentence_range": "347-350", + "Text": "You might have seen a\ncommonly available decorative lamp with fine\nplastic fibres with their free ends forming a\nfountain like structure The other end of the\nfibres is fixed over an electric lamp When the\nlamp is switched on, the light travels from the bottom of each fibre and\nappears at the tip of its free end as a dot of light The fibres in such\ndecorative lamps are optical fibres" + }, + { + "Chapter": "9", + "sentence_range": "348-351", + "Text": "The other end of the\nfibres is fixed over an electric lamp When the\nlamp is switched on, the light travels from the bottom of each fibre and\nappears at the tip of its free end as a dot of light The fibres in such\ndecorative lamps are optical fibres The main requirement in fabricating optical fibres is that there should\nbe very little absorption of light as it travels for long distances inside\nthem" + }, + { + "Chapter": "9", + "sentence_range": "349-352", + "Text": "When the\nlamp is switched on, the light travels from the bottom of each fibre and\nappears at the tip of its free end as a dot of light The fibres in such\ndecorative lamps are optical fibres The main requirement in fabricating optical fibres is that there should\nbe very little absorption of light as it travels for long distances inside\nthem This has been achieved by purification and special preparation of\nmaterials such as quartz" + }, + { + "Chapter": "9", + "sentence_range": "350-353", + "Text": "The fibres in such\ndecorative lamps are optical fibres The main requirement in fabricating optical fibres is that there should\nbe very little absorption of light as it travels for long distances inside\nthem This has been achieved by purification and special preparation of\nmaterials such as quartz In silica glass fibres, it is possible to transmit\nmore than 95% of the light over a fibre length of 1 km" + }, + { + "Chapter": "9", + "sentence_range": "351-354", + "Text": "The main requirement in fabricating optical fibres is that there should\nbe very little absorption of light as it travels for long distances inside\nthem This has been achieved by purification and special preparation of\nmaterials such as quartz In silica glass fibres, it is possible to transmit\nmore than 95% of the light over a fibre length of 1 km (Compare with\nwhat you expect for a block of ordinary window glass 1 km thick" + }, + { + "Chapter": "9", + "sentence_range": "352-355", + "Text": "This has been achieved by purification and special preparation of\nmaterials such as quartz In silica glass fibres, it is possible to transmit\nmore than 95% of the light over a fibre length of 1 km (Compare with\nwhat you expect for a block of ordinary window glass 1 km thick )\n9" + }, + { + "Chapter": "9", + "sentence_range": "353-356", + "Text": "In silica glass fibres, it is possible to transmit\nmore than 95% of the light over a fibre length of 1 km (Compare with\nwhat you expect for a block of ordinary window glass 1 km thick )\n9 5 REFRACTION AT SPHERICAL SURFACES\nAND BY LENSES\nWe have so far considered refraction at a plane interface" + }, + { + "Chapter": "9", + "sentence_range": "354-357", + "Text": "(Compare with\nwhat you expect for a block of ordinary window glass 1 km thick )\n9 5 REFRACTION AT SPHERICAL SURFACES\nAND BY LENSES\nWe have so far considered refraction at a plane interface We shall now\nconsider refraction at a spherical interface between two transparent media" + }, + { + "Chapter": "9", + "sentence_range": "355-358", + "Text": ")\n9 5 REFRACTION AT SPHERICAL SURFACES\nAND BY LENSES\nWe have so far considered refraction at a plane interface We shall now\nconsider refraction at a spherical interface between two transparent media An infinitesimal part of a spherical surface can be regarded as planar\nand the same laws of refraction can be applied at every point on the\nsurface" + }, + { + "Chapter": "9", + "sentence_range": "356-359", + "Text": "5 REFRACTION AT SPHERICAL SURFACES\nAND BY LENSES\nWe have so far considered refraction at a plane interface We shall now\nconsider refraction at a spherical interface between two transparent media An infinitesimal part of a spherical surface can be regarded as planar\nand the same laws of refraction can be applied at every point on the\nsurface Just as for reflection by a spherical mirror, the normal at the\npoint of incidence is perpendicular to the tangent plane to the spherical\nsurface at that point and, therefore, passes through its centre of\ncurvature" + }, + { + "Chapter": "9", + "sentence_range": "357-360", + "Text": "We shall now\nconsider refraction at a spherical interface between two transparent media An infinitesimal part of a spherical surface can be regarded as planar\nand the same laws of refraction can be applied at every point on the\nsurface Just as for reflection by a spherical mirror, the normal at the\npoint of incidence is perpendicular to the tangent plane to the spherical\nsurface at that point and, therefore, passes through its centre of\ncurvature We first consider refraction by a single spherical surface and\nfollow it by thin lenses" + }, + { + "Chapter": "9", + "sentence_range": "358-361", + "Text": "An infinitesimal part of a spherical surface can be regarded as planar\nand the same laws of refraction can be applied at every point on the\nsurface Just as for reflection by a spherical mirror, the normal at the\npoint of incidence is perpendicular to the tangent plane to the spherical\nsurface at that point and, therefore, passes through its centre of\ncurvature We first consider refraction by a single spherical surface and\nfollow it by thin lenses A thin lens is a transparent optical medium\nbounded by two surfaces; at least one of which should be spherical" + }, + { + "Chapter": "9", + "sentence_range": "359-362", + "Text": "Just as for reflection by a spherical mirror, the normal at the\npoint of incidence is perpendicular to the tangent plane to the spherical\nsurface at that point and, therefore, passes through its centre of\ncurvature We first consider refraction by a single spherical surface and\nfollow it by thin lenses A thin lens is a transparent optical medium\nbounded by two surfaces; at least one of which should be spherical Applying the formula for image formation by a single spherical surface\nsuccessively at the two surfaces of a lens, we shall obtain the lens maker\u2019s\nformula and then the lens formula" + }, + { + "Chapter": "9", + "sentence_range": "360-363", + "Text": "We first consider refraction by a single spherical surface and\nfollow it by thin lenses A thin lens is a transparent optical medium\nbounded by two surfaces; at least one of which should be spherical Applying the formula for image formation by a single spherical surface\nsuccessively at the two surfaces of a lens, we shall obtain the lens maker\u2019s\nformula and then the lens formula 9" + }, + { + "Chapter": "9", + "sentence_range": "361-364", + "Text": "A thin lens is a transparent optical medium\nbounded by two surfaces; at least one of which should be spherical Applying the formula for image formation by a single spherical surface\nsuccessively at the two surfaces of a lens, we shall obtain the lens maker\u2019s\nformula and then the lens formula 9 5" + }, + { + "Chapter": "9", + "sentence_range": "362-365", + "Text": "Applying the formula for image formation by a single spherical surface\nsuccessively at the two surfaces of a lens, we shall obtain the lens maker\u2019s\nformula and then the lens formula 9 5 1 Refraction at a spherical surface\nFigure 9" + }, + { + "Chapter": "9", + "sentence_range": "363-366", + "Text": "9 5 1 Refraction at a spherical surface\nFigure 9 15 shows the geometry of formation of image I of an object O on\nthe principal axis of a spherical surface with centre of curvature C, and\nradius of curvature R" + }, + { + "Chapter": "9", + "sentence_range": "364-367", + "Text": "5 1 Refraction at a spherical surface\nFigure 9 15 shows the geometry of formation of image I of an object O on\nthe principal axis of a spherical surface with centre of curvature C, and\nradius of curvature R The rays are incident from a medium of refractive\nindex n1, to another of refractive index n 2" + }, + { + "Chapter": "9", + "sentence_range": "365-368", + "Text": "1 Refraction at a spherical surface\nFigure 9 15 shows the geometry of formation of image I of an object O on\nthe principal axis of a spherical surface with centre of curvature C, and\nradius of curvature R The rays are incident from a medium of refractive\nindex n1, to another of refractive index n 2 As before, we take the aperture\n(or the lateral size) of the surface to be small compared to other distances\ninvolved, so that small angle approximation can be made" + }, + { + "Chapter": "9", + "sentence_range": "366-369", + "Text": "15 shows the geometry of formation of image I of an object O on\nthe principal axis of a spherical surface with centre of curvature C, and\nradius of curvature R The rays are incident from a medium of refractive\nindex n1, to another of refractive index n 2 As before, we take the aperture\n(or the lateral size) of the surface to be small compared to other distances\ninvolved, so that small angle approximation can be made In particular,\nNM will be taken to be nearly equal to the length of the perpendicular\nfrom the point N on the principal axis" + }, + { + "Chapter": "9", + "sentence_range": "367-370", + "Text": "The rays are incident from a medium of refractive\nindex n1, to another of refractive index n 2 As before, we take the aperture\n(or the lateral size) of the surface to be small compared to other distances\ninvolved, so that small angle approximation can be made In particular,\nNM will be taken to be nearly equal to the length of the perpendicular\nfrom the point N on the principal axis We have, for small angles,\ntan \u00d0NOM = MN\nOM\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "368-371", + "Text": "As before, we take the aperture\n(or the lateral size) of the surface to be small compared to other distances\ninvolved, so that small angle approximation can be made In particular,\nNM will be taken to be nearly equal to the length of the perpendicular\nfrom the point N on the principal axis We have, for small angles,\ntan \u00d0NOM = MN\nOM\nFIGURE 9 14 Light undergoes successive total\ninternal reflections as it moves through an\noptical fibre" + }, + { + "Chapter": "9", + "sentence_range": "369-372", + "Text": "In particular,\nNM will be taken to be nearly equal to the length of the perpendicular\nfrom the point N on the principal axis We have, for small angles,\ntan \u00d0NOM = MN\nOM\nFIGURE 9 14 Light undergoes successive total\ninternal reflections as it moves through an\noptical fibre Rationalised 2023-24\nRay Optics and\nOptical Instruments\n233\n EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "370-373", + "Text": "We have, for small angles,\ntan \u00d0NOM = MN\nOM\nFIGURE 9 14 Light undergoes successive total\ninternal reflections as it moves through an\noptical fibre Rationalised 2023-24\nRay Optics and\nOptical Instruments\n233\n EXAMPLE 9 5\ntan \u00d0NCM = MN\nMC\ntan \u00d0NIM = MN\nMI\nNow, for DNOC, i is the exterior angle" + }, + { + "Chapter": "9", + "sentence_range": "371-374", + "Text": "14 Light undergoes successive total\ninternal reflections as it moves through an\noptical fibre Rationalised 2023-24\nRay Optics and\nOptical Instruments\n233\n EXAMPLE 9 5\ntan \u00d0NCM = MN\nMC\ntan \u00d0NIM = MN\nMI\nNow, for DNOC, i is the exterior angle Therefore, i\n= \u00d0NOM + \u00d0NCM\ni = MN\nMN\nOM\n+MC\n(9" + }, + { + "Chapter": "9", + "sentence_range": "372-375", + "Text": "Rationalised 2023-24\nRay Optics and\nOptical Instruments\n233\n EXAMPLE 9 5\ntan \u00d0NCM = MN\nMC\ntan \u00d0NIM = MN\nMI\nNow, for DNOC, i is the exterior angle Therefore, i\n= \u00d0NOM + \u00d0NCM\ni = MN\nMN\nOM\n+MC\n(9 13)\nSimilarly,\nr = \u00d0NCM \u2013 \u00d0NIM\ni" + }, + { + "Chapter": "9", + "sentence_range": "373-376", + "Text": "5\ntan \u00d0NCM = MN\nMC\ntan \u00d0NIM = MN\nMI\nNow, for DNOC, i is the exterior angle Therefore, i\n= \u00d0NOM + \u00d0NCM\ni = MN\nMN\nOM\n+MC\n(9 13)\nSimilarly,\nr = \u00d0NCM \u2013 \u00d0NIM\ni e" + }, + { + "Chapter": "9", + "sentence_range": "374-377", + "Text": "Therefore, i\n= \u00d0NOM + \u00d0NCM\ni = MN\nMN\nOM\n+MC\n(9 13)\nSimilarly,\nr = \u00d0NCM \u2013 \u00d0NIM\ni e , r = MN\nMN\nMC\nMI\n\u2212\n(9" + }, + { + "Chapter": "9", + "sentence_range": "375-378", + "Text": "13)\nSimilarly,\nr = \u00d0NCM \u2013 \u00d0NIM\ni e , r = MN\nMN\nMC\nMI\n\u2212\n(9 14)\nNow, by Snell\u2019s law\nn1 sin i = n 2 sin r\nor for small angles\nn1i = n 2r\nSubstituting i and r from Eqs" + }, + { + "Chapter": "9", + "sentence_range": "376-379", + "Text": "e , r = MN\nMN\nMC\nMI\n\u2212\n(9 14)\nNow, by Snell\u2019s law\nn1 sin i = n 2 sin r\nor for small angles\nn1i = n 2r\nSubstituting i and r from Eqs (9" + }, + { + "Chapter": "9", + "sentence_range": "377-380", + "Text": ", r = MN\nMN\nMC\nMI\n\u2212\n(9 14)\nNow, by Snell\u2019s law\nn1 sin i = n 2 sin r\nor for small angles\nn1i = n 2r\nSubstituting i and r from Eqs (9 13) and (9" + }, + { + "Chapter": "9", + "sentence_range": "378-381", + "Text": "14)\nNow, by Snell\u2019s law\nn1 sin i = n 2 sin r\nor for small angles\nn1i = n 2r\nSubstituting i and r from Eqs (9 13) and (9 14), we get\n1\n2\n2\n1\nOM\nMI\nMC\nn\nn\nn\nn\n\u2212\n+\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "379-382", + "Text": "(9 13) and (9 14), we get\n1\n2\n2\n1\nOM\nMI\nMC\nn\nn\nn\nn\n\u2212\n+\n=\n(9 15)\nHere, OM, MI and MC represent magnitudes of distances" + }, + { + "Chapter": "9", + "sentence_range": "380-383", + "Text": "13) and (9 14), we get\n1\n2\n2\n1\nOM\nMI\nMC\nn\nn\nn\nn\n\u2212\n+\n=\n(9 15)\nHere, OM, MI and MC represent magnitudes of distances Applying the\nCartesian sign convention,\nOM = \u2013u, MI = +v, MC = +R\nSubstituting these in Eq" + }, + { + "Chapter": "9", + "sentence_range": "381-384", + "Text": "14), we get\n1\n2\n2\n1\nOM\nMI\nMC\nn\nn\nn\nn\n\u2212\n+\n=\n(9 15)\nHere, OM, MI and MC represent magnitudes of distances Applying the\nCartesian sign convention,\nOM = \u2013u, MI = +v, MC = +R\nSubstituting these in Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "382-385", + "Text": "15)\nHere, OM, MI and MC represent magnitudes of distances Applying the\nCartesian sign convention,\nOM = \u2013u, MI = +v, MC = +R\nSubstituting these in Eq (9 15), we get\n2\n1\n2\n1\nn\nn\nn\nn\nv\nu\n\u2212R\n\u2212\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "383-386", + "Text": "Applying the\nCartesian sign convention,\nOM = \u2013u, MI = +v, MC = +R\nSubstituting these in Eq (9 15), we get\n2\n1\n2\n1\nn\nn\nn\nn\nv\nu\n\u2212R\n\u2212\n=\n(9 16)\nEquation (9" + }, + { + "Chapter": "9", + "sentence_range": "384-387", + "Text": "(9 15), we get\n2\n1\n2\n1\nn\nn\nn\nn\nv\nu\n\u2212R\n\u2212\n=\n(9 16)\nEquation (9 16) gives us a relation between object and image distance\nin terms of refractive index of the medium and the radius of\ncurvature of the curved spherical surface" + }, + { + "Chapter": "9", + "sentence_range": "385-388", + "Text": "15), we get\n2\n1\n2\n1\nn\nn\nn\nn\nv\nu\n\u2212R\n\u2212\n=\n(9 16)\nEquation (9 16) gives us a relation between object and image distance\nin terms of refractive index of the medium and the radius of\ncurvature of the curved spherical surface It holds for any curved\nspherical surface" + }, + { + "Chapter": "9", + "sentence_range": "386-389", + "Text": "16)\nEquation (9 16) gives us a relation between object and image distance\nin terms of refractive index of the medium and the radius of\ncurvature of the curved spherical surface It holds for any curved\nspherical surface Example 9" + }, + { + "Chapter": "9", + "sentence_range": "387-390", + "Text": "16) gives us a relation between object and image distance\nin terms of refractive index of the medium and the radius of\ncurvature of the curved spherical surface It holds for any curved\nspherical surface Example 9 5 Light from a point source in air falls on a spherical\nglass surface (n = 1" + }, + { + "Chapter": "9", + "sentence_range": "388-391", + "Text": "It holds for any curved\nspherical surface Example 9 5 Light from a point source in air falls on a spherical\nglass surface (n = 1 5 and radius of curvature = 20 cm)" + }, + { + "Chapter": "9", + "sentence_range": "389-392", + "Text": "Example 9 5 Light from a point source in air falls on a spherical\nglass surface (n = 1 5 and radius of curvature = 20 cm) The distance\nof the light source from the glass surface is 100 cm" + }, + { + "Chapter": "9", + "sentence_range": "390-393", + "Text": "5 Light from a point source in air falls on a spherical\nglass surface (n = 1 5 and radius of curvature = 20 cm) The distance\nof the light source from the glass surface is 100 cm At what position\nthe image is formed" + }, + { + "Chapter": "9", + "sentence_range": "391-394", + "Text": "5 and radius of curvature = 20 cm) The distance\nof the light source from the glass surface is 100 cm At what position\nthe image is formed Solution\nWe use the relation given by Eq" + }, + { + "Chapter": "9", + "sentence_range": "392-395", + "Text": "The distance\nof the light source from the glass surface is 100 cm At what position\nthe image is formed Solution\nWe use the relation given by Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "393-396", + "Text": "At what position\nthe image is formed Solution\nWe use the relation given by Eq (9 16)" + }, + { + "Chapter": "9", + "sentence_range": "394-397", + "Text": "Solution\nWe use the relation given by Eq (9 16) Here\nu = \u2013 100 cm, v =" + }, + { + "Chapter": "9", + "sentence_range": "395-398", + "Text": "(9 16) Here\nu = \u2013 100 cm, v = , R = + 20 cm, n1 = 1, and n2 = 1" + }, + { + "Chapter": "9", + "sentence_range": "396-399", + "Text": "16) Here\nu = \u2013 100 cm, v = , R = + 20 cm, n1 = 1, and n2 = 1 5" + }, + { + "Chapter": "9", + "sentence_range": "397-400", + "Text": "Here\nu = \u2013 100 cm, v = , R = + 20 cm, n1 = 1, and n2 = 1 5 We then have\n1" + }, + { + "Chapter": "9", + "sentence_range": "398-401", + "Text": ", R = + 20 cm, n1 = 1, and n2 = 1 5 We then have\n1 5\n1\n0" + }, + { + "Chapter": "9", + "sentence_range": "399-402", + "Text": "5 We then have\n1 5\n1\n0 5\n100\n20\nv +\n=\nor v = +100 cm\nThe image is formed at a distance of 100 cm from the glass surface,\nin the direction of incident light" + }, + { + "Chapter": "9", + "sentence_range": "400-403", + "Text": "We then have\n1 5\n1\n0 5\n100\n20\nv +\n=\nor v = +100 cm\nThe image is formed at a distance of 100 cm from the glass surface,\nin the direction of incident light FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "401-404", + "Text": "5\n1\n0 5\n100\n20\nv +\n=\nor v = +100 cm\nThe image is formed at a distance of 100 cm from the glass surface,\nin the direction of incident light FIGURE 9 15 Refraction at a spherical\nsurface separating two media" + }, + { + "Chapter": "9", + "sentence_range": "402-405", + "Text": "5\n100\n20\nv +\n=\nor v = +100 cm\nThe image is formed at a distance of 100 cm from the glass surface,\nin the direction of incident light FIGURE 9 15 Refraction at a spherical\nsurface separating two media Rationalised 2023-24\nPhysics\n234\n9" + }, + { + "Chapter": "9", + "sentence_range": "403-406", + "Text": "FIGURE 9 15 Refraction at a spherical\nsurface separating two media Rationalised 2023-24\nPhysics\n234\n9 5" + }, + { + "Chapter": "9", + "sentence_range": "404-407", + "Text": "15 Refraction at a spherical\nsurface separating two media Rationalised 2023-24\nPhysics\n234\n9 5 2 Refraction by a lens\nFigure 9" + }, + { + "Chapter": "9", + "sentence_range": "405-408", + "Text": "Rationalised 2023-24\nPhysics\n234\n9 5 2 Refraction by a lens\nFigure 9 16(a) shows the geometry of image formation by a double convex\nlens" + }, + { + "Chapter": "9", + "sentence_range": "406-409", + "Text": "5 2 Refraction by a lens\nFigure 9 16(a) shows the geometry of image formation by a double convex\nlens The image formation can be seen in terms of two steps:\n(i) The first refracting surface forms the image I1 of the object O\n[Fig" + }, + { + "Chapter": "9", + "sentence_range": "407-410", + "Text": "2 Refraction by a lens\nFigure 9 16(a) shows the geometry of image formation by a double convex\nlens The image formation can be seen in terms of two steps:\n(i) The first refracting surface forms the image I1 of the object O\n[Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "408-411", + "Text": "16(a) shows the geometry of image formation by a double convex\nlens The image formation can be seen in terms of two steps:\n(i) The first refracting surface forms the image I1 of the object O\n[Fig 9 16(b)]" + }, + { + "Chapter": "9", + "sentence_range": "409-412", + "Text": "The image formation can be seen in terms of two steps:\n(i) The first refracting surface forms the image I1 of the object O\n[Fig 9 16(b)] The image I1 acts as a virtual object for the second surface\nthat forms the image at I [Fig" + }, + { + "Chapter": "9", + "sentence_range": "410-413", + "Text": "9 16(b)] The image I1 acts as a virtual object for the second surface\nthat forms the image at I [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "411-414", + "Text": "16(b)] The image I1 acts as a virtual object for the second surface\nthat forms the image at I [Fig 9 16(c)]" + }, + { + "Chapter": "9", + "sentence_range": "412-415", + "Text": "The image I1 acts as a virtual object for the second surface\nthat forms the image at I [Fig 9 16(c)] Applying Eq" + }, + { + "Chapter": "9", + "sentence_range": "413-416", + "Text": "9 16(c)] Applying Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "414-417", + "Text": "16(c)] Applying Eq (9 15) to the first\ninterface ABC, we get\n1\n2\n2\n1\n1\n1\nOB\nBI\nBC\nn\nn\nn\n\u2212n\n+\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "415-418", + "Text": "Applying Eq (9 15) to the first\ninterface ABC, we get\n1\n2\n2\n1\n1\n1\nOB\nBI\nBC\nn\nn\nn\n\u2212n\n+\n=\n(9 17)\nA similar procedure applied to the second\ninterface* ADC gives,\n2\n1\n2\n1\n1\n2\nDI\nDI\nDC\nn\nn\nn\n\u2212n\n\u2212\n+\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "416-419", + "Text": "(9 15) to the first\ninterface ABC, we get\n1\n2\n2\n1\n1\n1\nOB\nBI\nBC\nn\nn\nn\n\u2212n\n+\n=\n(9 17)\nA similar procedure applied to the second\ninterface* ADC gives,\n2\n1\n2\n1\n1\n2\nDI\nDI\nDC\nn\nn\nn\n\u2212n\n\u2212\n+\n=\n(9 18)\nFor a thin lens, BI1 = DI1" + }, + { + "Chapter": "9", + "sentence_range": "417-420", + "Text": "15) to the first\ninterface ABC, we get\n1\n2\n2\n1\n1\n1\nOB\nBI\nBC\nn\nn\nn\n\u2212n\n+\n=\n(9 17)\nA similar procedure applied to the second\ninterface* ADC gives,\n2\n1\n2\n1\n1\n2\nDI\nDI\nDC\nn\nn\nn\n\u2212n\n\u2212\n+\n=\n(9 18)\nFor a thin lens, BI1 = DI1 Adding\nEqs" + }, + { + "Chapter": "9", + "sentence_range": "418-421", + "Text": "17)\nA similar procedure applied to the second\ninterface* ADC gives,\n2\n1\n2\n1\n1\n2\nDI\nDI\nDC\nn\nn\nn\n\u2212n\n\u2212\n+\n=\n(9 18)\nFor a thin lens, BI1 = DI1 Adding\nEqs (9" + }, + { + "Chapter": "9", + "sentence_range": "419-422", + "Text": "18)\nFor a thin lens, BI1 = DI1 Adding\nEqs (9 17) and (9" + }, + { + "Chapter": "9", + "sentence_range": "420-423", + "Text": "Adding\nEqs (9 17) and (9 18), we get\nn\nn\nn\nn\n1\n1\n2\n1\n1\n1\nOB\nDI\nBC\nDC\n1\n2\n+\n=\n\u2212\n+\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n(\n)\n(9" + }, + { + "Chapter": "9", + "sentence_range": "421-424", + "Text": "(9 17) and (9 18), we get\nn\nn\nn\nn\n1\n1\n2\n1\n1\n1\nOB\nDI\nBC\nDC\n1\n2\n+\n=\n\u2212\n+\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n(\n)\n(9 19)\nSuppose the object is at infinity, i" + }, + { + "Chapter": "9", + "sentence_range": "422-425", + "Text": "17) and (9 18), we get\nn\nn\nn\nn\n1\n1\n2\n1\n1\n1\nOB\nDI\nBC\nDC\n1\n2\n+\n=\n\u2212\n+\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n(\n)\n(9 19)\nSuppose the object is at infinity, i e" + }, + { + "Chapter": "9", + "sentence_range": "423-426", + "Text": "18), we get\nn\nn\nn\nn\n1\n1\n2\n1\n1\n1\nOB\nDI\nBC\nDC\n1\n2\n+\n=\n\u2212\n+\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n(\n)\n(9 19)\nSuppose the object is at infinity, i e ,\nOB \u00ae \u00a5 and DI = f, Eq" + }, + { + "Chapter": "9", + "sentence_range": "424-427", + "Text": "19)\nSuppose the object is at infinity, i e ,\nOB \u00ae \u00a5 and DI = f, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "425-428", + "Text": "e ,\nOB \u00ae \u00a5 and DI = f, Eq (9 19) gives\nfn\nn\nn\n1\n2\n1\n1\n1\n=\n\u2212\n+\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n(\n)\nBC\nDC\n1\n2\n(9" + }, + { + "Chapter": "9", + "sentence_range": "426-429", + "Text": ",\nOB \u00ae \u00a5 and DI = f, Eq (9 19) gives\nfn\nn\nn\n1\n2\n1\n1\n1\n=\n\u2212\n+\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n(\n)\nBC\nDC\n1\n2\n(9 20)\nThe point where image of an object\nplaced at infinity is formed is called the\nfocus F, of the lens and the distance f gives\nits focal length" + }, + { + "Chapter": "9", + "sentence_range": "427-430", + "Text": "(9 19) gives\nfn\nn\nn\n1\n2\n1\n1\n1\n=\n\u2212\n+\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n(\n)\nBC\nDC\n1\n2\n(9 20)\nThe point where image of an object\nplaced at infinity is formed is called the\nfocus F, of the lens and the distance f gives\nits focal length A lens has two foci, F and\nF\u00a2, on either side of it (Fig" + }, + { + "Chapter": "9", + "sentence_range": "428-431", + "Text": "19) gives\nfn\nn\nn\n1\n2\n1\n1\n1\n=\n\u2212\n+\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n(\n)\nBC\nDC\n1\n2\n(9 20)\nThe point where image of an object\nplaced at infinity is formed is called the\nfocus F, of the lens and the distance f gives\nits focal length A lens has two foci, F and\nF\u00a2, on either side of it (Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "429-432", + "Text": "20)\nThe point where image of an object\nplaced at infinity is formed is called the\nfocus F, of the lens and the distance f gives\nits focal length A lens has two foci, F and\nF\u00a2, on either side of it (Fig 9 16)" + }, + { + "Chapter": "9", + "sentence_range": "430-433", + "Text": "A lens has two foci, F and\nF\u00a2, on either side of it (Fig 9 16) By the\nsign convention,\nBC1 = + R1,\nDC2 = \u2013R2\nSo Eq" + }, + { + "Chapter": "9", + "sentence_range": "431-434", + "Text": "9 16) By the\nsign convention,\nBC1 = + R1,\nDC2 = \u2013R2\nSo Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "432-435", + "Text": "16) By the\nsign convention,\nBC1 = + R1,\nDC2 = \u2013R2\nSo Eq (9 20) can be written as\n(9" + }, + { + "Chapter": "9", + "sentence_range": "433-436", + "Text": "By the\nsign convention,\nBC1 = + R1,\nDC2 = \u2013R2\nSo Eq (9 20) can be written as\n(9 21)\nEquation (9" + }, + { + "Chapter": "9", + "sentence_range": "434-437", + "Text": "(9 20) can be written as\n(9 21)\nEquation (9 21) is known as the lens\nmaker\u2019s formula" + }, + { + "Chapter": "9", + "sentence_range": "435-438", + "Text": "20) can be written as\n(9 21)\nEquation (9 21) is known as the lens\nmaker\u2019s formula It is useful to design\nlenses of desired focal length using surfaces\nof suitable radii of curvature" + }, + { + "Chapter": "9", + "sentence_range": "436-439", + "Text": "21)\nEquation (9 21) is known as the lens\nmaker\u2019s formula It is useful to design\nlenses of desired focal length using surfaces\nof suitable radii of curvature Note that the\nformula is true for a concave lens also" + }, + { + "Chapter": "9", + "sentence_range": "437-440", + "Text": "21) is known as the lens\nmaker\u2019s formula It is useful to design\nlenses of desired focal length using surfaces\nof suitable radii of curvature Note that the\nformula is true for a concave lens also In\nthat case R1is negative, R 2 positive and\ntherefore, f is negative" + }, + { + "Chapter": "9", + "sentence_range": "438-441", + "Text": "It is useful to design\nlenses of desired focal length using surfaces\nof suitable radii of curvature Note that the\nformula is true for a concave lens also In\nthat case R1is negative, R 2 positive and\ntherefore, f is negative FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "439-442", + "Text": "Note that the\nformula is true for a concave lens also In\nthat case R1is negative, R 2 positive and\ntherefore, f is negative FIGURE 9 16 (a) The position of object, and the\nimage formed by a double convex lens,\n(b) Refraction at the first spherical surface and\n(c) Refraction at the second spherical surface" + }, + { + "Chapter": "9", + "sentence_range": "440-443", + "Text": "In\nthat case R1is negative, R 2 positive and\ntherefore, f is negative FIGURE 9 16 (a) The position of object, and the\nimage formed by a double convex lens,\n(b) Refraction at the first spherical surface and\n(c) Refraction at the second spherical surface *\nNote that now the refractive index of the medium on the right side of ADC is n1\nwhile on its left it is n2" + }, + { + "Chapter": "9", + "sentence_range": "441-444", + "Text": "FIGURE 9 16 (a) The position of object, and the\nimage formed by a double convex lens,\n(b) Refraction at the first spherical surface and\n(c) Refraction at the second spherical surface *\nNote that now the refractive index of the medium on the right side of ADC is n1\nwhile on its left it is n2 Further DI1 is negative as the distance is measured\nagainst the direction of incident light" + }, + { + "Chapter": "9", + "sentence_range": "442-445", + "Text": "16 (a) The position of object, and the\nimage formed by a double convex lens,\n(b) Refraction at the first spherical surface and\n(c) Refraction at the second spherical surface *\nNote that now the refractive index of the medium on the right side of ADC is n1\nwhile on its left it is n2 Further DI1 is negative as the distance is measured\nagainst the direction of incident light Rationalised 2023-24\nRay Optics and\nOptical Instruments\n235\nFrom Eqs" + }, + { + "Chapter": "9", + "sentence_range": "443-446", + "Text": "*\nNote that now the refractive index of the medium on the right side of ADC is n1\nwhile on its left it is n2 Further DI1 is negative as the distance is measured\nagainst the direction of incident light Rationalised 2023-24\nRay Optics and\nOptical Instruments\n235\nFrom Eqs (9" + }, + { + "Chapter": "9", + "sentence_range": "444-447", + "Text": "Further DI1 is negative as the distance is measured\nagainst the direction of incident light Rationalised 2023-24\nRay Optics and\nOptical Instruments\n235\nFrom Eqs (9 19) and (9" + }, + { + "Chapter": "9", + "sentence_range": "445-448", + "Text": "Rationalised 2023-24\nRay Optics and\nOptical Instruments\n235\nFrom Eqs (9 19) and (9 20), we get\n1\n1\n1\nOB\nDI\nn\nn\nfn\n+\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "446-449", + "Text": "(9 19) and (9 20), we get\n1\n1\n1\nOB\nDI\nn\nn\nfn\n+\n=\n(9 22)\nAgain, in the thin lens approximation, B and D are both close to the\noptical centre of the lens" + }, + { + "Chapter": "9", + "sentence_range": "447-450", + "Text": "19) and (9 20), we get\n1\n1\n1\nOB\nDI\nn\nn\nfn\n+\n=\n(9 22)\nAgain, in the thin lens approximation, B and D are both close to the\noptical centre of the lens Applying the sign convention,\nBO = \u2013 u, DI = +v, we get\n1\n1\n1\nv\nu\nf\n\u2212\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "448-451", + "Text": "20), we get\n1\n1\n1\nOB\nDI\nn\nn\nfn\n+\n=\n(9 22)\nAgain, in the thin lens approximation, B and D are both close to the\noptical centre of the lens Applying the sign convention,\nBO = \u2013 u, DI = +v, we get\n1\n1\n1\nv\nu\nf\n\u2212\n=\n(9 23)\nEquation (9" + }, + { + "Chapter": "9", + "sentence_range": "449-452", + "Text": "22)\nAgain, in the thin lens approximation, B and D are both close to the\noptical centre of the lens Applying the sign convention,\nBO = \u2013 u, DI = +v, we get\n1\n1\n1\nv\nu\nf\n\u2212\n=\n(9 23)\nEquation (9 23) is the familiar thin lens formula" + }, + { + "Chapter": "9", + "sentence_range": "450-453", + "Text": "Applying the sign convention,\nBO = \u2013 u, DI = +v, we get\n1\n1\n1\nv\nu\nf\n\u2212\n=\n(9 23)\nEquation (9 23) is the familiar thin lens formula Though we derived\nit for a real image formed by a convex lens, the formula is valid for both\nconvex as well as concave lenses and for both real and virtual images" + }, + { + "Chapter": "9", + "sentence_range": "451-454", + "Text": "23)\nEquation (9 23) is the familiar thin lens formula Though we derived\nit for a real image formed by a convex lens, the formula is valid for both\nconvex as well as concave lenses and for both real and virtual images It is worth mentioning that the two foci, F and F\u00a2, of a double convex\nor concave lens are equidistant from the optical centre" + }, + { + "Chapter": "9", + "sentence_range": "452-455", + "Text": "23) is the familiar thin lens formula Though we derived\nit for a real image formed by a convex lens, the formula is valid for both\nconvex as well as concave lenses and for both real and virtual images It is worth mentioning that the two foci, F and F\u00a2, of a double convex\nor concave lens are equidistant from the optical centre The focus on the\nside of the (original) source of light is called the first focal point, whereas\nthe other is called the second focal point" + }, + { + "Chapter": "9", + "sentence_range": "453-456", + "Text": "Though we derived\nit for a real image formed by a convex lens, the formula is valid for both\nconvex as well as concave lenses and for both real and virtual images It is worth mentioning that the two foci, F and F\u00a2, of a double convex\nor concave lens are equidistant from the optical centre The focus on the\nside of the (original) source of light is called the first focal point, whereas\nthe other is called the second focal point To find the image of an object by a lens, we can, in principle, take any\ntwo rays emanating from a point on an object; trace their paths using the\nlaws of refraction and find the point where the refracted rays meet (or\nappear to meet)" + }, + { + "Chapter": "9", + "sentence_range": "454-457", + "Text": "It is worth mentioning that the two foci, F and F\u00a2, of a double convex\nor concave lens are equidistant from the optical centre The focus on the\nside of the (original) source of light is called the first focal point, whereas\nthe other is called the second focal point To find the image of an object by a lens, we can, in principle, take any\ntwo rays emanating from a point on an object; trace their paths using the\nlaws of refraction and find the point where the refracted rays meet (or\nappear to meet) In practice, however, it is convenient to choose any two\nof the following rays:\n(i)\nA ray emanating from the object parallel to the principal axis of the\nlens after refraction passes through the second principal focus F\u00a2 (in\na convex lens) or appears to diverge (in a concave lens) from the first\nprincipal focus F" + }, + { + "Chapter": "9", + "sentence_range": "455-458", + "Text": "The focus on the\nside of the (original) source of light is called the first focal point, whereas\nthe other is called the second focal point To find the image of an object by a lens, we can, in principle, take any\ntwo rays emanating from a point on an object; trace their paths using the\nlaws of refraction and find the point where the refracted rays meet (or\nappear to meet) In practice, however, it is convenient to choose any two\nof the following rays:\n(i)\nA ray emanating from the object parallel to the principal axis of the\nlens after refraction passes through the second principal focus F\u00a2 (in\na convex lens) or appears to diverge (in a concave lens) from the first\nprincipal focus F (ii) A ray of light, passing through the optical\ncentre of the lens, emerges without any\ndeviation after refraction" + }, + { + "Chapter": "9", + "sentence_range": "456-459", + "Text": "To find the image of an object by a lens, we can, in principle, take any\ntwo rays emanating from a point on an object; trace their paths using the\nlaws of refraction and find the point where the refracted rays meet (or\nappear to meet) In practice, however, it is convenient to choose any two\nof the following rays:\n(i)\nA ray emanating from the object parallel to the principal axis of the\nlens after refraction passes through the second principal focus F\u00a2 (in\na convex lens) or appears to diverge (in a concave lens) from the first\nprincipal focus F (ii) A ray of light, passing through the optical\ncentre of the lens, emerges without any\ndeviation after refraction (iii) (a) A ray of light passing through the first\nprincipal focus of a convex lens [Fig" + }, + { + "Chapter": "9", + "sentence_range": "457-460", + "Text": "In practice, however, it is convenient to choose any two\nof the following rays:\n(i)\nA ray emanating from the object parallel to the principal axis of the\nlens after refraction passes through the second principal focus F\u00a2 (in\na convex lens) or appears to diverge (in a concave lens) from the first\nprincipal focus F (ii) A ray of light, passing through the optical\ncentre of the lens, emerges without any\ndeviation after refraction (iii) (a) A ray of light passing through the first\nprincipal focus of a convex lens [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "458-461", + "Text": "(ii) A ray of light, passing through the optical\ncentre of the lens, emerges without any\ndeviation after refraction (iii) (a) A ray of light passing through the first\nprincipal focus of a convex lens [Fig 9 17(a)]\nemerges parallel to the principal axis after\nrefraction" + }, + { + "Chapter": "9", + "sentence_range": "459-462", + "Text": "(iii) (a) A ray of light passing through the first\nprincipal focus of a convex lens [Fig 9 17(a)]\nemerges parallel to the principal axis after\nrefraction (b) A ray of light incident on a concave lens\nappearing to meet the principal axis at\nsecond focus point emerges parallel to the\nprincipal axis after refraction [Fig" + }, + { + "Chapter": "9", + "sentence_range": "460-463", + "Text": "9 17(a)]\nemerges parallel to the principal axis after\nrefraction (b) A ray of light incident on a concave lens\nappearing to meet the principal axis at\nsecond focus point emerges parallel to the\nprincipal axis after refraction [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "461-464", + "Text": "17(a)]\nemerges parallel to the principal axis after\nrefraction (b) A ray of light incident on a concave lens\nappearing to meet the principal axis at\nsecond focus point emerges parallel to the\nprincipal axis after refraction [Fig 9 17(b)]" + }, + { + "Chapter": "9", + "sentence_range": "462-465", + "Text": "(b) A ray of light incident on a concave lens\nappearing to meet the principal axis at\nsecond focus point emerges parallel to the\nprincipal axis after refraction [Fig 9 17(b)] Figures 9" + }, + { + "Chapter": "9", + "sentence_range": "463-466", + "Text": "9 17(b)] Figures 9 17(a) and (b) illustrate these rules\nfor a convex and a concave lens, respectively" + }, + { + "Chapter": "9", + "sentence_range": "464-467", + "Text": "17(b)] Figures 9 17(a) and (b) illustrate these rules\nfor a convex and a concave lens, respectively You should practice drawing similar ray\ndiagrams for different positions of the object with\nrespect to the lens and also verify that the lens\nformula, Eq" + }, + { + "Chapter": "9", + "sentence_range": "465-468", + "Text": "Figures 9 17(a) and (b) illustrate these rules\nfor a convex and a concave lens, respectively You should practice drawing similar ray\ndiagrams for different positions of the object with\nrespect to the lens and also verify that the lens\nformula, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "466-469", + "Text": "17(a) and (b) illustrate these rules\nfor a convex and a concave lens, respectively You should practice drawing similar ray\ndiagrams for different positions of the object with\nrespect to the lens and also verify that the lens\nformula, Eq (9 23), holds good for all cases" + }, + { + "Chapter": "9", + "sentence_range": "467-470", + "Text": "You should practice drawing similar ray\ndiagrams for different positions of the object with\nrespect to the lens and also verify that the lens\nformula, Eq (9 23), holds good for all cases Here again it must be remembered that each\npoint on an object gives out infinite number of\nrays" + }, + { + "Chapter": "9", + "sentence_range": "468-471", + "Text": "(9 23), holds good for all cases Here again it must be remembered that each\npoint on an object gives out infinite number of\nrays All these rays will pass through the same\nimage point after refraction at the lens" + }, + { + "Chapter": "9", + "sentence_range": "469-472", + "Text": "23), holds good for all cases Here again it must be remembered that each\npoint on an object gives out infinite number of\nrays All these rays will pass through the same\nimage point after refraction at the lens Magnification (m) produced by a lens is\ndefined, like that for a mirror, as the ratio of the\nsize of the image to that of the object" + }, + { + "Chapter": "9", + "sentence_range": "470-473", + "Text": "Here again it must be remembered that each\npoint on an object gives out infinite number of\nrays All these rays will pass through the same\nimage point after refraction at the lens Magnification (m) produced by a lens is\ndefined, like that for a mirror, as the ratio of the\nsize of the image to that of the object Proceeding\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "471-474", + "Text": "All these rays will pass through the same\nimage point after refraction at the lens Magnification (m) produced by a lens is\ndefined, like that for a mirror, as the ratio of the\nsize of the image to that of the object Proceeding\nFIGURE 9 17 Tracing rays through (a)\nconvex lens (b) concave lens" + }, + { + "Chapter": "9", + "sentence_range": "472-475", + "Text": "Magnification (m) produced by a lens is\ndefined, like that for a mirror, as the ratio of the\nsize of the image to that of the object Proceeding\nFIGURE 9 17 Tracing rays through (a)\nconvex lens (b) concave lens Rationalised 2023-24\nPhysics\n236\n EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "473-476", + "Text": "Proceeding\nFIGURE 9 17 Tracing rays through (a)\nconvex lens (b) concave lens Rationalised 2023-24\nPhysics\n236\n EXAMPLE 9 6\nin the same way as for spherical mirrors, it is easily seen that\nfor a lens\nm = \nh\nh\n\u2032 = \nuv\n(9" + }, + { + "Chapter": "9", + "sentence_range": "474-477", + "Text": "17 Tracing rays through (a)\nconvex lens (b) concave lens Rationalised 2023-24\nPhysics\n236\n EXAMPLE 9 6\nin the same way as for spherical mirrors, it is easily seen that\nfor a lens\nm = \nh\nh\n\u2032 = \nuv\n(9 24)\nWhen we apply the sign convention, we see that, for erect (and virtual)\nimage formed by a convex or concave lens, m is positive, while for an\ninverted (and real) image, m is negative" + }, + { + "Chapter": "9", + "sentence_range": "475-478", + "Text": "Rationalised 2023-24\nPhysics\n236\n EXAMPLE 9 6\nin the same way as for spherical mirrors, it is easily seen that\nfor a lens\nm = \nh\nh\n\u2032 = \nuv\n(9 24)\nWhen we apply the sign convention, we see that, for erect (and virtual)\nimage formed by a convex or concave lens, m is positive, while for an\ninverted (and real) image, m is negative Example 9" + }, + { + "Chapter": "9", + "sentence_range": "476-479", + "Text": "6\nin the same way as for spherical mirrors, it is easily seen that\nfor a lens\nm = \nh\nh\n\u2032 = \nuv\n(9 24)\nWhen we apply the sign convention, we see that, for erect (and virtual)\nimage formed by a convex or concave lens, m is positive, while for an\ninverted (and real) image, m is negative Example 9 6 A magician during a show makes a glass lens with\nn = 1" + }, + { + "Chapter": "9", + "sentence_range": "477-480", + "Text": "24)\nWhen we apply the sign convention, we see that, for erect (and virtual)\nimage formed by a convex or concave lens, m is positive, while for an\ninverted (and real) image, m is negative Example 9 6 A magician during a show makes a glass lens with\nn = 1 47 disappear in a trough of liquid" + }, + { + "Chapter": "9", + "sentence_range": "478-481", + "Text": "Example 9 6 A magician during a show makes a glass lens with\nn = 1 47 disappear in a trough of liquid What is the refractive index\nof the liquid" + }, + { + "Chapter": "9", + "sentence_range": "479-482", + "Text": "6 A magician during a show makes a glass lens with\nn = 1 47 disappear in a trough of liquid What is the refractive index\nof the liquid Could the liquid be water" + }, + { + "Chapter": "9", + "sentence_range": "480-483", + "Text": "47 disappear in a trough of liquid What is the refractive index\nof the liquid Could the liquid be water Solution\nThe refractive index of the liquid must be equal to 1" + }, + { + "Chapter": "9", + "sentence_range": "481-484", + "Text": "What is the refractive index\nof the liquid Could the liquid be water Solution\nThe refractive index of the liquid must be equal to 1 47 in order to\nmake the lens disappear" + }, + { + "Chapter": "9", + "sentence_range": "482-485", + "Text": "Could the liquid be water Solution\nThe refractive index of the liquid must be equal to 1 47 in order to\nmake the lens disappear This means n1 = n2" + }, + { + "Chapter": "9", + "sentence_range": "483-486", + "Text": "Solution\nThe refractive index of the liquid must be equal to 1 47 in order to\nmake the lens disappear This means n1 = n2 This gives 1/f =0 or\nf \u00ae \u00a5" + }, + { + "Chapter": "9", + "sentence_range": "484-487", + "Text": "47 in order to\nmake the lens disappear This means n1 = n2 This gives 1/f =0 or\nf \u00ae \u00a5 The lens in the liquid will act like a plane sheet of glass" + }, + { + "Chapter": "9", + "sentence_range": "485-488", + "Text": "This means n1 = n2 This gives 1/f =0 or\nf \u00ae \u00a5 The lens in the liquid will act like a plane sheet of glass No,\nthe liquid is not water" + }, + { + "Chapter": "9", + "sentence_range": "486-489", + "Text": "This gives 1/f =0 or\nf \u00ae \u00a5 The lens in the liquid will act like a plane sheet of glass No,\nthe liquid is not water It could be glycerine" + }, + { + "Chapter": "9", + "sentence_range": "487-490", + "Text": "The lens in the liquid will act like a plane sheet of glass No,\nthe liquid is not water It could be glycerine FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "488-491", + "Text": "No,\nthe liquid is not water It could be glycerine FIGURE 9 18 Power of a lens" + }, + { + "Chapter": "9", + "sentence_range": "489-492", + "Text": "It could be glycerine FIGURE 9 18 Power of a lens 9" + }, + { + "Chapter": "9", + "sentence_range": "490-493", + "Text": "FIGURE 9 18 Power of a lens 9 5" + }, + { + "Chapter": "9", + "sentence_range": "491-494", + "Text": "18 Power of a lens 9 5 3 Power of a lens\nPower of a lens is a measure of the convergence or\ndivergence, which a lens introduces in the light falling on\nit" + }, + { + "Chapter": "9", + "sentence_range": "492-495", + "Text": "9 5 3 Power of a lens\nPower of a lens is a measure of the convergence or\ndivergence, which a lens introduces in the light falling on\nit Clearly, a lens of shorter focal length bends the incident\nlight more, while converging it in case of a convex lens\nand diverging it in case of a concave lens" + }, + { + "Chapter": "9", + "sentence_range": "493-496", + "Text": "5 3 Power of a lens\nPower of a lens is a measure of the convergence or\ndivergence, which a lens introduces in the light falling on\nit Clearly, a lens of shorter focal length bends the incident\nlight more, while converging it in case of a convex lens\nand diverging it in case of a concave lens The power P of\na lens is defined as the tangent of the angle by which it\nconverges or diverges a beam of light parallel to the\nprincipal axis falling at unit distance from the optical\ncentre (Fig" + }, + { + "Chapter": "9", + "sentence_range": "494-497", + "Text": "3 Power of a lens\nPower of a lens is a measure of the convergence or\ndivergence, which a lens introduces in the light falling on\nit Clearly, a lens of shorter focal length bends the incident\nlight more, while converging it in case of a convex lens\nand diverging it in case of a concave lens The power P of\na lens is defined as the tangent of the angle by which it\nconverges or diverges a beam of light parallel to the\nprincipal axis falling at unit distance from the optical\ncentre (Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "495-498", + "Text": "Clearly, a lens of shorter focal length bends the incident\nlight more, while converging it in case of a convex lens\nand diverging it in case of a concave lens The power P of\na lens is defined as the tangent of the angle by which it\nconverges or diverges a beam of light parallel to the\nprincipal axis falling at unit distance from the optical\ncentre (Fig 9 18)" + }, + { + "Chapter": "9", + "sentence_range": "496-499", + "Text": "The power P of\na lens is defined as the tangent of the angle by which it\nconverges or diverges a beam of light parallel to the\nprincipal axis falling at unit distance from the optical\ncentre (Fig 9 18) tan\n;\n,\ntan\n\u03b4\n\u03b4\n=\n=\n=\nfh\nh\nf\nif\n1\n1\n or \n\u03b4 =f1\n for small\nvalue of d" + }, + { + "Chapter": "9", + "sentence_range": "497-500", + "Text": "9 18) tan\n;\n,\ntan\n\u03b4\n\u03b4\n=\n=\n=\nfh\nh\nf\nif\n1\n1\n or \n\u03b4 =f1\n for small\nvalue of d Thus,\nP = \nf1\n(9" + }, + { + "Chapter": "9", + "sentence_range": "498-501", + "Text": "18) tan\n;\n,\ntan\n\u03b4\n\u03b4\n=\n=\n=\nfh\nh\nf\nif\n1\n1\n or \n\u03b4 =f1\n for small\nvalue of d Thus,\nP = \nf1\n(9 25)\nThe SI unit for power of a lens is dioptre (D): 1D = 1m\u20131" + }, + { + "Chapter": "9", + "sentence_range": "499-502", + "Text": "tan\n;\n,\ntan\n\u03b4\n\u03b4\n=\n=\n=\nfh\nh\nf\nif\n1\n1\n or \n\u03b4 =f1\n for small\nvalue of d Thus,\nP = \nf1\n(9 25)\nThe SI unit for power of a lens is dioptre (D): 1D = 1m\u20131 The power of\na lens of focal length of 1 metre is one dioptre" + }, + { + "Chapter": "9", + "sentence_range": "500-503", + "Text": "Thus,\nP = \nf1\n(9 25)\nThe SI unit for power of a lens is dioptre (D): 1D = 1m\u20131 The power of\na lens of focal length of 1 metre is one dioptre Power of a lens is positive\nfor a converging lens and negative for a diverging lens" + }, + { + "Chapter": "9", + "sentence_range": "501-504", + "Text": "25)\nThe SI unit for power of a lens is dioptre (D): 1D = 1m\u20131 The power of\na lens of focal length of 1 metre is one dioptre Power of a lens is positive\nfor a converging lens and negative for a diverging lens Thus, when an\noptician prescribes a corrective lens of power + 2" + }, + { + "Chapter": "9", + "sentence_range": "502-505", + "Text": "The power of\na lens of focal length of 1 metre is one dioptre Power of a lens is positive\nfor a converging lens and negative for a diverging lens Thus, when an\noptician prescribes a corrective lens of power + 2 5 D, the required lens is\na convex lens of focal length + 40 cm" + }, + { + "Chapter": "9", + "sentence_range": "503-506", + "Text": "Power of a lens is positive\nfor a converging lens and negative for a diverging lens Thus, when an\noptician prescribes a corrective lens of power + 2 5 D, the required lens is\na convex lens of focal length + 40 cm A lens of power of \u2013 4" + }, + { + "Chapter": "9", + "sentence_range": "504-507", + "Text": "Thus, when an\noptician prescribes a corrective lens of power + 2 5 D, the required lens is\na convex lens of focal length + 40 cm A lens of power of \u2013 4 0 D means a\nconcave lens of focal length \u2013 25 cm" + }, + { + "Chapter": "9", + "sentence_range": "505-508", + "Text": "5 D, the required lens is\na convex lens of focal length + 40 cm A lens of power of \u2013 4 0 D means a\nconcave lens of focal length \u2013 25 cm Example 9" + }, + { + "Chapter": "9", + "sentence_range": "506-509", + "Text": "A lens of power of \u2013 4 0 D means a\nconcave lens of focal length \u2013 25 cm Example 9 7 (i) If f = 0" + }, + { + "Chapter": "9", + "sentence_range": "507-510", + "Text": "0 D means a\nconcave lens of focal length \u2013 25 cm Example 9 7 (i) If f = 0 5 m for a glass lens, what is the power of the\nlens" + }, + { + "Chapter": "9", + "sentence_range": "508-511", + "Text": "Example 9 7 (i) If f = 0 5 m for a glass lens, what is the power of the\nlens (ii) The radii of curvature of the faces of a double convex lens\nare 10 cm and 15 cm" + }, + { + "Chapter": "9", + "sentence_range": "509-512", + "Text": "7 (i) If f = 0 5 m for a glass lens, what is the power of the\nlens (ii) The radii of curvature of the faces of a double convex lens\nare 10 cm and 15 cm Its focal length is 12 cm" + }, + { + "Chapter": "9", + "sentence_range": "510-513", + "Text": "5 m for a glass lens, what is the power of the\nlens (ii) The radii of curvature of the faces of a double convex lens\nare 10 cm and 15 cm Its focal length is 12 cm What is the refractive\nindex of glass" + }, + { + "Chapter": "9", + "sentence_range": "511-514", + "Text": "(ii) The radii of curvature of the faces of a double convex lens\nare 10 cm and 15 cm Its focal length is 12 cm What is the refractive\nindex of glass (iii) A convex lens has 20 cm focal length in air" + }, + { + "Chapter": "9", + "sentence_range": "512-515", + "Text": "Its focal length is 12 cm What is the refractive\nindex of glass (iii) A convex lens has 20 cm focal length in air What\nis focal length in water" + }, + { + "Chapter": "9", + "sentence_range": "513-516", + "Text": "What is the refractive\nindex of glass (iii) A convex lens has 20 cm focal length in air What\nis focal length in water (Refractive index of air-water = 1" + }, + { + "Chapter": "9", + "sentence_range": "514-517", + "Text": "(iii) A convex lens has 20 cm focal length in air What\nis focal length in water (Refractive index of air-water = 1 33, refractive\nindex for air-glass = 1" + }, + { + "Chapter": "9", + "sentence_range": "515-518", + "Text": "What\nis focal length in water (Refractive index of air-water = 1 33, refractive\nindex for air-glass = 1 5" + }, + { + "Chapter": "9", + "sentence_range": "516-519", + "Text": "(Refractive index of air-water = 1 33, refractive\nindex for air-glass = 1 5 )\n EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "517-520", + "Text": "33, refractive\nindex for air-glass = 1 5 )\n EXAMPLE 9 7\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n237\nSolution\n(i)\nPower = +2 dioptre" + }, + { + "Chapter": "9", + "sentence_range": "518-521", + "Text": "5 )\n EXAMPLE 9 7\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n237\nSolution\n(i)\nPower = +2 dioptre (ii) Here, we have f = +12 cm, R1 = +10 cm, R2 = \u201315 cm" + }, + { + "Chapter": "9", + "sentence_range": "519-522", + "Text": ")\n EXAMPLE 9 7\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n237\nSolution\n(i)\nPower = +2 dioptre (ii) Here, we have f = +12 cm, R1 = +10 cm, R2 = \u201315 cm Refractive index of air is taken as unity" + }, + { + "Chapter": "9", + "sentence_range": "520-523", + "Text": "7\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n237\nSolution\n(i)\nPower = +2 dioptre (ii) Here, we have f = +12 cm, R1 = +10 cm, R2 = \u201315 cm Refractive index of air is taken as unity We use the lens formula of Eq" + }, + { + "Chapter": "9", + "sentence_range": "521-524", + "Text": "(ii) Here, we have f = +12 cm, R1 = +10 cm, R2 = \u201315 cm Refractive index of air is taken as unity We use the lens formula of Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "522-525", + "Text": "Refractive index of air is taken as unity We use the lens formula of Eq (9 22)" + }, + { + "Chapter": "9", + "sentence_range": "523-526", + "Text": "We use the lens formula of Eq (9 22) The sign convention has to\nbe applied for f, R1 and R2" + }, + { + "Chapter": "9", + "sentence_range": "524-527", + "Text": "(9 22) The sign convention has to\nbe applied for f, R1 and R2 Substituting the values, we have\n1\n12\n1\n1\n10\n1\n15\n=\n\u2212\n\u2212 \u2212\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\n(\n)\nn\nThis gives n = 1" + }, + { + "Chapter": "9", + "sentence_range": "525-528", + "Text": "22) The sign convention has to\nbe applied for f, R1 and R2 Substituting the values, we have\n1\n12\n1\n1\n10\n1\n15\n=\n\u2212\n\u2212 \u2212\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\n(\n)\nn\nThis gives n = 1 5" + }, + { + "Chapter": "9", + "sentence_range": "526-529", + "Text": "The sign convention has to\nbe applied for f, R1 and R2 Substituting the values, we have\n1\n12\n1\n1\n10\n1\n15\n=\n\u2212\n\u2212 \u2212\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\n(\n)\nn\nThis gives n = 1 5 (iii) For a glass lens in air, n2 = 1" + }, + { + "Chapter": "9", + "sentence_range": "527-530", + "Text": "Substituting the values, we have\n1\n12\n1\n1\n10\n1\n15\n=\n\u2212\n\u2212 \u2212\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\n(\n)\nn\nThis gives n = 1 5 (iii) For a glass lens in air, n2 = 1 5, n1 = 1, f = +20 cm" + }, + { + "Chapter": "9", + "sentence_range": "528-531", + "Text": "5 (iii) For a glass lens in air, n2 = 1 5, n1 = 1, f = +20 cm Hence, the lens\nformula gives\n1\n20\n0 5\n1\n1\n1\n2\n=\n\u2212\n\uf8ee\n\uf8f0\uf8ef\n\uf8f9\n\uf8fb\uf8fa" + }, + { + "Chapter": "9", + "sentence_range": "529-532", + "Text": "(iii) For a glass lens in air, n2 = 1 5, n1 = 1, f = +20 cm Hence, the lens\nformula gives\n1\n20\n0 5\n1\n1\n1\n2\n=\n\u2212\n\uf8ee\n\uf8f0\uf8ef\n\uf8f9\n\uf8fb\uf8fa R\nR\nFor the same glass lens in water, n2 = 1" + }, + { + "Chapter": "9", + "sentence_range": "530-533", + "Text": "5, n1 = 1, f = +20 cm Hence, the lens\nformula gives\n1\n20\n0 5\n1\n1\n1\n2\n=\n\u2212\n\uf8ee\n\uf8f0\uf8ef\n\uf8f9\n\uf8fb\uf8fa R\nR\nFor the same glass lens in water, n2 = 1 5, n1 = 1" + }, + { + "Chapter": "9", + "sentence_range": "531-534", + "Text": "Hence, the lens\nformula gives\n1\n20\n0 5\n1\n1\n1\n2\n=\n\u2212\n\uf8ee\n\uf8f0\uf8ef\n\uf8f9\n\uf8fb\uf8fa R\nR\nFor the same glass lens in water, n2 = 1 5, n1 = 1 33" + }, + { + "Chapter": "9", + "sentence_range": "532-535", + "Text": "R\nR\nFor the same glass lens in water, n2 = 1 5, n1 = 1 33 Therefore,\n1 33\n1 5 1 33\n1\n1\n1\n2" + }, + { + "Chapter": "9", + "sentence_range": "533-536", + "Text": "5, n1 = 1 33 Therefore,\n1 33\n1 5 1 33\n1\n1\n1\n2 (" + }, + { + "Chapter": "9", + "sentence_range": "534-537", + "Text": "33 Therefore,\n1 33\n1 5 1 33\n1\n1\n1\n2 ( )\nf\nR\nR\n=\n\u2212\n\u2212\n\uf8ee\n\uf8f0\uf8ef\n\uf8f9\n\uf8fb\uf8fa\n(9" + }, + { + "Chapter": "9", + "sentence_range": "535-538", + "Text": "Therefore,\n1 33\n1 5 1 33\n1\n1\n1\n2 ( )\nf\nR\nR\n=\n\u2212\n\u2212\n\uf8ee\n\uf8f0\uf8ef\n\uf8f9\n\uf8fb\uf8fa\n(9 26)\nCombining these two equations, we find f = + 78" + }, + { + "Chapter": "9", + "sentence_range": "536-539", + "Text": "( )\nf\nR\nR\n=\n\u2212\n\u2212\n\uf8ee\n\uf8f0\uf8ef\n\uf8f9\n\uf8fb\uf8fa\n(9 26)\nCombining these two equations, we find f = + 78 2 cm" + }, + { + "Chapter": "9", + "sentence_range": "537-540", + "Text": ")\nf\nR\nR\n=\n\u2212\n\u2212\n\uf8ee\n\uf8f0\uf8ef\n\uf8f9\n\uf8fb\uf8fa\n(9 26)\nCombining these two equations, we find f = + 78 2 cm 9" + }, + { + "Chapter": "9", + "sentence_range": "538-541", + "Text": "26)\nCombining these two equations, we find f = + 78 2 cm 9 5" + }, + { + "Chapter": "9", + "sentence_range": "539-542", + "Text": "2 cm 9 5 4 Combination of thin lenses in contact\nConsider two lenses A and B of focal length f1 and\nf2 placed in contact with each other" + }, + { + "Chapter": "9", + "sentence_range": "540-543", + "Text": "9 5 4 Combination of thin lenses in contact\nConsider two lenses A and B of focal length f1 and\nf2 placed in contact with each other Let the object\nbe placed at a point O beyond the focus of the first\nlens A (Fig" + }, + { + "Chapter": "9", + "sentence_range": "541-544", + "Text": "5 4 Combination of thin lenses in contact\nConsider two lenses A and B of focal length f1 and\nf2 placed in contact with each other Let the object\nbe placed at a point O beyond the focus of the first\nlens A (Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "542-545", + "Text": "4 Combination of thin lenses in contact\nConsider two lenses A and B of focal length f1 and\nf2 placed in contact with each other Let the object\nbe placed at a point O beyond the focus of the first\nlens A (Fig 9 19)" + }, + { + "Chapter": "9", + "sentence_range": "543-546", + "Text": "Let the object\nbe placed at a point O beyond the focus of the first\nlens A (Fig 9 19) The first lens produces an image\nat I1" + }, + { + "Chapter": "9", + "sentence_range": "544-547", + "Text": "9 19) The first lens produces an image\nat I1 Since image I1 is real, it serves as a virtual\nobject for the second lens B, producing the final\nimage at I" + }, + { + "Chapter": "9", + "sentence_range": "545-548", + "Text": "19) The first lens produces an image\nat I1 Since image I1 is real, it serves as a virtual\nobject for the second lens B, producing the final\nimage at I It must, however, be borne in mind that\nformation of image by the first lens is presumed\nonly to facilitate determination of the position of the\nfinal image" + }, + { + "Chapter": "9", + "sentence_range": "546-549", + "Text": "The first lens produces an image\nat I1 Since image I1 is real, it serves as a virtual\nobject for the second lens B, producing the final\nimage at I It must, however, be borne in mind that\nformation of image by the first lens is presumed\nonly to facilitate determination of the position of the\nfinal image In fact, the direction of rays emerging\nfrom the first lens gets modified in accordance with\nthe angle at which they strike the second lens" + }, + { + "Chapter": "9", + "sentence_range": "547-550", + "Text": "Since image I1 is real, it serves as a virtual\nobject for the second lens B, producing the final\nimage at I It must, however, be borne in mind that\nformation of image by the first lens is presumed\nonly to facilitate determination of the position of the\nfinal image In fact, the direction of rays emerging\nfrom the first lens gets modified in accordance with\nthe angle at which they strike the second lens Since the lenses are thin,\nwe assume the optical centres of the lenses to be coincident" + }, + { + "Chapter": "9", + "sentence_range": "548-551", + "Text": "It must, however, be borne in mind that\nformation of image by the first lens is presumed\nonly to facilitate determination of the position of the\nfinal image In fact, the direction of rays emerging\nfrom the first lens gets modified in accordance with\nthe angle at which they strike the second lens Since the lenses are thin,\nwe assume the optical centres of the lenses to be coincident Let this\ncentral point be denoted by P" + }, + { + "Chapter": "9", + "sentence_range": "549-552", + "Text": "In fact, the direction of rays emerging\nfrom the first lens gets modified in accordance with\nthe angle at which they strike the second lens Since the lenses are thin,\nwe assume the optical centres of the lenses to be coincident Let this\ncentral point be denoted by P For the image formed by the first lens A, we get\n1\n1\n1\n1\n1\nv\nu\nf\n\u2212\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "550-553", + "Text": "Since the lenses are thin,\nwe assume the optical centres of the lenses to be coincident Let this\ncentral point be denoted by P For the image formed by the first lens A, we get\n1\n1\n1\n1\n1\nv\nu\nf\n\u2212\n=\n(9 27)\nFor the image formed by the second lens B, we get\n1\n2\n1\n1\n1\nv\nv\nf\n\u2212\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "551-554", + "Text": "Let this\ncentral point be denoted by P For the image formed by the first lens A, we get\n1\n1\n1\n1\n1\nv\nu\nf\n\u2212\n=\n(9 27)\nFor the image formed by the second lens B, we get\n1\n2\n1\n1\n1\nv\nv\nf\n\u2212\n=\n(9 28)\nAdding Eqs" + }, + { + "Chapter": "9", + "sentence_range": "552-555", + "Text": "For the image formed by the first lens A, we get\n1\n1\n1\n1\n1\nv\nu\nf\n\u2212\n=\n(9 27)\nFor the image formed by the second lens B, we get\n1\n2\n1\n1\n1\nv\nv\nf\n\u2212\n=\n(9 28)\nAdding Eqs (9" + }, + { + "Chapter": "9", + "sentence_range": "553-556", + "Text": "27)\nFor the image formed by the second lens B, we get\n1\n2\n1\n1\n1\nv\nv\nf\n\u2212\n=\n(9 28)\nAdding Eqs (9 27) and (9" + }, + { + "Chapter": "9", + "sentence_range": "554-557", + "Text": "28)\nAdding Eqs (9 27) and (9 28), we get\n1\n2\n1\n1\n1\n1\nv\nu\nf\nf\n\u2212\n=\n+\n(9" + }, + { + "Chapter": "9", + "sentence_range": "555-558", + "Text": "(9 27) and (9 28), we get\n1\n2\n1\n1\n1\n1\nv\nu\nf\nf\n\u2212\n=\n+\n(9 29)\nIf the two lens-system is regarded as equivalent to a single lens of\nfocal length f, we have\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "556-559", + "Text": "27) and (9 28), we get\n1\n2\n1\n1\n1\n1\nv\nu\nf\nf\n\u2212\n=\n+\n(9 29)\nIf the two lens-system is regarded as equivalent to a single lens of\nfocal length f, we have\nFIGURE 9 19 Image formation by a\ncombination of two thin lenses in contact" + }, + { + "Chapter": "9", + "sentence_range": "557-560", + "Text": "28), we get\n1\n2\n1\n1\n1\n1\nv\nu\nf\nf\n\u2212\n=\n+\n(9 29)\nIf the two lens-system is regarded as equivalent to a single lens of\nfocal length f, we have\nFIGURE 9 19 Image formation by a\ncombination of two thin lenses in contact EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "558-561", + "Text": "29)\nIf the two lens-system is regarded as equivalent to a single lens of\nfocal length f, we have\nFIGURE 9 19 Image formation by a\ncombination of two thin lenses in contact EXAMPLE 9 7\nRationalised 2023-24\nPhysics\n238\n EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "559-562", + "Text": "19 Image formation by a\ncombination of two thin lenses in contact EXAMPLE 9 7\nRationalised 2023-24\nPhysics\n238\n EXAMPLE 9 8\n1\n1\n1\nv\nu\nf\n\u2212\n=\nso that we get\n1\n2\n1\n1\n1\nf\nf\nf\n=\n+\n(9" + }, + { + "Chapter": "9", + "sentence_range": "560-563", + "Text": "EXAMPLE 9 7\nRationalised 2023-24\nPhysics\n238\n EXAMPLE 9 8\n1\n1\n1\nv\nu\nf\n\u2212\n=\nso that we get\n1\n2\n1\n1\n1\nf\nf\nf\n=\n+\n(9 30)\nThe derivation is valid for any number of thin lenses in contact" + }, + { + "Chapter": "9", + "sentence_range": "561-564", + "Text": "7\nRationalised 2023-24\nPhysics\n238\n EXAMPLE 9 8\n1\n1\n1\nv\nu\nf\n\u2212\n=\nso that we get\n1\n2\n1\n1\n1\nf\nf\nf\n=\n+\n(9 30)\nThe derivation is valid for any number of thin lenses in contact If\nseveral thin lenses of focal length f1, f2, f3," + }, + { + "Chapter": "9", + "sentence_range": "562-565", + "Text": "8\n1\n1\n1\nv\nu\nf\n\u2212\n=\nso that we get\n1\n2\n1\n1\n1\nf\nf\nf\n=\n+\n(9 30)\nThe derivation is valid for any number of thin lenses in contact If\nseveral thin lenses of focal length f1, f2, f3, are in contact, the effective\nfocal length of their combination is given by\n1\n2\n3\n1\n1\n1\n1\nf\nf\nf\nf\n=\n+\n+\n+ \u2026\n(9" + }, + { + "Chapter": "9", + "sentence_range": "563-566", + "Text": "30)\nThe derivation is valid for any number of thin lenses in contact If\nseveral thin lenses of focal length f1, f2, f3, are in contact, the effective\nfocal length of their combination is given by\n1\n2\n3\n1\n1\n1\n1\nf\nf\nf\nf\n=\n+\n+\n+ \u2026\n(9 31)\nIn terms of power, Eq" + }, + { + "Chapter": "9", + "sentence_range": "564-567", + "Text": "If\nseveral thin lenses of focal length f1, f2, f3, are in contact, the effective\nfocal length of their combination is given by\n1\n2\n3\n1\n1\n1\n1\nf\nf\nf\nf\n=\n+\n+\n+ \u2026\n(9 31)\nIn terms of power, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "565-568", + "Text": "are in contact, the effective\nfocal length of their combination is given by\n1\n2\n3\n1\n1\n1\n1\nf\nf\nf\nf\n=\n+\n+\n+ \u2026\n(9 31)\nIn terms of power, Eq (9 31) can be written as\nP = P1 + P2 + P3 + \u2026\n(9" + }, + { + "Chapter": "9", + "sentence_range": "566-569", + "Text": "31)\nIn terms of power, Eq (9 31) can be written as\nP = P1 + P2 + P3 + \u2026\n(9 32)\nwhere P is the net power of the lens combination" + }, + { + "Chapter": "9", + "sentence_range": "567-570", + "Text": "(9 31) can be written as\nP = P1 + P2 + P3 + \u2026\n(9 32)\nwhere P is the net power of the lens combination Note that the sum in\nEq" + }, + { + "Chapter": "9", + "sentence_range": "568-571", + "Text": "31) can be written as\nP = P1 + P2 + P3 + \u2026\n(9 32)\nwhere P is the net power of the lens combination Note that the sum in\nEq (9" + }, + { + "Chapter": "9", + "sentence_range": "569-572", + "Text": "32)\nwhere P is the net power of the lens combination Note that the sum in\nEq (9 32) is an algebraic sum of individual powers, so some of the terms\non the right side may be positive (for convex lenses) and some negative\n(for concave lenses)" + }, + { + "Chapter": "9", + "sentence_range": "570-573", + "Text": "Note that the sum in\nEq (9 32) is an algebraic sum of individual powers, so some of the terms\non the right side may be positive (for convex lenses) and some negative\n(for concave lenses) Combination of lenses helps to obtain diverging or\nconverging lenses of desired magnification" + }, + { + "Chapter": "9", + "sentence_range": "571-574", + "Text": "(9 32) is an algebraic sum of individual powers, so some of the terms\non the right side may be positive (for convex lenses) and some negative\n(for concave lenses) Combination of lenses helps to obtain diverging or\nconverging lenses of desired magnification It also enhances sharpness\nof the image" + }, + { + "Chapter": "9", + "sentence_range": "572-575", + "Text": "32) is an algebraic sum of individual powers, so some of the terms\non the right side may be positive (for convex lenses) and some negative\n(for concave lenses) Combination of lenses helps to obtain diverging or\nconverging lenses of desired magnification It also enhances sharpness\nof the image Since the image formed by the first lens becomes the object\nfor the second, Eq" + }, + { + "Chapter": "9", + "sentence_range": "573-576", + "Text": "Combination of lenses helps to obtain diverging or\nconverging lenses of desired magnification It also enhances sharpness\nof the image Since the image formed by the first lens becomes the object\nfor the second, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "574-577", + "Text": "It also enhances sharpness\nof the image Since the image formed by the first lens becomes the object\nfor the second, Eq (9 25) implies that the total magnification m of the\ncombination is a product of magnification (m1, m 2, m 3," + }, + { + "Chapter": "9", + "sentence_range": "575-578", + "Text": "Since the image formed by the first lens becomes the object\nfor the second, Eq (9 25) implies that the total magnification m of the\ncombination is a product of magnification (m1, m 2, m 3, ) of individual\nlenses\nm = m1 m2 m3" + }, + { + "Chapter": "9", + "sentence_range": "576-579", + "Text": "(9 25) implies that the total magnification m of the\ncombination is a product of magnification (m1, m 2, m 3, ) of individual\nlenses\nm = m1 m2 m3 (9" + }, + { + "Chapter": "9", + "sentence_range": "577-580", + "Text": "25) implies that the total magnification m of the\ncombination is a product of magnification (m1, m 2, m 3, ) of individual\nlenses\nm = m1 m2 m3 (9 33)\nSuch a system of combination of lenses is commonly used in designing\nlenses for cameras, microscopes, telescopes and other optical instruments" + }, + { + "Chapter": "9", + "sentence_range": "578-581", + "Text": ") of individual\nlenses\nm = m1 m2 m3 (9 33)\nSuch a system of combination of lenses is commonly used in designing\nlenses for cameras, microscopes, telescopes and other optical instruments Example 9" + }, + { + "Chapter": "9", + "sentence_range": "579-582", + "Text": "(9 33)\nSuch a system of combination of lenses is commonly used in designing\nlenses for cameras, microscopes, telescopes and other optical instruments Example 9 8 Find the position of the image formed by the lens\ncombination given in the Fig" + }, + { + "Chapter": "9", + "sentence_range": "580-583", + "Text": "33)\nSuch a system of combination of lenses is commonly used in designing\nlenses for cameras, microscopes, telescopes and other optical instruments Example 9 8 Find the position of the image formed by the lens\ncombination given in the Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "581-584", + "Text": "Example 9 8 Find the position of the image formed by the lens\ncombination given in the Fig 9 20" + }, + { + "Chapter": "9", + "sentence_range": "582-585", + "Text": "8 Find the position of the image formed by the lens\ncombination given in the Fig 9 20 FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "583-586", + "Text": "9 20 FIGURE 9 20\nSolution Image formed by the first lens\n1\n1\n1\n1\n1\n1\nv\nu\nf\n\u2212\n=\n1\n1\n1\n1\n30\n10\nv \u2212\n=\n\u2212\nor\nv1 = 15 cm\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n239\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "584-587", + "Text": "20 FIGURE 9 20\nSolution Image formed by the first lens\n1\n1\n1\n1\n1\n1\nv\nu\nf\n\u2212\n=\n1\n1\n1\n1\n30\n10\nv \u2212\n=\n\u2212\nor\nv1 = 15 cm\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n239\nFIGURE 9 21 A ray of light passing through\na triangular glass prism" + }, + { + "Chapter": "9", + "sentence_range": "585-588", + "Text": "FIGURE 9 20\nSolution Image formed by the first lens\n1\n1\n1\n1\n1\n1\nv\nu\nf\n\u2212\n=\n1\n1\n1\n1\n30\n10\nv \u2212\n=\n\u2212\nor\nv1 = 15 cm\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n239\nFIGURE 9 21 A ray of light passing through\na triangular glass prism EXAMPLE 9" + }, + { + "Chapter": "9", + "sentence_range": "586-589", + "Text": "20\nSolution Image formed by the first lens\n1\n1\n1\n1\n1\n1\nv\nu\nf\n\u2212\n=\n1\n1\n1\n1\n30\n10\nv \u2212\n=\n\u2212\nor\nv1 = 15 cm\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n239\nFIGURE 9 21 A ray of light passing through\na triangular glass prism EXAMPLE 9 8\nThe image formed by the first lens serves as the object for the second" + }, + { + "Chapter": "9", + "sentence_range": "587-590", + "Text": "21 A ray of light passing through\na triangular glass prism EXAMPLE 9 8\nThe image formed by the first lens serves as the object for the second This is at a distance of (15 \u2013 5) cm = 10 cm to the right of the second\nlens" + }, + { + "Chapter": "9", + "sentence_range": "588-591", + "Text": "EXAMPLE 9 8\nThe image formed by the first lens serves as the object for the second This is at a distance of (15 \u2013 5) cm = 10 cm to the right of the second\nlens Though the image is real, it serves as a virtual object for the\nsecond lens, which means that the rays appear to come from it for\nthe second lens" + }, + { + "Chapter": "9", + "sentence_range": "589-592", + "Text": "8\nThe image formed by the first lens serves as the object for the second This is at a distance of (15 \u2013 5) cm = 10 cm to the right of the second\nlens Though the image is real, it serves as a virtual object for the\nsecond lens, which means that the rays appear to come from it for\nthe second lens 2\n1\n1\n1\n10\n10\nv \u2212\n= \u2212\nor\nv2 = \u00a5\nThe virtual image is formed at an infinite distance to the left of the\nsecond lens" + }, + { + "Chapter": "9", + "sentence_range": "590-593", + "Text": "This is at a distance of (15 \u2013 5) cm = 10 cm to the right of the second\nlens Though the image is real, it serves as a virtual object for the\nsecond lens, which means that the rays appear to come from it for\nthe second lens 2\n1\n1\n1\n10\n10\nv \u2212\n= \u2212\nor\nv2 = \u00a5\nThe virtual image is formed at an infinite distance to the left of the\nsecond lens This acts as an object for the third lens" + }, + { + "Chapter": "9", + "sentence_range": "591-594", + "Text": "Though the image is real, it serves as a virtual object for the\nsecond lens, which means that the rays appear to come from it for\nthe second lens 2\n1\n1\n1\n10\n10\nv \u2212\n= \u2212\nor\nv2 = \u00a5\nThe virtual image is formed at an infinite distance to the left of the\nsecond lens This acts as an object for the third lens 3\n3\n3\n1\n1\n1\nv\nu\nf\n\u2212\n=\nor\n \n3\n1\n1\n1\n30\nv =\n+\n\u221e\nor\nv3 = 30 cm\nThe final image is formed 30 cm to the right of the third lens" + }, + { + "Chapter": "9", + "sentence_range": "592-595", + "Text": "2\n1\n1\n1\n10\n10\nv \u2212\n= \u2212\nor\nv2 = \u00a5\nThe virtual image is formed at an infinite distance to the left of the\nsecond lens This acts as an object for the third lens 3\n3\n3\n1\n1\n1\nv\nu\nf\n\u2212\n=\nor\n \n3\n1\n1\n1\n30\nv =\n+\n\u221e\nor\nv3 = 30 cm\nThe final image is formed 30 cm to the right of the third lens 9" + }, + { + "Chapter": "9", + "sentence_range": "593-596", + "Text": "This acts as an object for the third lens 3\n3\n3\n1\n1\n1\nv\nu\nf\n\u2212\n=\nor\n \n3\n1\n1\n1\n30\nv =\n+\n\u221e\nor\nv3 = 30 cm\nThe final image is formed 30 cm to the right of the third lens 9 6 REFRACTION THROUGH A PRISM\nFigure 9" + }, + { + "Chapter": "9", + "sentence_range": "594-597", + "Text": "3\n3\n3\n1\n1\n1\nv\nu\nf\n\u2212\n=\nor\n \n3\n1\n1\n1\n30\nv =\n+\n\u221e\nor\nv3 = 30 cm\nThe final image is formed 30 cm to the right of the third lens 9 6 REFRACTION THROUGH A PRISM\nFigure 9 21 shows the passage of light through\na triangular prism ABC" + }, + { + "Chapter": "9", + "sentence_range": "595-598", + "Text": "9 6 REFRACTION THROUGH A PRISM\nFigure 9 21 shows the passage of light through\na triangular prism ABC The angles of incidence\nand refraction at the first face AB are i and r1,\nwhile the angle of incidence (from glass to air) at\nthe second face AC is r2 and the angle of refraction\nor emergence e" + }, + { + "Chapter": "9", + "sentence_range": "596-599", + "Text": "6 REFRACTION THROUGH A PRISM\nFigure 9 21 shows the passage of light through\na triangular prism ABC The angles of incidence\nand refraction at the first face AB are i and r1,\nwhile the angle of incidence (from glass to air) at\nthe second face AC is r2 and the angle of refraction\nor emergence e The angle between the emergent\nray RS and the direction of the incident ray PQ\nis called the angle of deviation, d" + }, + { + "Chapter": "9", + "sentence_range": "597-600", + "Text": "21 shows the passage of light through\na triangular prism ABC The angles of incidence\nand refraction at the first face AB are i and r1,\nwhile the angle of incidence (from glass to air) at\nthe second face AC is r2 and the angle of refraction\nor emergence e The angle between the emergent\nray RS and the direction of the incident ray PQ\nis called the angle of deviation, d In the quadrilateral AQNR, two of the angles\n(at the vertices Q and R) are right angles" + }, + { + "Chapter": "9", + "sentence_range": "598-601", + "Text": "The angles of incidence\nand refraction at the first face AB are i and r1,\nwhile the angle of incidence (from glass to air) at\nthe second face AC is r2 and the angle of refraction\nor emergence e The angle between the emergent\nray RS and the direction of the incident ray PQ\nis called the angle of deviation, d In the quadrilateral AQNR, two of the angles\n(at the vertices Q and R) are right angles Therefore, the sum of the other angles of the\nquadrilateral is 180\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "599-602", + "Text": "The angle between the emergent\nray RS and the direction of the incident ray PQ\nis called the angle of deviation, d In the quadrilateral AQNR, two of the angles\n(at the vertices Q and R) are right angles Therefore, the sum of the other angles of the\nquadrilateral is 180\u00b0 \u00d0A + \u00d0QNR = 180\u00b0\nFrom the triangle QNR,\nr1 + r2 + \u00d0QNR = 180\u00b0\nComparing these two equations, we get\nr1 + r2 = A\n(9" + }, + { + "Chapter": "9", + "sentence_range": "600-603", + "Text": "In the quadrilateral AQNR, two of the angles\n(at the vertices Q and R) are right angles Therefore, the sum of the other angles of the\nquadrilateral is 180\u00b0 \u00d0A + \u00d0QNR = 180\u00b0\nFrom the triangle QNR,\nr1 + r2 + \u00d0QNR = 180\u00b0\nComparing these two equations, we get\nr1 + r2 = A\n(9 34)\nThe total deviation d is the sum of deviations at the two faces,\nd = (i \u2013 r1 ) + (e \u2013 r2 )\nthat is,\nd = i + e \u2013 A\n(9" + }, + { + "Chapter": "9", + "sentence_range": "601-604", + "Text": "Therefore, the sum of the other angles of the\nquadrilateral is 180\u00b0 \u00d0A + \u00d0QNR = 180\u00b0\nFrom the triangle QNR,\nr1 + r2 + \u00d0QNR = 180\u00b0\nComparing these two equations, we get\nr1 + r2 = A\n(9 34)\nThe total deviation d is the sum of deviations at the two faces,\nd = (i \u2013 r1 ) + (e \u2013 r2 )\nthat is,\nd = i + e \u2013 A\n(9 35)\nThus, the angle of deviation depends on the angle of incidence" + }, + { + "Chapter": "9", + "sentence_range": "602-605", + "Text": "\u00d0A + \u00d0QNR = 180\u00b0\nFrom the triangle QNR,\nr1 + r2 + \u00d0QNR = 180\u00b0\nComparing these two equations, we get\nr1 + r2 = A\n(9 34)\nThe total deviation d is the sum of deviations at the two faces,\nd = (i \u2013 r1 ) + (e \u2013 r2 )\nthat is,\nd = i + e \u2013 A\n(9 35)\nThus, the angle of deviation depends on the angle of incidence A plot\nbetween the angle of deviation and angle of incidence is shown in\nFig" + }, + { + "Chapter": "9", + "sentence_range": "603-606", + "Text": "34)\nThe total deviation d is the sum of deviations at the two faces,\nd = (i \u2013 r1 ) + (e \u2013 r2 )\nthat is,\nd = i + e \u2013 A\n(9 35)\nThus, the angle of deviation depends on the angle of incidence A plot\nbetween the angle of deviation and angle of incidence is shown in\nFig 9" + }, + { + "Chapter": "9", + "sentence_range": "604-607", + "Text": "35)\nThus, the angle of deviation depends on the angle of incidence A plot\nbetween the angle of deviation and angle of incidence is shown in\nFig 9 22" + }, + { + "Chapter": "9", + "sentence_range": "605-608", + "Text": "A plot\nbetween the angle of deviation and angle of incidence is shown in\nFig 9 22 You can see that, in general, any given value of d, except for\ni = e, corresponds to two values i and hence of e" + }, + { + "Chapter": "9", + "sentence_range": "606-609", + "Text": "9 22 You can see that, in general, any given value of d, except for\ni = e, corresponds to two values i and hence of e This, in fact, is expected\nfrom the symmetry of i and e in Eq" + }, + { + "Chapter": "9", + "sentence_range": "607-610", + "Text": "22 You can see that, in general, any given value of d, except for\ni = e, corresponds to two values i and hence of e This, in fact, is expected\nfrom the symmetry of i and e in Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "608-611", + "Text": "You can see that, in general, any given value of d, except for\ni = e, corresponds to two values i and hence of e This, in fact, is expected\nfrom the symmetry of i and e in Eq (9 35), i" + }, + { + "Chapter": "9", + "sentence_range": "609-612", + "Text": "This, in fact, is expected\nfrom the symmetry of i and e in Eq (9 35), i e" + }, + { + "Chapter": "9", + "sentence_range": "610-613", + "Text": "(9 35), i e , d remains the same if i\nRationalised 2023-24\nPhysics\n240\nand e are interchanged" + }, + { + "Chapter": "9", + "sentence_range": "611-614", + "Text": "35), i e , d remains the same if i\nRationalised 2023-24\nPhysics\n240\nand e are interchanged Physically, this is related\nto the fact that the path of ray in Fig" + }, + { + "Chapter": "9", + "sentence_range": "612-615", + "Text": "e , d remains the same if i\nRationalised 2023-24\nPhysics\n240\nand e are interchanged Physically, this is related\nto the fact that the path of ray in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "613-616", + "Text": ", d remains the same if i\nRationalised 2023-24\nPhysics\n240\nand e are interchanged Physically, this is related\nto the fact that the path of ray in Fig 9 21 can be\ntraced back, resulting in the same angle of\ndeviation" + }, + { + "Chapter": "9", + "sentence_range": "614-617", + "Text": "Physically, this is related\nto the fact that the path of ray in Fig 9 21 can be\ntraced back, resulting in the same angle of\ndeviation At the minimum deviation Dm, the\nrefracted ray inside the prism becomes parallel\nto its base" + }, + { + "Chapter": "9", + "sentence_range": "615-618", + "Text": "9 21 can be\ntraced back, resulting in the same angle of\ndeviation At the minimum deviation Dm, the\nrefracted ray inside the prism becomes parallel\nto its base We have\nd = Dm, i = e which implies r1 = r2" + }, + { + "Chapter": "9", + "sentence_range": "616-619", + "Text": "21 can be\ntraced back, resulting in the same angle of\ndeviation At the minimum deviation Dm, the\nrefracted ray inside the prism becomes parallel\nto its base We have\nd = Dm, i = e which implies r1 = r2 Equation (9" + }, + { + "Chapter": "9", + "sentence_range": "617-620", + "Text": "At the minimum deviation Dm, the\nrefracted ray inside the prism becomes parallel\nto its base We have\nd = Dm, i = e which implies r1 = r2 Equation (9 34) gives\n2r = A or r = 2\nA\n(9" + }, + { + "Chapter": "9", + "sentence_range": "618-621", + "Text": "We have\nd = Dm, i = e which implies r1 = r2 Equation (9 34) gives\n2r = A or r = 2\nA\n(9 36)\nIn the same way, Eq" + }, + { + "Chapter": "9", + "sentence_range": "619-622", + "Text": "Equation (9 34) gives\n2r = A or r = 2\nA\n(9 36)\nIn the same way, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "620-623", + "Text": "34) gives\n2r = A or r = 2\nA\n(9 36)\nIn the same way, Eq (9 35) gives\nDm = 2i \u2013 A, or i = (A + Dm)/2\n (9" + }, + { + "Chapter": "9", + "sentence_range": "621-624", + "Text": "36)\nIn the same way, Eq (9 35) gives\nDm = 2i \u2013 A, or i = (A + Dm)/2\n (9 37)\nThe refractive index of the prism is\n2\n21\n1\nsin[(\n)/2]\nsin[\n/2]\nm\nA\nD\nn\nn\nn\n+A\n=\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "622-625", + "Text": "(9 35) gives\nDm = 2i \u2013 A, or i = (A + Dm)/2\n (9 37)\nThe refractive index of the prism is\n2\n21\n1\nsin[(\n)/2]\nsin[\n/2]\nm\nA\nD\nn\nn\nn\n+A\n=\n=\n(9 38)\nThe angles A and Dm can be measured experimentally" + }, + { + "Chapter": "9", + "sentence_range": "623-626", + "Text": "35) gives\nDm = 2i \u2013 A, or i = (A + Dm)/2\n (9 37)\nThe refractive index of the prism is\n2\n21\n1\nsin[(\n)/2]\nsin[\n/2]\nm\nA\nD\nn\nn\nn\n+A\n=\n=\n(9 38)\nThe angles A and Dm can be measured experimentally Equation\n(9" + }, + { + "Chapter": "9", + "sentence_range": "624-627", + "Text": "37)\nThe refractive index of the prism is\n2\n21\n1\nsin[(\n)/2]\nsin[\n/2]\nm\nA\nD\nn\nn\nn\n+A\n=\n=\n(9 38)\nThe angles A and Dm can be measured experimentally Equation\n(9 38) thus provides a method of determining refractive index of the\nmaterial of the prism" + }, + { + "Chapter": "9", + "sentence_range": "625-628", + "Text": "38)\nThe angles A and Dm can be measured experimentally Equation\n(9 38) thus provides a method of determining refractive index of the\nmaterial of the prism For a small angle prism, i" + }, + { + "Chapter": "9", + "sentence_range": "626-629", + "Text": "Equation\n(9 38) thus provides a method of determining refractive index of the\nmaterial of the prism For a small angle prism, i e" + }, + { + "Chapter": "9", + "sentence_range": "627-630", + "Text": "38) thus provides a method of determining refractive index of the\nmaterial of the prism For a small angle prism, i e , a thin prism, Dm is also very small, and\nwe get\n(\n)\n21\n/2\nsin[(\n)/2]\nsin[\n/2]\n/2\nm\nm\nA\nD\nA\nD\nn\nA\nA\n+\n+\n=\n\u2243\nDm = (n21\u20131)A\nIt implies that, thin prisms do not deviate light much" + }, + { + "Chapter": "9", + "sentence_range": "628-631", + "Text": "For a small angle prism, i e , a thin prism, Dm is also very small, and\nwe get\n(\n)\n21\n/2\nsin[(\n)/2]\nsin[\n/2]\n/2\nm\nm\nA\nD\nA\nD\nn\nA\nA\n+\n+\n=\n\u2243\nDm = (n21\u20131)A\nIt implies that, thin prisms do not deviate light much 9" + }, + { + "Chapter": "9", + "sentence_range": "629-632", + "Text": "e , a thin prism, Dm is also very small, and\nwe get\n(\n)\n21\n/2\nsin[(\n)/2]\nsin[\n/2]\n/2\nm\nm\nA\nD\nA\nD\nn\nA\nA\n+\n+\n=\n\u2243\nDm = (n21\u20131)A\nIt implies that, thin prisms do not deviate light much 9 7 OPTICAL INSTRUMENTS\nA number of optical devices and instruments have been designed utilising\nreflecting and refracting properties of mirrors, lenses and prisms" + }, + { + "Chapter": "9", + "sentence_range": "630-633", + "Text": ", a thin prism, Dm is also very small, and\nwe get\n(\n)\n21\n/2\nsin[(\n)/2]\nsin[\n/2]\n/2\nm\nm\nA\nD\nA\nD\nn\nA\nA\n+\n+\n=\n\u2243\nDm = (n21\u20131)A\nIt implies that, thin prisms do not deviate light much 9 7 OPTICAL INSTRUMENTS\nA number of optical devices and instruments have been designed utilising\nreflecting and refracting properties of mirrors, lenses and prisms Periscope, kaleidoscope, binoculars, telescopes, microscopes are some\nexamples of optical devices and instruments that are in common use" + }, + { + "Chapter": "9", + "sentence_range": "631-634", + "Text": "9 7 OPTICAL INSTRUMENTS\nA number of optical devices and instruments have been designed utilising\nreflecting and refracting properties of mirrors, lenses and prisms Periscope, kaleidoscope, binoculars, telescopes, microscopes are some\nexamples of optical devices and instruments that are in common use Our eye is, of course, one of the most important optical device the nature\nhas endowed us with" + }, + { + "Chapter": "9", + "sentence_range": "632-635", + "Text": "7 OPTICAL INSTRUMENTS\nA number of optical devices and instruments have been designed utilising\nreflecting and refracting properties of mirrors, lenses and prisms Periscope, kaleidoscope, binoculars, telescopes, microscopes are some\nexamples of optical devices and instruments that are in common use Our eye is, of course, one of the most important optical device the nature\nhas endowed us with We have already studied about the human eye in\nClass X" + }, + { + "Chapter": "9", + "sentence_range": "633-636", + "Text": "Periscope, kaleidoscope, binoculars, telescopes, microscopes are some\nexamples of optical devices and instruments that are in common use Our eye is, of course, one of the most important optical device the nature\nhas endowed us with We have already studied about the human eye in\nClass X We now go on to describe the principles of working of the\nmicroscope and the telescope" + }, + { + "Chapter": "9", + "sentence_range": "634-637", + "Text": "Our eye is, of course, one of the most important optical device the nature\nhas endowed us with We have already studied about the human eye in\nClass X We now go on to describe the principles of working of the\nmicroscope and the telescope 9" + }, + { + "Chapter": "9", + "sentence_range": "635-638", + "Text": "We have already studied about the human eye in\nClass X We now go on to describe the principles of working of the\nmicroscope and the telescope 9 7" + }, + { + "Chapter": "9", + "sentence_range": "636-639", + "Text": "We now go on to describe the principles of working of the\nmicroscope and the telescope 9 7 1 The microscope\nA simple magnifier or microscope is a converging lens of small focal length\n(Fig" + }, + { + "Chapter": "9", + "sentence_range": "637-640", + "Text": "9 7 1 The microscope\nA simple magnifier or microscope is a converging lens of small focal length\n(Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "638-641", + "Text": "7 1 The microscope\nA simple magnifier or microscope is a converging lens of small focal length\n(Fig 9 23)" + }, + { + "Chapter": "9", + "sentence_range": "639-642", + "Text": "1 The microscope\nA simple magnifier or microscope is a converging lens of small focal length\n(Fig 9 23) In order to use such a lens as a microscope, the lens is held\nnear the object, one focal length away or less, and the eye is positioned\nclose to the lens on the other side" + }, + { + "Chapter": "9", + "sentence_range": "640-643", + "Text": "9 23) In order to use such a lens as a microscope, the lens is held\nnear the object, one focal length away or less, and the eye is positioned\nclose to the lens on the other side The idea is to get an erect, magnified\nand virtual image of the object at a distance so that it can be viewed\ncomfortably, i" + }, + { + "Chapter": "9", + "sentence_range": "641-644", + "Text": "23) In order to use such a lens as a microscope, the lens is held\nnear the object, one focal length away or less, and the eye is positioned\nclose to the lens on the other side The idea is to get an erect, magnified\nand virtual image of the object at a distance so that it can be viewed\ncomfortably, i e" + }, + { + "Chapter": "9", + "sentence_range": "642-645", + "Text": "In order to use such a lens as a microscope, the lens is held\nnear the object, one focal length away or less, and the eye is positioned\nclose to the lens on the other side The idea is to get an erect, magnified\nand virtual image of the object at a distance so that it can be viewed\ncomfortably, i e , at 25 cm or more" + }, + { + "Chapter": "9", + "sentence_range": "643-646", + "Text": "The idea is to get an erect, magnified\nand virtual image of the object at a distance so that it can be viewed\ncomfortably, i e , at 25 cm or more If the object is at a distance f, the\nimage is at infinity" + }, + { + "Chapter": "9", + "sentence_range": "644-647", + "Text": "e , at 25 cm or more If the object is at a distance f, the\nimage is at infinity However, if the object is at a distance slightly less\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "645-648", + "Text": ", at 25 cm or more If the object is at a distance f, the\nimage is at infinity However, if the object is at a distance slightly less\nFIGURE 9 22 Plot of angle of deviation (d)\nversus angle of incidence (i) for a\ntriangular prism" + }, + { + "Chapter": "9", + "sentence_range": "646-649", + "Text": "If the object is at a distance f, the\nimage is at infinity However, if the object is at a distance slightly less\nFIGURE 9 22 Plot of angle of deviation (d)\nversus angle of incidence (i) for a\ntriangular prism Rationalised 2023-24\nRay Optics and\nOptical Instruments\n241\nthan the focal length of the lens, the image is virtual and closer than\ninfinity" + }, + { + "Chapter": "9", + "sentence_range": "647-650", + "Text": "However, if the object is at a distance slightly less\nFIGURE 9 22 Plot of angle of deviation (d)\nversus angle of incidence (i) for a\ntriangular prism Rationalised 2023-24\nRay Optics and\nOptical Instruments\n241\nthan the focal length of the lens, the image is virtual and closer than\ninfinity Although the closest comfortable distance for viewing the image\nis when it is at the near point (distance D @ 25 cm), it causes some strain\non the eye" + }, + { + "Chapter": "9", + "sentence_range": "648-651", + "Text": "22 Plot of angle of deviation (d)\nversus angle of incidence (i) for a\ntriangular prism Rationalised 2023-24\nRay Optics and\nOptical Instruments\n241\nthan the focal length of the lens, the image is virtual and closer than\ninfinity Although the closest comfortable distance for viewing the image\nis when it is at the near point (distance D @ 25 cm), it causes some strain\non the eye Therefore, the image formed at infinity is often considered\nmost suitable for viewing by the relaxed eye" + }, + { + "Chapter": "9", + "sentence_range": "649-652", + "Text": "Rationalised 2023-24\nRay Optics and\nOptical Instruments\n241\nthan the focal length of the lens, the image is virtual and closer than\ninfinity Although the closest comfortable distance for viewing the image\nis when it is at the near point (distance D @ 25 cm), it causes some strain\non the eye Therefore, the image formed at infinity is often considered\nmost suitable for viewing by the relaxed eye We show both cases, the\nfirst in Fig" + }, + { + "Chapter": "9", + "sentence_range": "650-653", + "Text": "Although the closest comfortable distance for viewing the image\nis when it is at the near point (distance D @ 25 cm), it causes some strain\non the eye Therefore, the image formed at infinity is often considered\nmost suitable for viewing by the relaxed eye We show both cases, the\nfirst in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "651-654", + "Text": "Therefore, the image formed at infinity is often considered\nmost suitable for viewing by the relaxed eye We show both cases, the\nfirst in Fig 9 23(a), and the second in Fig" + }, + { + "Chapter": "9", + "sentence_range": "652-655", + "Text": "We show both cases, the\nfirst in Fig 9 23(a), and the second in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "653-656", + "Text": "9 23(a), and the second in Fig 9 23(b) and (c)" + }, + { + "Chapter": "9", + "sentence_range": "654-657", + "Text": "23(a), and the second in Fig 9 23(b) and (c) The linear magnification m, for the image formed at the near point D,\nby a simple microscope can be obtained by using the relation\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "655-658", + "Text": "9 23(b) and (c) The linear magnification m, for the image formed at the near point D,\nby a simple microscope can be obtained by using the relation\nFIGURE 9 23 A simple microscope; (a) the magnifying lens is located\nsuch that the image is at the near point, (b) the angle subtanded by the\nobject, is the same as that at the near point, and (c) the object near the\nfocal point of the lens; the image is far off but closer than infinity" + }, + { + "Chapter": "9", + "sentence_range": "656-659", + "Text": "23(b) and (c) The linear magnification m, for the image formed at the near point D,\nby a simple microscope can be obtained by using the relation\nFIGURE 9 23 A simple microscope; (a) the magnifying lens is located\nsuch that the image is at the near point, (b) the angle subtanded by the\nobject, is the same as that at the near point, and (c) the object near the\nfocal point of the lens; the image is far off but closer than infinity Rationalised 2023-24\nPhysics\n242\nm\nuv\nv v\nf\nfv\n=\n=\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 = \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n1\n1\n1\n\u2013\n\u2013\nNow according to our sign convention, v is negative, and is equal in\nmagnitude to D" + }, + { + "Chapter": "9", + "sentence_range": "657-660", + "Text": "The linear magnification m, for the image formed at the near point D,\nby a simple microscope can be obtained by using the relation\nFIGURE 9 23 A simple microscope; (a) the magnifying lens is located\nsuch that the image is at the near point, (b) the angle subtanded by the\nobject, is the same as that at the near point, and (c) the object near the\nfocal point of the lens; the image is far off but closer than infinity Rationalised 2023-24\nPhysics\n242\nm\nuv\nv v\nf\nfv\n=\n=\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 = \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n1\n1\n1\n\u2013\n\u2013\nNow according to our sign convention, v is negative, and is equal in\nmagnitude to D Thus, the magnification is\nm\nfD\n=\n\uf8ed\uf8ec\uf8eb+\n\uf8f8\uf8f7\uf8f6\n1\n(9" + }, + { + "Chapter": "9", + "sentence_range": "658-661", + "Text": "23 A simple microscope; (a) the magnifying lens is located\nsuch that the image is at the near point, (b) the angle subtanded by the\nobject, is the same as that at the near point, and (c) the object near the\nfocal point of the lens; the image is far off but closer than infinity Rationalised 2023-24\nPhysics\n242\nm\nuv\nv v\nf\nfv\n=\n=\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 = \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n1\n1\n1\n\u2013\n\u2013\nNow according to our sign convention, v is negative, and is equal in\nmagnitude to D Thus, the magnification is\nm\nfD\n=\n\uf8ed\uf8ec\uf8eb+\n\uf8f8\uf8f7\uf8f6\n1\n(9 39)\nSince D is about 25 cm, to have a magnification of six, one needs a convex\nlens of focal length, f = 5 cm" + }, + { + "Chapter": "9", + "sentence_range": "659-662", + "Text": "Rationalised 2023-24\nPhysics\n242\nm\nuv\nv v\nf\nfv\n=\n=\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 = \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\n1\n1\n1\n\u2013\n\u2013\nNow according to our sign convention, v is negative, and is equal in\nmagnitude to D Thus, the magnification is\nm\nfD\n=\n\uf8ed\uf8ec\uf8eb+\n\uf8f8\uf8f7\uf8f6\n1\n(9 39)\nSince D is about 25 cm, to have a magnification of six, one needs a convex\nlens of focal length, f = 5 cm Note that m = h\u00a2/h where h is the size of the object and h\u00a2 the size of\nthe image" + }, + { + "Chapter": "9", + "sentence_range": "660-663", + "Text": "Thus, the magnification is\nm\nfD\n=\n\uf8ed\uf8ec\uf8eb+\n\uf8f8\uf8f7\uf8f6\n1\n(9 39)\nSince D is about 25 cm, to have a magnification of six, one needs a convex\nlens of focal length, f = 5 cm Note that m = h\u00a2/h where h is the size of the object and h\u00a2 the size of\nthe image This is also the ratio of the angle subtended by the image\nto that subtended by the object, if placed at D for comfortable viewing" + }, + { + "Chapter": "9", + "sentence_range": "661-664", + "Text": "39)\nSince D is about 25 cm, to have a magnification of six, one needs a convex\nlens of focal length, f = 5 cm Note that m = h\u00a2/h where h is the size of the object and h\u00a2 the size of\nthe image This is also the ratio of the angle subtended by the image\nto that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the\neye, which is h/u" + }, + { + "Chapter": "9", + "sentence_range": "662-665", + "Text": "Note that m = h\u00a2/h where h is the size of the object and h\u00a2 the size of\nthe image This is also the ratio of the angle subtended by the image\nto that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the\neye, which is h/u ) What a single-lens simple magnifier achieves is that it\nallows the object to be brought closer to the eye than D" + }, + { + "Chapter": "9", + "sentence_range": "663-666", + "Text": "This is also the ratio of the angle subtended by the image\nto that subtended by the object, if placed at D for comfortable viewing (Note that this is not the angle actually subtended by the object at the\neye, which is h/u ) What a single-lens simple magnifier achieves is that it\nallows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity" + }, + { + "Chapter": "9", + "sentence_range": "664-667", + "Text": "(Note that this is not the angle actually subtended by the object at the\neye, which is h/u ) What a single-lens simple magnifier achieves is that it\nallows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity In\nthis case we will have to obtained the angular magnification" + }, + { + "Chapter": "9", + "sentence_range": "665-668", + "Text": ") What a single-lens simple magnifier achieves is that it\nallows the object to be brought closer to the eye than D We will now find the magnification when the image is at infinity In\nthis case we will have to obtained the angular magnification Suppose\nthe object has a height h" + }, + { + "Chapter": "9", + "sentence_range": "666-669", + "Text": "We will now find the magnification when the image is at infinity In\nthis case we will have to obtained the angular magnification Suppose\nthe object has a height h The maximum angle it can subtend, and be\nclearly visible (without a lens), is when it is at the near point, i" + }, + { + "Chapter": "9", + "sentence_range": "667-670", + "Text": "In\nthis case we will have to obtained the angular magnification Suppose\nthe object has a height h The maximum angle it can subtend, and be\nclearly visible (without a lens), is when it is at the near point, i e" + }, + { + "Chapter": "9", + "sentence_range": "668-671", + "Text": "Suppose\nthe object has a height h The maximum angle it can subtend, and be\nclearly visible (without a lens), is when it is at the near point, i e , a distance\nD" + }, + { + "Chapter": "9", + "sentence_range": "669-672", + "Text": "The maximum angle it can subtend, and be\nclearly visible (without a lens), is when it is at the near point, i e , a distance\nD The angle subtended is then given by\ntan \u03b8o\n= \uf8ebDh\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 \u00bb qo\n(9" + }, + { + "Chapter": "9", + "sentence_range": "670-673", + "Text": "e , a distance\nD The angle subtended is then given by\ntan \u03b8o\n= \uf8ebDh\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 \u00bb qo\n(9 40)\nWe now find the angle subtended at the eye by the image when the\nobject is at u" + }, + { + "Chapter": "9", + "sentence_range": "671-674", + "Text": ", a distance\nD The angle subtended is then given by\ntan \u03b8o\n= \uf8ebDh\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 \u00bb qo\n(9 40)\nWe now find the angle subtended at the eye by the image when the\nobject is at u From the relations\n \nh\nv\nm\nh\nu\n\u2032 =\n=\nwe have the angle subtended by the image\n tan \ni\nh\nh\nv\nh\nv\nv u\nu\n\u03b8\n\u2032\n=\n=\n\u22c5\n=\n\u2212\n\u2212\n\u2212\n\u00bbq" + }, + { + "Chapter": "9", + "sentence_range": "672-675", + "Text": "The angle subtended is then given by\ntan \u03b8o\n= \uf8ebDh\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 \u00bb qo\n(9 40)\nWe now find the angle subtended at the eye by the image when the\nobject is at u From the relations\n \nh\nv\nm\nh\nu\n\u2032 =\n=\nwe have the angle subtended by the image\n tan \ni\nh\nh\nv\nh\nv\nv u\nu\n\u03b8\n\u2032\n=\n=\n\u22c5\n=\n\u2212\n\u2212\n\u2212\n\u00bbq The angle subtended by the object, when it\nis at u = \u2013f" + }, + { + "Chapter": "9", + "sentence_range": "673-676", + "Text": "40)\nWe now find the angle subtended at the eye by the image when the\nobject is at u From the relations\n \nh\nv\nm\nh\nu\n\u2032 =\n=\nwe have the angle subtended by the image\n tan \ni\nh\nh\nv\nh\nv\nv u\nu\n\u03b8\n\u2032\n=\n=\n\u22c5\n=\n\u2212\n\u2212\n\u2212\n\u00bbq The angle subtended by the object, when it\nis at u = \u2013f \u03b8i\n= \uf8ebfh\n\uf8ed\uf8ec\n\uf8f8\uf8f7\uf8f6\n(9" + }, + { + "Chapter": "9", + "sentence_range": "674-677", + "Text": "From the relations\n \nh\nv\nm\nh\nu\n\u2032 =\n=\nwe have the angle subtended by the image\n tan \ni\nh\nh\nv\nh\nv\nv u\nu\n\u03b8\n\u2032\n=\n=\n\u22c5\n=\n\u2212\n\u2212\n\u2212\n\u00bbq The angle subtended by the object, when it\nis at u = \u2013f \u03b8i\n= \uf8ebfh\n\uf8ed\uf8ec\n\uf8f8\uf8f7\uf8f6\n(9 41)\nas is clear from Fig" + }, + { + "Chapter": "9", + "sentence_range": "675-678", + "Text": "The angle subtended by the object, when it\nis at u = \u2013f \u03b8i\n= \uf8ebfh\n\uf8ed\uf8ec\n\uf8f8\uf8f7\uf8f6\n(9 41)\nas is clear from Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "676-679", + "Text": "\u03b8i\n= \uf8ebfh\n\uf8ed\uf8ec\n\uf8f8\uf8f7\uf8f6\n(9 41)\nas is clear from Fig 9 23(c)" + }, + { + "Chapter": "9", + "sentence_range": "677-680", + "Text": "41)\nas is clear from Fig 9 23(c) The angular magnification is, therefore\nm\nD\nf\ni\no\n= \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\u03b8\u03b8\uf8f8\uf8f7 =\n(9" + }, + { + "Chapter": "9", + "sentence_range": "678-681", + "Text": "9 23(c) The angular magnification is, therefore\nm\nD\nf\ni\no\n= \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\u03b8\u03b8\uf8f8\uf8f7 =\n(9 42)\nThis is one less than the magnification when the image is at the near\npoint, Eq" + }, + { + "Chapter": "9", + "sentence_range": "679-682", + "Text": "23(c) The angular magnification is, therefore\nm\nD\nf\ni\no\n= \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\u03b8\u03b8\uf8f8\uf8f7 =\n(9 42)\nThis is one less than the magnification when the image is at the near\npoint, Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "680-683", + "Text": "The angular magnification is, therefore\nm\nD\nf\ni\no\n= \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\u03b8\u03b8\uf8f8\uf8f7 =\n(9 42)\nThis is one less than the magnification when the image is at the near\npoint, Eq (9 39), but the viewing is more comfortable and the difference\nin magnification is usually small" + }, + { + "Chapter": "9", + "sentence_range": "681-684", + "Text": "42)\nThis is one less than the magnification when the image is at the near\npoint, Eq (9 39), but the viewing is more comfortable and the difference\nin magnification is usually small In subsequent discussions of optical\ninstruments (microscope and telescope) we shall assume the image to be\nat infinity" + }, + { + "Chapter": "9", + "sentence_range": "682-685", + "Text": "(9 39), but the viewing is more comfortable and the difference\nin magnification is usually small In subsequent discussions of optical\ninstruments (microscope and telescope) we shall assume the image to be\nat infinity Rationalised 2023-24\nRay Optics and\nOptical Instruments\n243\nA simple microscope has a limited maximum magnification (\u00a3 9) for\nrealistic focal lengths" + }, + { + "Chapter": "9", + "sentence_range": "683-686", + "Text": "39), but the viewing is more comfortable and the difference\nin magnification is usually small In subsequent discussions of optical\ninstruments (microscope and telescope) we shall assume the image to be\nat infinity Rationalised 2023-24\nRay Optics and\nOptical Instruments\n243\nA simple microscope has a limited maximum magnification (\u00a3 9) for\nrealistic focal lengths For much larger magnifications, one uses two lenses,\none compounding the effect of the other" + }, + { + "Chapter": "9", + "sentence_range": "684-687", + "Text": "In subsequent discussions of optical\ninstruments (microscope and telescope) we shall assume the image to be\nat infinity Rationalised 2023-24\nRay Optics and\nOptical Instruments\n243\nA simple microscope has a limited maximum magnification (\u00a3 9) for\nrealistic focal lengths For much larger magnifications, one uses two lenses,\none compounding the effect of the other This is known as a compound\nmicroscope" + }, + { + "Chapter": "9", + "sentence_range": "685-688", + "Text": "Rationalised 2023-24\nRay Optics and\nOptical Instruments\n243\nA simple microscope has a limited maximum magnification (\u00a3 9) for\nrealistic focal lengths For much larger magnifications, one uses two lenses,\none compounding the effect of the other This is known as a compound\nmicroscope A schematic diagram of a compound microscope is shown\nin Fig" + }, + { + "Chapter": "9", + "sentence_range": "686-689", + "Text": "For much larger magnifications, one uses two lenses,\none compounding the effect of the other This is known as a compound\nmicroscope A schematic diagram of a compound microscope is shown\nin Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "687-690", + "Text": "This is known as a compound\nmicroscope A schematic diagram of a compound microscope is shown\nin Fig 9 24" + }, + { + "Chapter": "9", + "sentence_range": "688-691", + "Text": "A schematic diagram of a compound microscope is shown\nin Fig 9 24 The lens nearest the object, called the objective, forms a\nreal, inverted, magnified image of the object" + }, + { + "Chapter": "9", + "sentence_range": "689-692", + "Text": "9 24 The lens nearest the object, called the objective, forms a\nreal, inverted, magnified image of the object This serves as the object for\nthe second lens, the eyepiece, which functions essentially like a simple\nmicroscope or magnifier, produces the final image, which is enlarged\nand virtual" + }, + { + "Chapter": "9", + "sentence_range": "690-693", + "Text": "24 The lens nearest the object, called the objective, forms a\nreal, inverted, magnified image of the object This serves as the object for\nthe second lens, the eyepiece, which functions essentially like a simple\nmicroscope or magnifier, produces the final image, which is enlarged\nand virtual The first inverted image is thus near (at or within) the focal\nplane of the eyepiece, at a distance appropriate for final image formation\nat infinity, or a little closer for image formation at the near point" + }, + { + "Chapter": "9", + "sentence_range": "691-694", + "Text": "The lens nearest the object, called the objective, forms a\nreal, inverted, magnified image of the object This serves as the object for\nthe second lens, the eyepiece, which functions essentially like a simple\nmicroscope or magnifier, produces the final image, which is enlarged\nand virtual The first inverted image is thus near (at or within) the focal\nplane of the eyepiece, at a distance appropriate for final image formation\nat infinity, or a little closer for image formation at the near point Clearly,\nthe final image is inverted with respect to the original object" + }, + { + "Chapter": "9", + "sentence_range": "692-695", + "Text": "This serves as the object for\nthe second lens, the eyepiece, which functions essentially like a simple\nmicroscope or magnifier, produces the final image, which is enlarged\nand virtual The first inverted image is thus near (at or within) the focal\nplane of the eyepiece, at a distance appropriate for final image formation\nat infinity, or a little closer for image formation at the near point Clearly,\nthe final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope" + }, + { + "Chapter": "9", + "sentence_range": "693-696", + "Text": "The first inverted image is thus near (at or within) the focal\nplane of the eyepiece, at a distance appropriate for final image formation\nat infinity, or a little closer for image formation at the near point Clearly,\nthe final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope The ray diagram of Fig" + }, + { + "Chapter": "9", + "sentence_range": "694-697", + "Text": "Clearly,\nthe final image is inverted with respect to the original object We now obtain the magnification due to a compound microscope The ray diagram of Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "695-698", + "Text": "We now obtain the magnification due to a compound microscope The ray diagram of Fig 9 24 shows that the (linear) magnification due to\nthe objective, namely h\u00a2/h, equals\nO\no\nh\nL\nm\nh\nf\n\u2032\n=\n=\n(9" + }, + { + "Chapter": "9", + "sentence_range": "696-699", + "Text": "The ray diagram of Fig 9 24 shows that the (linear) magnification due to\nthe objective, namely h\u00a2/h, equals\nO\no\nh\nL\nm\nh\nf\n\u2032\n=\n=\n(9 43)\nwhere we have used the result\ntan\u03b2 = \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 =\n\u2032\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\nfh\nh\nL\no\nHere h\u00a2 is the size of the first image, the object size being h and fo\nbeing the focal length of the objective" + }, + { + "Chapter": "9", + "sentence_range": "697-700", + "Text": "9 24 shows that the (linear) magnification due to\nthe objective, namely h\u00a2/h, equals\nO\no\nh\nL\nm\nh\nf\n\u2032\n=\n=\n(9 43)\nwhere we have used the result\ntan\u03b2 = \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 =\n\u2032\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\nfh\nh\nL\no\nHere h\u00a2 is the size of the first image, the object size being h and fo\nbeing the focal length of the objective The first image is formed near the\nfocal point of the eyepiece" + }, + { + "Chapter": "9", + "sentence_range": "698-701", + "Text": "24 shows that the (linear) magnification due to\nthe objective, namely h\u00a2/h, equals\nO\no\nh\nL\nm\nh\nf\n\u2032\n=\n=\n(9 43)\nwhere we have used the result\ntan\u03b2 = \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 =\n\u2032\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\nfh\nh\nL\no\nHere h\u00a2 is the size of the first image, the object size being h and fo\nbeing the focal length of the objective The first image is formed near the\nfocal point of the eyepiece The distance L, i" + }, + { + "Chapter": "9", + "sentence_range": "699-702", + "Text": "43)\nwhere we have used the result\ntan\u03b2 = \uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7 =\n\u2032\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\nfh\nh\nL\no\nHere h\u00a2 is the size of the first image, the object size being h and fo\nbeing the focal length of the objective The first image is formed near the\nfocal point of the eyepiece The distance L, i e" + }, + { + "Chapter": "9", + "sentence_range": "700-703", + "Text": "The first image is formed near the\nfocal point of the eyepiece The distance L, i e , the distance between the\nsecond focal point of the objective and the first focal point of the eyepiece\n(focal length fe) is called the tube length of the compound microscope" + }, + { + "Chapter": "9", + "sentence_range": "701-704", + "Text": "The distance L, i e , the distance between the\nsecond focal point of the objective and the first focal point of the eyepiece\n(focal length fe) is called the tube length of the compound microscope The world\u2019s largest optical telescopes\nhttp://astro" + }, + { + "Chapter": "9", + "sentence_range": "702-705", + "Text": "e , the distance between the\nsecond focal point of the objective and the first focal point of the eyepiece\n(focal length fe) is called the tube length of the compound microscope The world\u2019s largest optical telescopes\nhttp://astro nineplanets" + }, + { + "Chapter": "9", + "sentence_range": "703-706", + "Text": ", the distance between the\nsecond focal point of the objective and the first focal point of the eyepiece\n(focal length fe) is called the tube length of the compound microscope The world\u2019s largest optical telescopes\nhttp://astro nineplanets org/bigeyes" + }, + { + "Chapter": "9", + "sentence_range": "704-707", + "Text": "The world\u2019s largest optical telescopes\nhttp://astro nineplanets org/bigeyes html\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "705-708", + "Text": "nineplanets org/bigeyes html\nFIGURE 9 24 Ray diagram for the formation of image by a\ncompound microscope" + }, + { + "Chapter": "9", + "sentence_range": "706-709", + "Text": "org/bigeyes html\nFIGURE 9 24 Ray diagram for the formation of image by a\ncompound microscope Rationalised 2023-24\nPhysics\n244\nAs the first inverted image is near the focal point of the eyepiece, we\nuse the result from the discussion above for the simple microscope to\nobtain the (angular) magnification me due to it [Eq" + }, + { + "Chapter": "9", + "sentence_range": "707-710", + "Text": "html\nFIGURE 9 24 Ray diagram for the formation of image by a\ncompound microscope Rationalised 2023-24\nPhysics\n244\nAs the first inverted image is near the focal point of the eyepiece, we\nuse the result from the discussion above for the simple microscope to\nobtain the (angular) magnification me due to it [Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "708-711", + "Text": "24 Ray diagram for the formation of image by a\ncompound microscope Rationalised 2023-24\nPhysics\n244\nAs the first inverted image is near the focal point of the eyepiece, we\nuse the result from the discussion above for the simple microscope to\nobtain the (angular) magnification me due to it [Eq (9 39)], when the\nfinal image is formed at the near point, is\nm\nfD\ne\ne\n=\n1+\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n[9" + }, + { + "Chapter": "9", + "sentence_range": "709-712", + "Text": "Rationalised 2023-24\nPhysics\n244\nAs the first inverted image is near the focal point of the eyepiece, we\nuse the result from the discussion above for the simple microscope to\nobtain the (angular) magnification me due to it [Eq (9 39)], when the\nfinal image is formed at the near point, is\nm\nfD\ne\ne\n=\n1+\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n[9 44(a)]\nWhen the final image is formed at infinity, the angular magnification\ndue to the eyepiece [Eq" + }, + { + "Chapter": "9", + "sentence_range": "710-713", + "Text": "(9 39)], when the\nfinal image is formed at the near point, is\nm\nfD\ne\ne\n=\n1+\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n[9 44(a)]\nWhen the final image is formed at infinity, the angular magnification\ndue to the eyepiece [Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "711-714", + "Text": "39)], when the\nfinal image is formed at the near point, is\nm\nfD\ne\ne\n=\n1+\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n[9 44(a)]\nWhen the final image is formed at infinity, the angular magnification\ndue to the eyepiece [Eq (9 42)] is\nme = (D/fe )\n[9" + }, + { + "Chapter": "9", + "sentence_range": "712-715", + "Text": "44(a)]\nWhen the final image is formed at infinity, the angular magnification\ndue to the eyepiece [Eq (9 42)] is\nme = (D/fe )\n[9 44(b)]\nThus, the total magnification [(according to Eq" + }, + { + "Chapter": "9", + "sentence_range": "713-716", + "Text": "(9 42)] is\nme = (D/fe )\n[9 44(b)]\nThus, the total magnification [(according to Eq (9" + }, + { + "Chapter": "9", + "sentence_range": "714-717", + "Text": "42)] is\nme = (D/fe )\n[9 44(b)]\nThus, the total magnification [(according to Eq (9 33)], when the\nimage is formed at infinity, is\nm\nm m\nfL\nfD\no\ne\no\ne\n=\n=\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f8\n\uf8f7 (9" + }, + { + "Chapter": "9", + "sentence_range": "715-718", + "Text": "44(b)]\nThus, the total magnification [(according to Eq (9 33)], when the\nimage is formed at infinity, is\nm\nm m\nfL\nfD\no\ne\no\ne\n=\n=\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f8\n\uf8f7 (9 45)\nClearly, to achieve a large magnification of a small object (hence the\nname microscope), the objective and eyepiece should have small focal\nlengths" + }, + { + "Chapter": "9", + "sentence_range": "716-719", + "Text": "(9 33)], when the\nimage is formed at infinity, is\nm\nm m\nfL\nfD\no\ne\no\ne\n=\n=\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f8\n\uf8f7 (9 45)\nClearly, to achieve a large magnification of a small object (hence the\nname microscope), the objective and eyepiece should have small focal\nlengths In practice, it is difficult to make the focal length much smaller\nthan 1 cm" + }, + { + "Chapter": "9", + "sentence_range": "717-720", + "Text": "33)], when the\nimage is formed at infinity, is\nm\nm m\nfL\nfD\no\ne\no\ne\n=\n=\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f8\n\uf8f7 (9 45)\nClearly, to achieve a large magnification of a small object (hence the\nname microscope), the objective and eyepiece should have small focal\nlengths In practice, it is difficult to make the focal length much smaller\nthan 1 cm Also large lenses are required to make L large" + }, + { + "Chapter": "9", + "sentence_range": "718-721", + "Text": "45)\nClearly, to achieve a large magnification of a small object (hence the\nname microscope), the objective and eyepiece should have small focal\nlengths In practice, it is difficult to make the focal length much smaller\nthan 1 cm Also large lenses are required to make L large For example, with an objective with fo = 1" + }, + { + "Chapter": "9", + "sentence_range": "719-722", + "Text": "In practice, it is difficult to make the focal length much smaller\nthan 1 cm Also large lenses are required to make L large For example, with an objective with fo = 1 0 cm, and an eyepiece with\nfocal length fe = 2" + }, + { + "Chapter": "9", + "sentence_range": "720-723", + "Text": "Also large lenses are required to make L large For example, with an objective with fo = 1 0 cm, and an eyepiece with\nfocal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is\nm\nm m\nfL\nfD\no\ne\no\ne\n=\n=\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f8\n\uf8f7\n \n20\n25\n250\n1\n2\n\ufffd\n\ufffd\n\ufffd\nVarious other factors such as illumination of the object, contribute to\nthe quality and visibility of the image" + }, + { + "Chapter": "9", + "sentence_range": "721-724", + "Text": "For example, with an objective with fo = 1 0 cm, and an eyepiece with\nfocal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is\nm\nm m\nfL\nfD\no\ne\no\ne\n=\n=\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f8\n\uf8f7\n \n20\n25\n250\n1\n2\n\ufffd\n\ufffd\n\ufffd\nVarious other factors such as illumination of the object, contribute to\nthe quality and visibility of the image In modern microscopes, multi-\ncomponent lenses are used for both the objective and the eyepiece to\nimprove image quality by minimising various optical aberrations (defects)\nin lenses" + }, + { + "Chapter": "9", + "sentence_range": "722-725", + "Text": "0 cm, and an eyepiece with\nfocal length fe = 2 0 cm, and a tube length of 20 cm, the magnification is\nm\nm m\nfL\nfD\no\ne\no\ne\n=\n=\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f8\n\uf8f7\n \n20\n25\n250\n1\n2\n\ufffd\n\ufffd\n\ufffd\nVarious other factors such as illumination of the object, contribute to\nthe quality and visibility of the image In modern microscopes, multi-\ncomponent lenses are used for both the objective and the eyepiece to\nimprove image quality by minimising various optical aberrations (defects)\nin lenses 9" + }, + { + "Chapter": "9", + "sentence_range": "723-726", + "Text": "0 cm, and a tube length of 20 cm, the magnification is\nm\nm m\nfL\nfD\no\ne\no\ne\n=\n=\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f7\uf8f8\n\uf8eb\n\uf8ec\uf8ed\n\uf8f6\n\uf8f8\n\uf8f7\n \n20\n25\n250\n1\n2\n\ufffd\n\ufffd\n\ufffd\nVarious other factors such as illumination of the object, contribute to\nthe quality and visibility of the image In modern microscopes, multi-\ncomponent lenses are used for both the objective and the eyepiece to\nimprove image quality by minimising various optical aberrations (defects)\nin lenses 9 7" + }, + { + "Chapter": "9", + "sentence_range": "724-727", + "Text": "In modern microscopes, multi-\ncomponent lenses are used for both the objective and the eyepiece to\nimprove image quality by minimising various optical aberrations (defects)\nin lenses 9 7 2 Telescope\nThe telescope is used to provide angular magnification of distant objects\n(Fig" + }, + { + "Chapter": "9", + "sentence_range": "725-728", + "Text": "9 7 2 Telescope\nThe telescope is used to provide angular magnification of distant objects\n(Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "726-729", + "Text": "7 2 Telescope\nThe telescope is used to provide angular magnification of distant objects\n(Fig 9 25)" + }, + { + "Chapter": "9", + "sentence_range": "727-730", + "Text": "2 Telescope\nThe telescope is used to provide angular magnification of distant objects\n(Fig 9 25) It also has an objective and an eyepiece" + }, + { + "Chapter": "9", + "sentence_range": "728-731", + "Text": "9 25) It also has an objective and an eyepiece But here, the objective\nhas a large focal length and a much larger aperture than the eyepiece" + }, + { + "Chapter": "9", + "sentence_range": "729-732", + "Text": "25) It also has an objective and an eyepiece But here, the objective\nhas a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed\nin the tube at its second focal point" + }, + { + "Chapter": "9", + "sentence_range": "730-733", + "Text": "It also has an objective and an eyepiece But here, the objective\nhas a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed\nin the tube at its second focal point The eyepiece magnifies this image\nproducing a final inverted image" + }, + { + "Chapter": "9", + "sentence_range": "731-734", + "Text": "But here, the objective\nhas a large focal length and a much larger aperture than the eyepiece Light from a distant object enters the objective and a real image is formed\nin the tube at its second focal point The eyepiece magnifies this image\nproducing a final inverted image The magnifying power m is the ratio of\nthe angle b subtended at the eye by the final image to the angle a which\nthe object subtends at the lens or the eye" + }, + { + "Chapter": "9", + "sentence_range": "732-735", + "Text": "Light from a distant object enters the objective and a real image is formed\nin the tube at its second focal point The eyepiece magnifies this image\nproducing a final inverted image The magnifying power m is the ratio of\nthe angle b subtended at the eye by the final image to the angle a which\nthe object subtends at the lens or the eye Hence" + }, + { + "Chapter": "9", + "sentence_range": "733-736", + "Text": "The eyepiece magnifies this image\nproducing a final inverted image The magnifying power m is the ratio of\nthe angle b subtended at the eye by the final image to the angle a which\nthe object subtends at the lens or the eye Hence o\no\ne\ne\nf\nf\nh\nm\nf\nh\nf\n\ufffd\n\ufffd\n\ufffd\n\ufffd\ufffd\n (9" + }, + { + "Chapter": "9", + "sentence_range": "734-737", + "Text": "The magnifying power m is the ratio of\nthe angle b subtended at the eye by the final image to the angle a which\nthe object subtends at the lens or the eye Hence o\no\ne\ne\nf\nf\nh\nm\nf\nh\nf\n\ufffd\n\ufffd\n\ufffd\n\ufffd\ufffd\n (9 46)\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n245\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "735-738", + "Text": "Hence o\no\ne\ne\nf\nf\nh\nm\nf\nh\nf\n\ufffd\n\ufffd\n\ufffd\n\ufffd\ufffd\n (9 46)\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n245\nFIGURE 9 25 A refracting telescope" + }, + { + "Chapter": "9", + "sentence_range": "736-739", + "Text": "o\no\ne\ne\nf\nf\nh\nm\nf\nh\nf\n\ufffd\n\ufffd\n\ufffd\n\ufffd\ufffd\n (9 46)\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n245\nFIGURE 9 25 A refracting telescope In this case, the length of the telescope tube is fo + fe" + }, + { + "Chapter": "9", + "sentence_range": "737-740", + "Text": "46)\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n245\nFIGURE 9 25 A refracting telescope In this case, the length of the telescope tube is fo + fe Terrestrial telescopes have, in addition, a pair of inverting lenses to\nmake the final image erect" + }, + { + "Chapter": "9", + "sentence_range": "738-741", + "Text": "25 A refracting telescope In this case, the length of the telescope tube is fo + fe Terrestrial telescopes have, in addition, a pair of inverting lenses to\nmake the final image erect Refracting telescopes can be used both for\nterrestrial and astronomical observations" + }, + { + "Chapter": "9", + "sentence_range": "739-742", + "Text": "In this case, the length of the telescope tube is fo + fe Terrestrial telescopes have, in addition, a pair of inverting lenses to\nmake the final image erect Refracting telescopes can be used both for\nterrestrial and astronomical observations For example, consider\na telescope whose objective has a focal length of 100 cm and the eyepiece\na focal length of 1 cm" + }, + { + "Chapter": "9", + "sentence_range": "740-743", + "Text": "Terrestrial telescopes have, in addition, a pair of inverting lenses to\nmake the final image erect Refracting telescopes can be used both for\nterrestrial and astronomical observations For example, consider\na telescope whose objective has a focal length of 100 cm and the eyepiece\na focal length of 1 cm The magnifying power of this telescope is\nm = 100/1 = 100" + }, + { + "Chapter": "9", + "sentence_range": "741-744", + "Text": "Refracting telescopes can be used both for\nterrestrial and astronomical observations For example, consider\na telescope whose objective has a focal length of 100 cm and the eyepiece\na focal length of 1 cm The magnifying power of this telescope is\nm = 100/1 = 100 Let us consider a pair of stars of actual separation 1\u00a2 (one minute of\narc)" + }, + { + "Chapter": "9", + "sentence_range": "742-745", + "Text": "For example, consider\na telescope whose objective has a focal length of 100 cm and the eyepiece\na focal length of 1 cm The magnifying power of this telescope is\nm = 100/1 = 100 Let us consider a pair of stars of actual separation 1\u00a2 (one minute of\narc) The stars appear as though they are separated by an angle of 100 \u00d7\n1\u00a2 = 100\u00a2 =1" + }, + { + "Chapter": "9", + "sentence_range": "743-746", + "Text": "The magnifying power of this telescope is\nm = 100/1 = 100 Let us consider a pair of stars of actual separation 1\u00a2 (one minute of\narc) The stars appear as though they are separated by an angle of 100 \u00d7\n1\u00a2 = 100\u00a2 =1 67\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "744-747", + "Text": "Let us consider a pair of stars of actual separation 1\u00a2 (one minute of\narc) The stars appear as though they are separated by an angle of 100 \u00d7\n1\u00a2 = 100\u00a2 =1 67\u00b0 The main considerations with an astronomical telescope are its light\ngathering power and its resolution or resolving power" + }, + { + "Chapter": "9", + "sentence_range": "745-748", + "Text": "The stars appear as though they are separated by an angle of 100 \u00d7\n1\u00a2 = 100\u00a2 =1 67\u00b0 The main considerations with an astronomical telescope are its light\ngathering power and its resolution or resolving power The former clearly\ndepends on the area of the objective" + }, + { + "Chapter": "9", + "sentence_range": "746-749", + "Text": "67\u00b0 The main considerations with an astronomical telescope are its light\ngathering power and its resolution or resolving power The former clearly\ndepends on the area of the objective With larger diameters, fainter objects\ncan be observed" + }, + { + "Chapter": "9", + "sentence_range": "747-750", + "Text": "The main considerations with an astronomical telescope are its light\ngathering power and its resolution or resolving power The former clearly\ndepends on the area of the objective With larger diameters, fainter objects\ncan be observed The resolving power, or the ability to observe two objects\ndistinctly, which are in very nearly the same direction, also depends on\nthe diameter of the objective" + }, + { + "Chapter": "9", + "sentence_range": "748-751", + "Text": "The former clearly\ndepends on the area of the objective With larger diameters, fainter objects\ncan be observed The resolving power, or the ability to observe two objects\ndistinctly, which are in very nearly the same direction, also depends on\nthe diameter of the objective So, the desirable aim in optical telescopes is\nto make them with objective of large diameter" + }, + { + "Chapter": "9", + "sentence_range": "749-752", + "Text": "With larger diameters, fainter objects\ncan be observed The resolving power, or the ability to observe two objects\ndistinctly, which are in very nearly the same direction, also depends on\nthe diameter of the objective So, the desirable aim in optical telescopes is\nto make them with objective of large diameter The largest lens objective\nin use has a diameter of 40 inch (~1" + }, + { + "Chapter": "9", + "sentence_range": "750-753", + "Text": "The resolving power, or the ability to observe two objects\ndistinctly, which are in very nearly the same direction, also depends on\nthe diameter of the objective So, the desirable aim in optical telescopes is\nto make them with objective of large diameter The largest lens objective\nin use has a diameter of 40 inch (~1 02 m)" + }, + { + "Chapter": "9", + "sentence_range": "751-754", + "Text": "So, the desirable aim in optical telescopes is\nto make them with objective of large diameter The largest lens objective\nin use has a diameter of 40 inch (~1 02 m) It is at the Yerkes Observatory\nin Wisconsin, USA" + }, + { + "Chapter": "9", + "sentence_range": "752-755", + "Text": "The largest lens objective\nin use has a diameter of 40 inch (~1 02 m) It is at the Yerkes Observatory\nin Wisconsin, USA Such big lenses tend to be very heavy and therefore,\ndifficult to make and support by their edges" + }, + { + "Chapter": "9", + "sentence_range": "753-756", + "Text": "02 m) It is at the Yerkes Observatory\nin Wisconsin, USA Such big lenses tend to be very heavy and therefore,\ndifficult to make and support by their edges Further, it is rather difficult\nand expensive to make such large sized lenses which form images that\nare free from any kind of chromatic aberration and distortions" + }, + { + "Chapter": "9", + "sentence_range": "754-757", + "Text": "It is at the Yerkes Observatory\nin Wisconsin, USA Such big lenses tend to be very heavy and therefore,\ndifficult to make and support by their edges Further, it is rather difficult\nand expensive to make such large sized lenses which form images that\nare free from any kind of chromatic aberration and distortions For these reasons, modern telescopes use a concave mirror rather\nthan a lens for the objective" + }, + { + "Chapter": "9", + "sentence_range": "755-758", + "Text": "Such big lenses tend to be very heavy and therefore,\ndifficult to make and support by their edges Further, it is rather difficult\nand expensive to make such large sized lenses which form images that\nare free from any kind of chromatic aberration and distortions For these reasons, modern telescopes use a concave mirror rather\nthan a lens for the objective Telescopes with mirror objectives are called\nreflecting telescopes" + }, + { + "Chapter": "9", + "sentence_range": "756-759", + "Text": "Further, it is rather difficult\nand expensive to make such large sized lenses which form images that\nare free from any kind of chromatic aberration and distortions For these reasons, modern telescopes use a concave mirror rather\nthan a lens for the objective Telescopes with mirror objectives are called\nreflecting telescopes There is no chromatic aberration in a mirror" + }, + { + "Chapter": "9", + "sentence_range": "757-760", + "Text": "For these reasons, modern telescopes use a concave mirror rather\nthan a lens for the objective Telescopes with mirror objectives are called\nreflecting telescopes There is no chromatic aberration in a mirror Mechanical support is much less of a problem since a mirror weighs\nmuch less than a lens of equivalent optical quality, and can be supported\nover its entire back surface, not just over its rim" + }, + { + "Chapter": "9", + "sentence_range": "758-761", + "Text": "Telescopes with mirror objectives are called\nreflecting telescopes There is no chromatic aberration in a mirror Mechanical support is much less of a problem since a mirror weighs\nmuch less than a lens of equivalent optical quality, and can be supported\nover its entire back surface, not just over its rim One obvious problem\nwith a reflecting telescope is that the objective mirror focusses light inside\nRationalised 2023-24\nPhysics\n246\nSUMMARY\n1" + }, + { + "Chapter": "9", + "sentence_range": "759-762", + "Text": "There is no chromatic aberration in a mirror Mechanical support is much less of a problem since a mirror weighs\nmuch less than a lens of equivalent optical quality, and can be supported\nover its entire back surface, not just over its rim One obvious problem\nwith a reflecting telescope is that the objective mirror focusses light inside\nRationalised 2023-24\nPhysics\n246\nSUMMARY\n1 Reflection is governed by the equation \u00d0i = \u00d0r\u00a2 and refraction by the\nSnell\u2019s law, sini/sinr = n, where the incident ray, reflected ray, refracted\nray and normal lie in the same plane" + }, + { + "Chapter": "9", + "sentence_range": "760-763", + "Text": "Mechanical support is much less of a problem since a mirror weighs\nmuch less than a lens of equivalent optical quality, and can be supported\nover its entire back surface, not just over its rim One obvious problem\nwith a reflecting telescope is that the objective mirror focusses light inside\nRationalised 2023-24\nPhysics\n246\nSUMMARY\n1 Reflection is governed by the equation \u00d0i = \u00d0r\u00a2 and refraction by the\nSnell\u2019s law, sini/sinr = n, where the incident ray, reflected ray, refracted\nray and normal lie in the same plane Angles of incidence, reflection\nand refraction are i, r \u00a2 and r, respectively" + }, + { + "Chapter": "9", + "sentence_range": "761-764", + "Text": "One obvious problem\nwith a reflecting telescope is that the objective mirror focusses light inside\nRationalised 2023-24\nPhysics\n246\nSUMMARY\n1 Reflection is governed by the equation \u00d0i = \u00d0r\u00a2 and refraction by the\nSnell\u2019s law, sini/sinr = n, where the incident ray, reflected ray, refracted\nray and normal lie in the same plane Angles of incidence, reflection\nand refraction are i, r \u00a2 and r, respectively 2" + }, + { + "Chapter": "9", + "sentence_range": "762-765", + "Text": "Reflection is governed by the equation \u00d0i = \u00d0r\u00a2 and refraction by the\nSnell\u2019s law, sini/sinr = n, where the incident ray, reflected ray, refracted\nray and normal lie in the same plane Angles of incidence, reflection\nand refraction are i, r \u00a2 and r, respectively 2 The critical angle of incidence ic for a ray incident from a denser to rarer\nmedium, is that angle for which the angle of refraction is 90\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "763-766", + "Text": "Angles of incidence, reflection\nand refraction are i, r \u00a2 and r, respectively 2 The critical angle of incidence ic for a ray incident from a denser to rarer\nmedium, is that angle for which the angle of refraction is 90\u00b0 For\ni > ic, total internal reflection occurs" + }, + { + "Chapter": "9", + "sentence_range": "764-767", + "Text": "2 The critical angle of incidence ic for a ray incident from a denser to rarer\nmedium, is that angle for which the angle of refraction is 90\u00b0 For\ni > ic, total internal reflection occurs Multiple internal reflections in\ndiamond (ic @ 24" + }, + { + "Chapter": "9", + "sentence_range": "765-768", + "Text": "The critical angle of incidence ic for a ray incident from a denser to rarer\nmedium, is that angle for which the angle of refraction is 90\u00b0 For\ni > ic, total internal reflection occurs Multiple internal reflections in\ndiamond (ic @ 24 4\u00b0), totally reflecting prisms and mirage, are some\nexamples of total internal reflection" + }, + { + "Chapter": "9", + "sentence_range": "766-769", + "Text": "For\ni > ic, total internal reflection occurs Multiple internal reflections in\ndiamond (ic @ 24 4\u00b0), totally reflecting prisms and mirage, are some\nexamples of total internal reflection Optical fibres consist of glass\nfibres coated with a thin layer of material of lower refractive index" + }, + { + "Chapter": "9", + "sentence_range": "767-770", + "Text": "Multiple internal reflections in\ndiamond (ic @ 24 4\u00b0), totally reflecting prisms and mirage, are some\nexamples of total internal reflection Optical fibres consist of glass\nfibres coated with a thin layer of material of lower refractive index Light incident at an angle at one end comes out at the other, after\nmultiple internal reflections, even if the fibre is bent" + }, + { + "Chapter": "9", + "sentence_range": "768-771", + "Text": "4\u00b0), totally reflecting prisms and mirage, are some\nexamples of total internal reflection Optical fibres consist of glass\nfibres coated with a thin layer of material of lower refractive index Light incident at an angle at one end comes out at the other, after\nmultiple internal reflections, even if the fibre is bent FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "769-772", + "Text": "Optical fibres consist of glass\nfibres coated with a thin layer of material of lower refractive index Light incident at an angle at one end comes out at the other, after\nmultiple internal reflections, even if the fibre is bent FIGURE 9 26 Schematic diagram of a reflecting telescope (Cassegrain)" + }, + { + "Chapter": "9", + "sentence_range": "770-773", + "Text": "Light incident at an angle at one end comes out at the other, after\nmultiple internal reflections, even if the fibre is bent FIGURE 9 26 Schematic diagram of a reflecting telescope (Cassegrain) the telescope tube" + }, + { + "Chapter": "9", + "sentence_range": "771-774", + "Text": "FIGURE 9 26 Schematic diagram of a reflecting telescope (Cassegrain) the telescope tube One must have an eyepiece and the observer right\nthere, obstructing some light (depending on the size of the observer cage)" + }, + { + "Chapter": "9", + "sentence_range": "772-775", + "Text": "26 Schematic diagram of a reflecting telescope (Cassegrain) the telescope tube One must have an eyepiece and the observer right\nthere, obstructing some light (depending on the size of the observer cage) This is what is done in the very large 200 inch (~5" + }, + { + "Chapter": "9", + "sentence_range": "773-776", + "Text": "the telescope tube One must have an eyepiece and the observer right\nthere, obstructing some light (depending on the size of the observer cage) This is what is done in the very large 200 inch (~5 08 m) diameters, Mt" + }, + { + "Chapter": "9", + "sentence_range": "774-777", + "Text": "One must have an eyepiece and the observer right\nthere, obstructing some light (depending on the size of the observer cage) This is what is done in the very large 200 inch (~5 08 m) diameters, Mt Palomar telescope, California" + }, + { + "Chapter": "9", + "sentence_range": "775-778", + "Text": "This is what is done in the very large 200 inch (~5 08 m) diameters, Mt Palomar telescope, California The viewer sits near the focal point of the\nmirror, in a small cage" + }, + { + "Chapter": "9", + "sentence_range": "776-779", + "Text": "08 m) diameters, Mt Palomar telescope, California The viewer sits near the focal point of the\nmirror, in a small cage Another solution to the problem is to deflect the\nlight being focussed by another mirror" + }, + { + "Chapter": "9", + "sentence_range": "777-780", + "Text": "Palomar telescope, California The viewer sits near the focal point of the\nmirror, in a small cage Another solution to the problem is to deflect the\nlight being focussed by another mirror One such arrangement using a\nconvex secondary mirror to focus the incident light, which now passes\nthrough a hole in the objective primary mirror, is shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "778-781", + "Text": "The viewer sits near the focal point of the\nmirror, in a small cage Another solution to the problem is to deflect the\nlight being focussed by another mirror One such arrangement using a\nconvex secondary mirror to focus the incident light, which now passes\nthrough a hole in the objective primary mirror, is shown in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "779-782", + "Text": "Another solution to the problem is to deflect the\nlight being focussed by another mirror One such arrangement using a\nconvex secondary mirror to focus the incident light, which now passes\nthrough a hole in the objective primary mirror, is shown in Fig 9 26" + }, + { + "Chapter": "9", + "sentence_range": "780-783", + "Text": "One such arrangement using a\nconvex secondary mirror to focus the incident light, which now passes\nthrough a hole in the objective primary mirror, is shown in Fig 9 26 This is known as a Cassegrain telescope, after its inventor" + }, + { + "Chapter": "9", + "sentence_range": "781-784", + "Text": "9 26 This is known as a Cassegrain telescope, after its inventor It has the\nadvantages of a large focal length in a short telescope" + }, + { + "Chapter": "9", + "sentence_range": "782-785", + "Text": "26 This is known as a Cassegrain telescope, after its inventor It has the\nadvantages of a large focal length in a short telescope The largest telescope\nin India is in Kavalur, Tamil Nadu" + }, + { + "Chapter": "9", + "sentence_range": "783-786", + "Text": "This is known as a Cassegrain telescope, after its inventor It has the\nadvantages of a large focal length in a short telescope The largest telescope\nin India is in Kavalur, Tamil Nadu It is a 2" + }, + { + "Chapter": "9", + "sentence_range": "784-787", + "Text": "It has the\nadvantages of a large focal length in a short telescope The largest telescope\nin India is in Kavalur, Tamil Nadu It is a 2 34 m diameter reflecting\ntelescope (Cassegrain)" + }, + { + "Chapter": "9", + "sentence_range": "785-788", + "Text": "The largest telescope\nin India is in Kavalur, Tamil Nadu It is a 2 34 m diameter reflecting\ntelescope (Cassegrain) It was ground, polished, set up, and is being used\nby the Indian Institute of Astrophysics, Bangalore" + }, + { + "Chapter": "9", + "sentence_range": "786-789", + "Text": "It is a 2 34 m diameter reflecting\ntelescope (Cassegrain) It was ground, polished, set up, and is being used\nby the Indian Institute of Astrophysics, Bangalore The largest reflecting\ntelescopes in the world are the pair of Keck telescopes in Hawaii, USA,\nwith a reflector of 10 metre in diameter" + }, + { + "Chapter": "9", + "sentence_range": "787-790", + "Text": "34 m diameter reflecting\ntelescope (Cassegrain) It was ground, polished, set up, and is being used\nby the Indian Institute of Astrophysics, Bangalore The largest reflecting\ntelescopes in the world are the pair of Keck telescopes in Hawaii, USA,\nwith a reflector of 10 metre in diameter Rationalised 2023-24\nRay Optics and\nOptical Instruments\n247\n3" + }, + { + "Chapter": "9", + "sentence_range": "788-791", + "Text": "It was ground, polished, set up, and is being used\nby the Indian Institute of Astrophysics, Bangalore The largest reflecting\ntelescopes in the world are the pair of Keck telescopes in Hawaii, USA,\nwith a reflector of 10 metre in diameter Rationalised 2023-24\nRay Optics and\nOptical Instruments\n247\n3 Cartesian sign convention: Distances measured in the same direction\nas the incident light are positive; those measured in the opposite\ndirection are negative" + }, + { + "Chapter": "9", + "sentence_range": "789-792", + "Text": "The largest reflecting\ntelescopes in the world are the pair of Keck telescopes in Hawaii, USA,\nwith a reflector of 10 metre in diameter Rationalised 2023-24\nRay Optics and\nOptical Instruments\n247\n3 Cartesian sign convention: Distances measured in the same direction\nas the incident light are positive; those measured in the opposite\ndirection are negative All distances are measured from the pole/optic\ncentre of the mirror/lens on the principal axis" + }, + { + "Chapter": "9", + "sentence_range": "790-793", + "Text": "Rationalised 2023-24\nRay Optics and\nOptical Instruments\n247\n3 Cartesian sign convention: Distances measured in the same direction\nas the incident light are positive; those measured in the opposite\ndirection are negative All distances are measured from the pole/optic\ncentre of the mirror/lens on the principal axis The heights measured\nupwards above x-axis and normal to the principal axis of the mirror/\nlens are taken as positive" + }, + { + "Chapter": "9", + "sentence_range": "791-794", + "Text": "Cartesian sign convention: Distances measured in the same direction\nas the incident light are positive; those measured in the opposite\ndirection are negative All distances are measured from the pole/optic\ncentre of the mirror/lens on the principal axis The heights measured\nupwards above x-axis and normal to the principal axis of the mirror/\nlens are taken as positive The heights measured downwards are taken\nas negative" + }, + { + "Chapter": "9", + "sentence_range": "792-795", + "Text": "All distances are measured from the pole/optic\ncentre of the mirror/lens on the principal axis The heights measured\nupwards above x-axis and normal to the principal axis of the mirror/\nlens are taken as positive The heights measured downwards are taken\nas negative 4" + }, + { + "Chapter": "9", + "sentence_range": "793-796", + "Text": "The heights measured\nupwards above x-axis and normal to the principal axis of the mirror/\nlens are taken as positive The heights measured downwards are taken\nas negative 4 Mirror equation:\n1\n1\n1\nv\nu\nf\n+\n=\nwhere u and v are object and image distances, respectively and f is the\nfocal length of the mirror" + }, + { + "Chapter": "9", + "sentence_range": "794-797", + "Text": "The heights measured downwards are taken\nas negative 4 Mirror equation:\n1\n1\n1\nv\nu\nf\n+\n=\nwhere u and v are object and image distances, respectively and f is the\nfocal length of the mirror f is (approximately) half the radius of\ncurvature R" + }, + { + "Chapter": "9", + "sentence_range": "795-798", + "Text": "4 Mirror equation:\n1\n1\n1\nv\nu\nf\n+\n=\nwhere u and v are object and image distances, respectively and f is the\nfocal length of the mirror f is (approximately) half the radius of\ncurvature R f is negative for concave mirror; f is positive for a convex\nmirror" + }, + { + "Chapter": "9", + "sentence_range": "796-799", + "Text": "Mirror equation:\n1\n1\n1\nv\nu\nf\n+\n=\nwhere u and v are object and image distances, respectively and f is the\nfocal length of the mirror f is (approximately) half the radius of\ncurvature R f is negative for concave mirror; f is positive for a convex\nmirror 5" + }, + { + "Chapter": "9", + "sentence_range": "797-800", + "Text": "f is (approximately) half the radius of\ncurvature R f is negative for concave mirror; f is positive for a convex\nmirror 5 For a prism of the angle A, of refractive index n 2 placed in a medium\nof refractive index n1,\nn\nn\nn\nA\nD\nA\nm\n21\n2\n1\n2\n2\n=\n=\n+\n(\n)\n\uf8ee\uf8f0\n\uf8f9\uf8fb\n(\n)\nsin\n/\nsin\n/\nwhere Dm is the angle of minimum deviation" + }, + { + "Chapter": "9", + "sentence_range": "798-801", + "Text": "f is negative for concave mirror; f is positive for a convex\nmirror 5 For a prism of the angle A, of refractive index n 2 placed in a medium\nof refractive index n1,\nn\nn\nn\nA\nD\nA\nm\n21\n2\n1\n2\n2\n=\n=\n+\n(\n)\n\uf8ee\uf8f0\n\uf8f9\uf8fb\n(\n)\nsin\n/\nsin\n/\nwhere Dm is the angle of minimum deviation 6" + }, + { + "Chapter": "9", + "sentence_range": "799-802", + "Text": "5 For a prism of the angle A, of refractive index n 2 placed in a medium\nof refractive index n1,\nn\nn\nn\nA\nD\nA\nm\n21\n2\n1\n2\n2\n=\n=\n+\n(\n)\n\uf8ee\uf8f0\n\uf8f9\uf8fb\n(\n)\nsin\n/\nsin\n/\nwhere Dm is the angle of minimum deviation 6 For refraction through a spherical interface (from medium 1 to 2 of\nrefractive index n1 and n 2, respectively)\n2\n1\n2\n1\nn\nn\nn\nn\nv\nu\n\u2212R\n\u2212\n=\nThin lens formula\n1\n1\n1\nv\nu\nf\n\u2212\n=\nLens maker\u2019s formula\n1\n1\n1\n2\n1\n1\n1\n2\nf\nn\nn\nn\nR\nR\n=\n\u2212\n(\n)\n\u2212\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\nR1 and R2 are the radii of curvature of the lens surfaces" + }, + { + "Chapter": "9", + "sentence_range": "800-803", + "Text": "For a prism of the angle A, of refractive index n 2 placed in a medium\nof refractive index n1,\nn\nn\nn\nA\nD\nA\nm\n21\n2\n1\n2\n2\n=\n=\n+\n(\n)\n\uf8ee\uf8f0\n\uf8f9\uf8fb\n(\n)\nsin\n/\nsin\n/\nwhere Dm is the angle of minimum deviation 6 For refraction through a spherical interface (from medium 1 to 2 of\nrefractive index n1 and n 2, respectively)\n2\n1\n2\n1\nn\nn\nn\nn\nv\nu\n\u2212R\n\u2212\n=\nThin lens formula\n1\n1\n1\nv\nu\nf\n\u2212\n=\nLens maker\u2019s formula\n1\n1\n1\n2\n1\n1\n1\n2\nf\nn\nn\nn\nR\nR\n=\n\u2212\n(\n)\n\u2212\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\nR1 and R2 are the radii of curvature of the lens surfaces f is positive\nfor a converging lens; f is negative for a diverging lens" + }, + { + "Chapter": "9", + "sentence_range": "801-804", + "Text": "6 For refraction through a spherical interface (from medium 1 to 2 of\nrefractive index n1 and n 2, respectively)\n2\n1\n2\n1\nn\nn\nn\nn\nv\nu\n\u2212R\n\u2212\n=\nThin lens formula\n1\n1\n1\nv\nu\nf\n\u2212\n=\nLens maker\u2019s formula\n1\n1\n1\n2\n1\n1\n1\n2\nf\nn\nn\nn\nR\nR\n=\n\u2212\n(\n)\n\u2212\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\nR1 and R2 are the radii of curvature of the lens surfaces f is positive\nfor a converging lens; f is negative for a diverging lens The power of a\nlens P = 1/f" + }, + { + "Chapter": "9", + "sentence_range": "802-805", + "Text": "For refraction through a spherical interface (from medium 1 to 2 of\nrefractive index n1 and n 2, respectively)\n2\n1\n2\n1\nn\nn\nn\nn\nv\nu\n\u2212R\n\u2212\n=\nThin lens formula\n1\n1\n1\nv\nu\nf\n\u2212\n=\nLens maker\u2019s formula\n1\n1\n1\n2\n1\n1\n1\n2\nf\nn\nn\nn\nR\nR\n=\n\u2212\n(\n)\n\u2212\n\uf8eb\n\uf8ed\uf8ec\n\uf8f6\n\uf8f8\uf8f7\nR1 and R2 are the radii of curvature of the lens surfaces f is positive\nfor a converging lens; f is negative for a diverging lens The power of a\nlens P = 1/f The SI unit for power of a lens is dioptre (D): 1 D = 1 m\u20131" + }, + { + "Chapter": "9", + "sentence_range": "803-806", + "Text": "f is positive\nfor a converging lens; f is negative for a diverging lens The power of a\nlens P = 1/f The SI unit for power of a lens is dioptre (D): 1 D = 1 m\u20131 If several thin lenses of focal length f1, f2, f3," + }, + { + "Chapter": "9", + "sentence_range": "804-807", + "Text": "The power of a\nlens P = 1/f The SI unit for power of a lens is dioptre (D): 1 D = 1 m\u20131 If several thin lenses of focal length f1, f2, f3, are in contact, the\neffective focal length of their combination, is given by\n1\n2\n3\n1\n1\n1\n1\nf\nf\nf\nf\n=\n+\n+\n+ \u2026\nThe total power of a combination of several lenses is\nP = P1 + P2 + P3 + \u2026\n7" + }, + { + "Chapter": "9", + "sentence_range": "805-808", + "Text": "The SI unit for power of a lens is dioptre (D): 1 D = 1 m\u20131 If several thin lenses of focal length f1, f2, f3, are in contact, the\neffective focal length of their combination, is given by\n1\n2\n3\n1\n1\n1\n1\nf\nf\nf\nf\n=\n+\n+\n+ \u2026\nThe total power of a combination of several lenses is\nP = P1 + P2 + P3 + \u2026\n7 Dispersion is the splitting of light into its constituent colour" + }, + { + "Chapter": "9", + "sentence_range": "806-809", + "Text": "If several thin lenses of focal length f1, f2, f3, are in contact, the\neffective focal length of their combination, is given by\n1\n2\n3\n1\n1\n1\n1\nf\nf\nf\nf\n=\n+\n+\n+ \u2026\nThe total power of a combination of several lenses is\nP = P1 + P2 + P3 + \u2026\n7 Dispersion is the splitting of light into its constituent colour Rationalised 2023-24\nPhysics\n248\nPOINTS TO PONDER\n1" + }, + { + "Chapter": "9", + "sentence_range": "807-810", + "Text": "are in contact, the\neffective focal length of their combination, is given by\n1\n2\n3\n1\n1\n1\n1\nf\nf\nf\nf\n=\n+\n+\n+ \u2026\nThe total power of a combination of several lenses is\nP = P1 + P2 + P3 + \u2026\n7 Dispersion is the splitting of light into its constituent colour Rationalised 2023-24\nPhysics\n248\nPOINTS TO PONDER\n1 The laws of reflection and refraction are true for all surfaces and\npairs of media at the point of the incidence" + }, + { + "Chapter": "9", + "sentence_range": "808-811", + "Text": "Dispersion is the splitting of light into its constituent colour Rationalised 2023-24\nPhysics\n248\nPOINTS TO PONDER\n1 The laws of reflection and refraction are true for all surfaces and\npairs of media at the point of the incidence 2" + }, + { + "Chapter": "9", + "sentence_range": "809-812", + "Text": "Rationalised 2023-24\nPhysics\n248\nPOINTS TO PONDER\n1 The laws of reflection and refraction are true for all surfaces and\npairs of media at the point of the incidence 2 The real image of an object placed between f and 2f from a convex lens\ncan be seen on a screen placed at the image location" + }, + { + "Chapter": "9", + "sentence_range": "810-813", + "Text": "The laws of reflection and refraction are true for all surfaces and\npairs of media at the point of the incidence 2 The real image of an object placed between f and 2f from a convex lens\ncan be seen on a screen placed at the image location If the screen is\nremoved, is the image still there" + }, + { + "Chapter": "9", + "sentence_range": "811-814", + "Text": "2 The real image of an object placed between f and 2f from a convex lens\ncan be seen on a screen placed at the image location If the screen is\nremoved, is the image still there This question puzzles many, because\nit is difficult to reconcile ourselves with an image suspended in air\nwithout a screen" + }, + { + "Chapter": "9", + "sentence_range": "812-815", + "Text": "The real image of an object placed between f and 2f from a convex lens\ncan be seen on a screen placed at the image location If the screen is\nremoved, is the image still there This question puzzles many, because\nit is difficult to reconcile ourselves with an image suspended in air\nwithout a screen But the image does exist" + }, + { + "Chapter": "9", + "sentence_range": "813-816", + "Text": "If the screen is\nremoved, is the image still there This question puzzles many, because\nit is difficult to reconcile ourselves with an image suspended in air\nwithout a screen But the image does exist Rays from a given point\non the object are converging to an image point in space and diverging\naway" + }, + { + "Chapter": "9", + "sentence_range": "814-817", + "Text": "This question puzzles many, because\nit is difficult to reconcile ourselves with an image suspended in air\nwithout a screen But the image does exist Rays from a given point\non the object are converging to an image point in space and diverging\naway The screen simply diffuses these rays, some of which reach our\neye and we see the image" + }, + { + "Chapter": "9", + "sentence_range": "815-818", + "Text": "But the image does exist Rays from a given point\non the object are converging to an image point in space and diverging\naway The screen simply diffuses these rays, some of which reach our\neye and we see the image This can be seen by the images formed in\nair during a laser show" + }, + { + "Chapter": "9", + "sentence_range": "816-819", + "Text": "Rays from a given point\non the object are converging to an image point in space and diverging\naway The screen simply diffuses these rays, some of which reach our\neye and we see the image This can be seen by the images formed in\nair during a laser show 3" + }, + { + "Chapter": "9", + "sentence_range": "817-820", + "Text": "The screen simply diffuses these rays, some of which reach our\neye and we see the image This can be seen by the images formed in\nair during a laser show 3 Image formation needs regular reflection/refraction" + }, + { + "Chapter": "9", + "sentence_range": "818-821", + "Text": "This can be seen by the images formed in\nair during a laser show 3 Image formation needs regular reflection/refraction In principle, all\nrays from a given point should reach the same image point" + }, + { + "Chapter": "9", + "sentence_range": "819-822", + "Text": "3 Image formation needs regular reflection/refraction In principle, all\nrays from a given point should reach the same image point This is\nwhy you do not see your image by an irregular reflecting object, say\nthe page of a book" + }, + { + "Chapter": "9", + "sentence_range": "820-823", + "Text": "Image formation needs regular reflection/refraction In principle, all\nrays from a given point should reach the same image point This is\nwhy you do not see your image by an irregular reflecting object, say\nthe page of a book 4" + }, + { + "Chapter": "9", + "sentence_range": "821-824", + "Text": "In principle, all\nrays from a given point should reach the same image point This is\nwhy you do not see your image by an irregular reflecting object, say\nthe page of a book 4 Thick lenses give coloured images due to dispersion" + }, + { + "Chapter": "9", + "sentence_range": "822-825", + "Text": "This is\nwhy you do not see your image by an irregular reflecting object, say\nthe page of a book 4 Thick lenses give coloured images due to dispersion The variety in\ncolour of objects we see around us is due to the constituent colours\nof the light incident on them" + }, + { + "Chapter": "9", + "sentence_range": "823-826", + "Text": "4 Thick lenses give coloured images due to dispersion The variety in\ncolour of objects we see around us is due to the constituent colours\nof the light incident on them A monochromatic light may produce an\nentirely different perception about the colours on an object as seen in\nwhite light" + }, + { + "Chapter": "9", + "sentence_range": "824-827", + "Text": "Thick lenses give coloured images due to dispersion The variety in\ncolour of objects we see around us is due to the constituent colours\nof the light incident on them A monochromatic light may produce an\nentirely different perception about the colours on an object as seen in\nwhite light 5" + }, + { + "Chapter": "9", + "sentence_range": "825-828", + "Text": "The variety in\ncolour of objects we see around us is due to the constituent colours\nof the light incident on them A monochromatic light may produce an\nentirely different perception about the colours on an object as seen in\nwhite light 5 For a simple microscope, the angular size of the object equals the\nangular size of the image" + }, + { + "Chapter": "9", + "sentence_range": "826-829", + "Text": "A monochromatic light may produce an\nentirely different perception about the colours on an object as seen in\nwhite light 5 For a simple microscope, the angular size of the object equals the\nangular size of the image Yet it offers magnification because we can\nkeep the small object much closer to the eye than 25 cm and hence\nhave it subtend a large angle" + }, + { + "Chapter": "9", + "sentence_range": "827-830", + "Text": "5 For a simple microscope, the angular size of the object equals the\nangular size of the image Yet it offers magnification because we can\nkeep the small object much closer to the eye than 25 cm and hence\nhave it subtend a large angle The image is at 25 cm which we can see" + }, + { + "Chapter": "9", + "sentence_range": "828-831", + "Text": "For a simple microscope, the angular size of the object equals the\nangular size of the image Yet it offers magnification because we can\nkeep the small object much closer to the eye than 25 cm and hence\nhave it subtend a large angle The image is at 25 cm which we can see Without the microscope, you would need to keep the small object at\n25 cm which would subtend a very small angle" + }, + { + "Chapter": "9", + "sentence_range": "829-832", + "Text": "Yet it offers magnification because we can\nkeep the small object much closer to the eye than 25 cm and hence\nhave it subtend a large angle The image is at 25 cm which we can see Without the microscope, you would need to keep the small object at\n25 cm which would subtend a very small angle 8" + }, + { + "Chapter": "9", + "sentence_range": "830-833", + "Text": "The image is at 25 cm which we can see Without the microscope, you would need to keep the small object at\n25 cm which would subtend a very small angle 8 Magnifying power m of a simple microscope is given by m = 1 + (D/f),\nwhere D = 25 cm is the least distance of distinct vision and f is the\nfocal length of the convex lens" + }, + { + "Chapter": "9", + "sentence_range": "831-834", + "Text": "Without the microscope, you would need to keep the small object at\n25 cm which would subtend a very small angle 8 Magnifying power m of a simple microscope is given by m = 1 + (D/f),\nwhere D = 25 cm is the least distance of distinct vision and f is the\nfocal length of the convex lens If the image is at infinity, m = D/f" + }, + { + "Chapter": "9", + "sentence_range": "832-835", + "Text": "8 Magnifying power m of a simple microscope is given by m = 1 + (D/f),\nwhere D = 25 cm is the least distance of distinct vision and f is the\nfocal length of the convex lens If the image is at infinity, m = D/f For\na compound microscope, the magnifying power is given by m = me \u00d7 m0\nwhere me = 1 + (D/fe), is the magnification due to the eyepiece and mo\nis the magnification produced by the objective" + }, + { + "Chapter": "9", + "sentence_range": "833-836", + "Text": "Magnifying power m of a simple microscope is given by m = 1 + (D/f),\nwhere D = 25 cm is the least distance of distinct vision and f is the\nfocal length of the convex lens If the image is at infinity, m = D/f For\na compound microscope, the magnifying power is given by m = me \u00d7 m0\nwhere me = 1 + (D/fe), is the magnification due to the eyepiece and mo\nis the magnification produced by the objective Approximately,\no\ne\nL\nD\nm\nf\nf\n=\n\u00d7\nwhere fo and fe are the focal lengths of the objective and eyepiece,\nrespectively, and L is the distance between their focal points" + }, + { + "Chapter": "9", + "sentence_range": "834-837", + "Text": "If the image is at infinity, m = D/f For\na compound microscope, the magnifying power is given by m = me \u00d7 m0\nwhere me = 1 + (D/fe), is the magnification due to the eyepiece and mo\nis the magnification produced by the objective Approximately,\no\ne\nL\nD\nm\nf\nf\n=\n\u00d7\nwhere fo and fe are the focal lengths of the objective and eyepiece,\nrespectively, and L is the distance between their focal points 9" + }, + { + "Chapter": "9", + "sentence_range": "835-838", + "Text": "For\na compound microscope, the magnifying power is given by m = me \u00d7 m0\nwhere me = 1 + (D/fe), is the magnification due to the eyepiece and mo\nis the magnification produced by the objective Approximately,\no\ne\nL\nD\nm\nf\nf\n=\n\u00d7\nwhere fo and fe are the focal lengths of the objective and eyepiece,\nrespectively, and L is the distance between their focal points 9 Magnifying power m of a telescope is the ratio of the angle b subtended\nat the eye by the image to the angle a subtended at the eye by the\nobject" + }, + { + "Chapter": "9", + "sentence_range": "836-839", + "Text": "Approximately,\no\ne\nL\nD\nm\nf\nf\n=\n\u00d7\nwhere fo and fe are the focal lengths of the objective and eyepiece,\nrespectively, and L is the distance between their focal points 9 Magnifying power m of a telescope is the ratio of the angle b subtended\nat the eye by the image to the angle a subtended at the eye by the\nobject o\ne\nf\nm\nf\n=\u03b1\u03b2\n=\nwhere f0 and fe are the focal lengths of the objective and eyepiece,\nrespectively" + }, + { + "Chapter": "9", + "sentence_range": "837-840", + "Text": "9 Magnifying power m of a telescope is the ratio of the angle b subtended\nat the eye by the image to the angle a subtended at the eye by the\nobject o\ne\nf\nm\nf\n=\u03b1\u03b2\n=\nwhere f0 and fe are the focal lengths of the objective and eyepiece,\nrespectively Rationalised 2023-24\nRay Optics and\nOptical Instruments\n249\nEXERCISES\n9" + }, + { + "Chapter": "9", + "sentence_range": "838-841", + "Text": "Magnifying power m of a telescope is the ratio of the angle b subtended\nat the eye by the image to the angle a subtended at the eye by the\nobject o\ne\nf\nm\nf\n=\u03b1\u03b2\n=\nwhere f0 and fe are the focal lengths of the objective and eyepiece,\nrespectively Rationalised 2023-24\nRay Optics and\nOptical Instruments\n249\nEXERCISES\n9 1\nA small candle, 2" + }, + { + "Chapter": "9", + "sentence_range": "839-842", + "Text": "o\ne\nf\nm\nf\n=\u03b1\u03b2\n=\nwhere f0 and fe are the focal lengths of the objective and eyepiece,\nrespectively Rationalised 2023-24\nRay Optics and\nOptical Instruments\n249\nEXERCISES\n9 1\nA small candle, 2 5 cm in size is placed at 27 cm in front of a concave\nmirror of radius of curvature 36 cm" + }, + { + "Chapter": "9", + "sentence_range": "840-843", + "Text": "Rationalised 2023-24\nRay Optics and\nOptical Instruments\n249\nEXERCISES\n9 1\nA small candle, 2 5 cm in size is placed at 27 cm in front of a concave\nmirror of radius of curvature 36 cm At what distance from the mirror\nshould a screen be placed in order to obtain a sharp image" + }, + { + "Chapter": "9", + "sentence_range": "841-844", + "Text": "1\nA small candle, 2 5 cm in size is placed at 27 cm in front of a concave\nmirror of radius of curvature 36 cm At what distance from the mirror\nshould a screen be placed in order to obtain a sharp image Describe\nthe nature and size of the image" + }, + { + "Chapter": "9", + "sentence_range": "842-845", + "Text": "5 cm in size is placed at 27 cm in front of a concave\nmirror of radius of curvature 36 cm At what distance from the mirror\nshould a screen be placed in order to obtain a sharp image Describe\nthe nature and size of the image If the candle is moved closer to the\nmirror, how would the screen have to be moved" + }, + { + "Chapter": "9", + "sentence_range": "843-846", + "Text": "At what distance from the mirror\nshould a screen be placed in order to obtain a sharp image Describe\nthe nature and size of the image If the candle is moved closer to the\nmirror, how would the screen have to be moved 9" + }, + { + "Chapter": "9", + "sentence_range": "844-847", + "Text": "Describe\nthe nature and size of the image If the candle is moved closer to the\nmirror, how would the screen have to be moved 9 2\nA 4" + }, + { + "Chapter": "9", + "sentence_range": "845-848", + "Text": "If the candle is moved closer to the\nmirror, how would the screen have to be moved 9 2\nA 4 5 cm needle is placed 12 cm away from a convex mirror of focal\nlength 15 cm" + }, + { + "Chapter": "9", + "sentence_range": "846-849", + "Text": "9 2\nA 4 5 cm needle is placed 12 cm away from a convex mirror of focal\nlength 15 cm Give the location of the image and the magnification" + }, + { + "Chapter": "9", + "sentence_range": "847-850", + "Text": "2\nA 4 5 cm needle is placed 12 cm away from a convex mirror of focal\nlength 15 cm Give the location of the image and the magnification Describe what happens as the needle is moved farther from the mirror" + }, + { + "Chapter": "9", + "sentence_range": "848-851", + "Text": "5 cm needle is placed 12 cm away from a convex mirror of focal\nlength 15 cm Give the location of the image and the magnification Describe what happens as the needle is moved farther from the mirror 9" + }, + { + "Chapter": "9", + "sentence_range": "849-852", + "Text": "Give the location of the image and the magnification Describe what happens as the needle is moved farther from the mirror 9 3\nA tank is filled with water to a height of 12" + }, + { + "Chapter": "9", + "sentence_range": "850-853", + "Text": "Describe what happens as the needle is moved farther from the mirror 9 3\nA tank is filled with water to a height of 12 5 cm" + }, + { + "Chapter": "9", + "sentence_range": "851-854", + "Text": "9 3\nA tank is filled with water to a height of 12 5 cm The apparent\ndepth of a needle lying at the bottom of the tank is measured by a\nmicroscope to be 9" + }, + { + "Chapter": "9", + "sentence_range": "852-855", + "Text": "3\nA tank is filled with water to a height of 12 5 cm The apparent\ndepth of a needle lying at the bottom of the tank is measured by a\nmicroscope to be 9 4 cm" + }, + { + "Chapter": "9", + "sentence_range": "853-856", + "Text": "5 cm The apparent\ndepth of a needle lying at the bottom of the tank is measured by a\nmicroscope to be 9 4 cm What is the refractive index of water" + }, + { + "Chapter": "9", + "sentence_range": "854-857", + "Text": "The apparent\ndepth of a needle lying at the bottom of the tank is measured by a\nmicroscope to be 9 4 cm What is the refractive index of water If\nwater is replaced by a liquid of refractive index 1" + }, + { + "Chapter": "9", + "sentence_range": "855-858", + "Text": "4 cm What is the refractive index of water If\nwater is replaced by a liquid of refractive index 1 63 up to the same\nheight, by what distance would the microscope have to be moved to\nfocus on the needle again" + }, + { + "Chapter": "9", + "sentence_range": "856-859", + "Text": "What is the refractive index of water If\nwater is replaced by a liquid of refractive index 1 63 up to the same\nheight, by what distance would the microscope have to be moved to\nfocus on the needle again 9" + }, + { + "Chapter": "9", + "sentence_range": "857-860", + "Text": "If\nwater is replaced by a liquid of refractive index 1 63 up to the same\nheight, by what distance would the microscope have to be moved to\nfocus on the needle again 9 4\nFigures 9" + }, + { + "Chapter": "9", + "sentence_range": "858-861", + "Text": "63 up to the same\nheight, by what distance would the microscope have to be moved to\nfocus on the needle again 9 4\nFigures 9 27(a) and (b) show refraction of a ray in air incident at 60\u00b0\nwith the normal to a glass-air and water-air interface, respectively" + }, + { + "Chapter": "9", + "sentence_range": "859-862", + "Text": "9 4\nFigures 9 27(a) and (b) show refraction of a ray in air incident at 60\u00b0\nwith the normal to a glass-air and water-air interface, respectively Predict the angle of refraction in glass when the angle of incidence\nin water is 45\u00b0 with the normal to a water-glass interface [Fig" + }, + { + "Chapter": "9", + "sentence_range": "860-863", + "Text": "4\nFigures 9 27(a) and (b) show refraction of a ray in air incident at 60\u00b0\nwith the normal to a glass-air and water-air interface, respectively Predict the angle of refraction in glass when the angle of incidence\nin water is 45\u00b0 with the normal to a water-glass interface [Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "861-864", + "Text": "27(a) and (b) show refraction of a ray in air incident at 60\u00b0\nwith the normal to a glass-air and water-air interface, respectively Predict the angle of refraction in glass when the angle of incidence\nin water is 45\u00b0 with the normal to a water-glass interface [Fig 9 27(c)]" + }, + { + "Chapter": "9", + "sentence_range": "862-865", + "Text": "Predict the angle of refraction in glass when the angle of incidence\nin water is 45\u00b0 with the normal to a water-glass interface [Fig 9 27(c)] FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "863-866", + "Text": "9 27(c)] FIGURE 9 27\n9" + }, + { + "Chapter": "9", + "sentence_range": "864-867", + "Text": "27(c)] FIGURE 9 27\n9 5\nA small bulb is placed at the bottom of a tank containing water to a\ndepth of 80cm" + }, + { + "Chapter": "9", + "sentence_range": "865-868", + "Text": "FIGURE 9 27\n9 5\nA small bulb is placed at the bottom of a tank containing water to a\ndepth of 80cm What is the area of the surface of water through\nwhich light from the bulb can emerge out" + }, + { + "Chapter": "9", + "sentence_range": "866-869", + "Text": "27\n9 5\nA small bulb is placed at the bottom of a tank containing water to a\ndepth of 80cm What is the area of the surface of water through\nwhich light from the bulb can emerge out Refractive index of water\nis 1" + }, + { + "Chapter": "9", + "sentence_range": "867-870", + "Text": "5\nA small bulb is placed at the bottom of a tank containing water to a\ndepth of 80cm What is the area of the surface of water through\nwhich light from the bulb can emerge out Refractive index of water\nis 1 33" + }, + { + "Chapter": "9", + "sentence_range": "868-871", + "Text": "What is the area of the surface of water through\nwhich light from the bulb can emerge out Refractive index of water\nis 1 33 (Consider the bulb to be a point source" + }, + { + "Chapter": "9", + "sentence_range": "869-872", + "Text": "Refractive index of water\nis 1 33 (Consider the bulb to be a point source )\n9" + }, + { + "Chapter": "9", + "sentence_range": "870-873", + "Text": "33 (Consider the bulb to be a point source )\n9 6\nA prism is made of glass of unknown refractive index" + }, + { + "Chapter": "9", + "sentence_range": "871-874", + "Text": "(Consider the bulb to be a point source )\n9 6\nA prism is made of glass of unknown refractive index A parallel\nbeam of light is incident on a face of the prism" + }, + { + "Chapter": "9", + "sentence_range": "872-875", + "Text": ")\n9 6\nA prism is made of glass of unknown refractive index A parallel\nbeam of light is incident on a face of the prism The angle of minimum\ndeviation is measured to be 40\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "873-876", + "Text": "6\nA prism is made of glass of unknown refractive index A parallel\nbeam of light is incident on a face of the prism The angle of minimum\ndeviation is measured to be 40\u00b0 What is the refractive index of the\nmaterial of the prism" + }, + { + "Chapter": "9", + "sentence_range": "874-877", + "Text": "A parallel\nbeam of light is incident on a face of the prism The angle of minimum\ndeviation is measured to be 40\u00b0 What is the refractive index of the\nmaterial of the prism The refracting angle of the prism is 60\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "875-878", + "Text": "The angle of minimum\ndeviation is measured to be 40\u00b0 What is the refractive index of the\nmaterial of the prism The refracting angle of the prism is 60\u00b0 If the\nprism is placed in water (refractive index 1" + }, + { + "Chapter": "9", + "sentence_range": "876-879", + "Text": "What is the refractive index of the\nmaterial of the prism The refracting angle of the prism is 60\u00b0 If the\nprism is placed in water (refractive index 1 33), predict the new\nangle of minimum deviation of a parallel beam of light" + }, + { + "Chapter": "9", + "sentence_range": "877-880", + "Text": "The refracting angle of the prism is 60\u00b0 If the\nprism is placed in water (refractive index 1 33), predict the new\nangle of minimum deviation of a parallel beam of light 9" + }, + { + "Chapter": "9", + "sentence_range": "878-881", + "Text": "If the\nprism is placed in water (refractive index 1 33), predict the new\nangle of minimum deviation of a parallel beam of light 9 7\nDouble-convex lenses are to be manufactured from a glass of\nrefractive index 1" + }, + { + "Chapter": "9", + "sentence_range": "879-882", + "Text": "33), predict the new\nangle of minimum deviation of a parallel beam of light 9 7\nDouble-convex lenses are to be manufactured from a glass of\nrefractive index 1 55, with both faces of the same radius of\ncurvature" + }, + { + "Chapter": "9", + "sentence_range": "880-883", + "Text": "9 7\nDouble-convex lenses are to be manufactured from a glass of\nrefractive index 1 55, with both faces of the same radius of\ncurvature What is the radius of curvature required if the focal length\nis to be 20cm" + }, + { + "Chapter": "9", + "sentence_range": "881-884", + "Text": "7\nDouble-convex lenses are to be manufactured from a glass of\nrefractive index 1 55, with both faces of the same radius of\ncurvature What is the radius of curvature required if the focal length\nis to be 20cm 9" + }, + { + "Chapter": "9", + "sentence_range": "882-885", + "Text": "55, with both faces of the same radius of\ncurvature What is the radius of curvature required if the focal length\nis to be 20cm 9 8\nA beam of light converges at a point P" + }, + { + "Chapter": "9", + "sentence_range": "883-886", + "Text": "What is the radius of curvature required if the focal length\nis to be 20cm 9 8\nA beam of light converges at a point P Now a lens is placed in the\npath of the convergent beam 12cm from P" + }, + { + "Chapter": "9", + "sentence_range": "884-887", + "Text": "9 8\nA beam of light converges at a point P Now a lens is placed in the\npath of the convergent beam 12cm from P At what point does the\nbeam converge if the lens is (a) a convex lens of focal length 20cm,\nand (b) a concave lens of focal length 16cm" + }, + { + "Chapter": "9", + "sentence_range": "885-888", + "Text": "8\nA beam of light converges at a point P Now a lens is placed in the\npath of the convergent beam 12cm from P At what point does the\nbeam converge if the lens is (a) a convex lens of focal length 20cm,\nand (b) a concave lens of focal length 16cm 9" + }, + { + "Chapter": "9", + "sentence_range": "886-889", + "Text": "Now a lens is placed in the\npath of the convergent beam 12cm from P At what point does the\nbeam converge if the lens is (a) a convex lens of focal length 20cm,\nand (b) a concave lens of focal length 16cm 9 9\nAn object of size 3" + }, + { + "Chapter": "9", + "sentence_range": "887-890", + "Text": "At what point does the\nbeam converge if the lens is (a) a convex lens of focal length 20cm,\nand (b) a concave lens of focal length 16cm 9 9\nAn object of size 3 0cm is placed 14cm in front of a concave lens of\nfocal length 21cm" + }, + { + "Chapter": "9", + "sentence_range": "888-891", + "Text": "9 9\nAn object of size 3 0cm is placed 14cm in front of a concave lens of\nfocal length 21cm Describe the image produced by the lens" + }, + { + "Chapter": "9", + "sentence_range": "889-892", + "Text": "9\nAn object of size 3 0cm is placed 14cm in front of a concave lens of\nfocal length 21cm Describe the image produced by the lens What\nhappens if the object is moved further away from the lens" + }, + { + "Chapter": "9", + "sentence_range": "890-893", + "Text": "0cm is placed 14cm in front of a concave lens of\nfocal length 21cm Describe the image produced by the lens What\nhappens if the object is moved further away from the lens Rationalised 2023-24\nPhysics\n250\n9" + }, + { + "Chapter": "9", + "sentence_range": "891-894", + "Text": "Describe the image produced by the lens What\nhappens if the object is moved further away from the lens Rationalised 2023-24\nPhysics\n250\n9 10\nWhat is the focal length of a convex lens of focal length 30cm in\ncontact with a concave lens of focal length 20cm" + }, + { + "Chapter": "9", + "sentence_range": "892-895", + "Text": "What\nhappens if the object is moved further away from the lens Rationalised 2023-24\nPhysics\n250\n9 10\nWhat is the focal length of a convex lens of focal length 30cm in\ncontact with a concave lens of focal length 20cm Is the system a\nconverging or a diverging lens" + }, + { + "Chapter": "9", + "sentence_range": "893-896", + "Text": "Rationalised 2023-24\nPhysics\n250\n9 10\nWhat is the focal length of a convex lens of focal length 30cm in\ncontact with a concave lens of focal length 20cm Is the system a\nconverging or a diverging lens Ignore thickness of the lenses" + }, + { + "Chapter": "9", + "sentence_range": "894-897", + "Text": "10\nWhat is the focal length of a convex lens of focal length 30cm in\ncontact with a concave lens of focal length 20cm Is the system a\nconverging or a diverging lens Ignore thickness of the lenses 9" + }, + { + "Chapter": "9", + "sentence_range": "895-898", + "Text": "Is the system a\nconverging or a diverging lens Ignore thickness of the lenses 9 11\nA compound microscope consists of an objective lens of focal length\n2" + }, + { + "Chapter": "9", + "sentence_range": "896-899", + "Text": "Ignore thickness of the lenses 9 11\nA compound microscope consists of an objective lens of focal length\n2 0 cm and an eyepiece of focal length 6" + }, + { + "Chapter": "9", + "sentence_range": "897-900", + "Text": "9 11\nA compound microscope consists of an objective lens of focal length\n2 0 cm and an eyepiece of focal length 6 25 cm separated by a\ndistance of 15cm" + }, + { + "Chapter": "9", + "sentence_range": "898-901", + "Text": "11\nA compound microscope consists of an objective lens of focal length\n2 0 cm and an eyepiece of focal length 6 25 cm separated by a\ndistance of 15cm How far from the objective should an object be\nplaced in order to obtain the final image at (a) the least distance of\ndistinct vision (25cm), and (b) at infinity" + }, + { + "Chapter": "9", + "sentence_range": "899-902", + "Text": "0 cm and an eyepiece of focal length 6 25 cm separated by a\ndistance of 15cm How far from the objective should an object be\nplaced in order to obtain the final image at (a) the least distance of\ndistinct vision (25cm), and (b) at infinity What is the magnifying\npower of the microscope in each case" + }, + { + "Chapter": "9", + "sentence_range": "900-903", + "Text": "25 cm separated by a\ndistance of 15cm How far from the objective should an object be\nplaced in order to obtain the final image at (a) the least distance of\ndistinct vision (25cm), and (b) at infinity What is the magnifying\npower of the microscope in each case 9" + }, + { + "Chapter": "9", + "sentence_range": "901-904", + "Text": "How far from the objective should an object be\nplaced in order to obtain the final image at (a) the least distance of\ndistinct vision (25cm), and (b) at infinity What is the magnifying\npower of the microscope in each case 9 12\nA person with a normal near point (25 cm) using a compound\nmicroscope with objective of focal length 8" + }, + { + "Chapter": "9", + "sentence_range": "902-905", + "Text": "What is the magnifying\npower of the microscope in each case 9 12\nA person with a normal near point (25 cm) using a compound\nmicroscope with objective of focal length 8 0 mm and an eyepiece of\nfocal length 2" + }, + { + "Chapter": "9", + "sentence_range": "903-906", + "Text": "9 12\nA person with a normal near point (25 cm) using a compound\nmicroscope with objective of focal length 8 0 mm and an eyepiece of\nfocal length 2 5cm can bring an object placed at 9" + }, + { + "Chapter": "9", + "sentence_range": "904-907", + "Text": "12\nA person with a normal near point (25 cm) using a compound\nmicroscope with objective of focal length 8 0 mm and an eyepiece of\nfocal length 2 5cm can bring an object placed at 9 0mm from the\nobjective in sharp focus" + }, + { + "Chapter": "9", + "sentence_range": "905-908", + "Text": "0 mm and an eyepiece of\nfocal length 2 5cm can bring an object placed at 9 0mm from the\nobjective in sharp focus What is the separation between the two\nlenses" + }, + { + "Chapter": "9", + "sentence_range": "906-909", + "Text": "5cm can bring an object placed at 9 0mm from the\nobjective in sharp focus What is the separation between the two\nlenses Calculate the magnifying power of the microscope,\n9" + }, + { + "Chapter": "9", + "sentence_range": "907-910", + "Text": "0mm from the\nobjective in sharp focus What is the separation between the two\nlenses Calculate the magnifying power of the microscope,\n9 13\nA small telescope has an objective lens of focal length 144cm and\nan eyepiece of focal length 6" + }, + { + "Chapter": "9", + "sentence_range": "908-911", + "Text": "What is the separation between the two\nlenses Calculate the magnifying power of the microscope,\n9 13\nA small telescope has an objective lens of focal length 144cm and\nan eyepiece of focal length 6 0cm" + }, + { + "Chapter": "9", + "sentence_range": "909-912", + "Text": "Calculate the magnifying power of the microscope,\n9 13\nA small telescope has an objective lens of focal length 144cm and\nan eyepiece of focal length 6 0cm What is the magnifying power of\nthe telescope" + }, + { + "Chapter": "9", + "sentence_range": "910-913", + "Text": "13\nA small telescope has an objective lens of focal length 144cm and\nan eyepiece of focal length 6 0cm What is the magnifying power of\nthe telescope What is the separation between the objective and\nthe eyepiece" + }, + { + "Chapter": "9", + "sentence_range": "911-914", + "Text": "0cm What is the magnifying power of\nthe telescope What is the separation between the objective and\nthe eyepiece 9" + }, + { + "Chapter": "9", + "sentence_range": "912-915", + "Text": "What is the magnifying power of\nthe telescope What is the separation between the objective and\nthe eyepiece 9 14\n(a) A giant refracting telescope at an observatory has an objective\nlens of focal length 15m" + }, + { + "Chapter": "9", + "sentence_range": "913-916", + "Text": "What is the separation between the objective and\nthe eyepiece 9 14\n(a) A giant refracting telescope at an observatory has an objective\nlens of focal length 15m If an eyepiece of focal length 1" + }, + { + "Chapter": "9", + "sentence_range": "914-917", + "Text": "9 14\n(a) A giant refracting telescope at an observatory has an objective\nlens of focal length 15m If an eyepiece of focal length 1 0cm is\nused, what is the angular magnification of the telescope" + }, + { + "Chapter": "9", + "sentence_range": "915-918", + "Text": "14\n(a) A giant refracting telescope at an observatory has an objective\nlens of focal length 15m If an eyepiece of focal length 1 0cm is\nused, what is the angular magnification of the telescope (b) If this telescope is used to view the moon, what is the diameter\nof the image of the moon formed by the objective lens" + }, + { + "Chapter": "9", + "sentence_range": "916-919", + "Text": "If an eyepiece of focal length 1 0cm is\nused, what is the angular magnification of the telescope (b) If this telescope is used to view the moon, what is the diameter\nof the image of the moon formed by the objective lens The\ndiameter of the moon is 3" + }, + { + "Chapter": "9", + "sentence_range": "917-920", + "Text": "0cm is\nused, what is the angular magnification of the telescope (b) If this telescope is used to view the moon, what is the diameter\nof the image of the moon formed by the objective lens The\ndiameter of the moon is 3 48 \u00d7 106m, and the radius of lunar\norbit is 3" + }, + { + "Chapter": "9", + "sentence_range": "918-921", + "Text": "(b) If this telescope is used to view the moon, what is the diameter\nof the image of the moon formed by the objective lens The\ndiameter of the moon is 3 48 \u00d7 106m, and the radius of lunar\norbit is 3 8 \u00d7 108m" + }, + { + "Chapter": "9", + "sentence_range": "919-922", + "Text": "The\ndiameter of the moon is 3 48 \u00d7 106m, and the radius of lunar\norbit is 3 8 \u00d7 108m 9" + }, + { + "Chapter": "9", + "sentence_range": "920-923", + "Text": "48 \u00d7 106m, and the radius of lunar\norbit is 3 8 \u00d7 108m 9 15\nUse the mirror equation to deduce that:\n(a) an object placed between f and 2f of a concave mirror produces\na real image beyond 2f" + }, + { + "Chapter": "9", + "sentence_range": "921-924", + "Text": "8 \u00d7 108m 9 15\nUse the mirror equation to deduce that:\n(a) an object placed between f and 2f of a concave mirror produces\na real image beyond 2f (b) a convex mirror always produces a virtual image independent\nof the location of the object" + }, + { + "Chapter": "9", + "sentence_range": "922-925", + "Text": "9 15\nUse the mirror equation to deduce that:\n(a) an object placed between f and 2f of a concave mirror produces\na real image beyond 2f (b) a convex mirror always produces a virtual image independent\nof the location of the object (c) the virtual image produced by a convex mirror is always\ndiminished in size and is located between the focus and\nthe pole" + }, + { + "Chapter": "9", + "sentence_range": "923-926", + "Text": "15\nUse the mirror equation to deduce that:\n(a) an object placed between f and 2f of a concave mirror produces\na real image beyond 2f (b) a convex mirror always produces a virtual image independent\nof the location of the object (c) the virtual image produced by a convex mirror is always\ndiminished in size and is located between the focus and\nthe pole (d) an object placed between the pole and focus of a concave mirror\nproduces a virtual and enlarged image" + }, + { + "Chapter": "9", + "sentence_range": "924-927", + "Text": "(b) a convex mirror always produces a virtual image independent\nof the location of the object (c) the virtual image produced by a convex mirror is always\ndiminished in size and is located between the focus and\nthe pole (d) an object placed between the pole and focus of a concave mirror\nproduces a virtual and enlarged image [Note: This exercise helps you deduce algebraically properties of\nimages that one obtains from explicit ray diagrams" + }, + { + "Chapter": "9", + "sentence_range": "925-928", + "Text": "(c) the virtual image produced by a convex mirror is always\ndiminished in size and is located between the focus and\nthe pole (d) an object placed between the pole and focus of a concave mirror\nproduces a virtual and enlarged image [Note: This exercise helps you deduce algebraically properties of\nimages that one obtains from explicit ray diagrams ]\n9" + }, + { + "Chapter": "9", + "sentence_range": "926-929", + "Text": "(d) an object placed between the pole and focus of a concave mirror\nproduces a virtual and enlarged image [Note: This exercise helps you deduce algebraically properties of\nimages that one obtains from explicit ray diagrams ]\n9 16\nA small pin fixed on a table top is viewed from above from a distance\nof 50cm" + }, + { + "Chapter": "9", + "sentence_range": "927-930", + "Text": "[Note: This exercise helps you deduce algebraically properties of\nimages that one obtains from explicit ray diagrams ]\n9 16\nA small pin fixed on a table top is viewed from above from a distance\nof 50cm By what distance would the pin appear to be raised if it is\nviewed from the same point through a 15cm thick glass slab held\nparallel to the table" + }, + { + "Chapter": "9", + "sentence_range": "928-931", + "Text": "]\n9 16\nA small pin fixed on a table top is viewed from above from a distance\nof 50cm By what distance would the pin appear to be raised if it is\nviewed from the same point through a 15cm thick glass slab held\nparallel to the table Refractive index of glass = 1" + }, + { + "Chapter": "9", + "sentence_range": "929-932", + "Text": "16\nA small pin fixed on a table top is viewed from above from a distance\nof 50cm By what distance would the pin appear to be raised if it is\nviewed from the same point through a 15cm thick glass slab held\nparallel to the table Refractive index of glass = 1 5" + }, + { + "Chapter": "9", + "sentence_range": "930-933", + "Text": "By what distance would the pin appear to be raised if it is\nviewed from the same point through a 15cm thick glass slab held\nparallel to the table Refractive index of glass = 1 5 Does the answer\ndepend on the location of the slab" + }, + { + "Chapter": "9", + "sentence_range": "931-934", + "Text": "Refractive index of glass = 1 5 Does the answer\ndepend on the location of the slab 9" + }, + { + "Chapter": "9", + "sentence_range": "932-935", + "Text": "5 Does the answer\ndepend on the location of the slab 9 17\n(a) Figure 9" + }, + { + "Chapter": "9", + "sentence_range": "933-936", + "Text": "Does the answer\ndepend on the location of the slab 9 17\n(a) Figure 9 28 shows a cross-section of a \u2018light pipe\u2019 made of a\nglass fibre of refractive index 1" + }, + { + "Chapter": "9", + "sentence_range": "934-937", + "Text": "9 17\n(a) Figure 9 28 shows a cross-section of a \u2018light pipe\u2019 made of a\nglass fibre of refractive index 1 68" + }, + { + "Chapter": "9", + "sentence_range": "935-938", + "Text": "17\n(a) Figure 9 28 shows a cross-section of a \u2018light pipe\u2019 made of a\nglass fibre of refractive index 1 68 The outer covering of the\npipe is made of a material of refractive index 1" + }, + { + "Chapter": "9", + "sentence_range": "936-939", + "Text": "28 shows a cross-section of a \u2018light pipe\u2019 made of a\nglass fibre of refractive index 1 68 The outer covering of the\npipe is made of a material of refractive index 1 44" + }, + { + "Chapter": "9", + "sentence_range": "937-940", + "Text": "68 The outer covering of the\npipe is made of a material of refractive index 1 44 What is the\nrange of the angles of the incident rays with the axis of the pipe\nfor which total reflections inside the pipe take place, as shown\nin the figure" + }, + { + "Chapter": "9", + "sentence_range": "938-941", + "Text": "The outer covering of the\npipe is made of a material of refractive index 1 44 What is the\nrange of the angles of the incident rays with the axis of the pipe\nfor which total reflections inside the pipe take place, as shown\nin the figure FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "939-942", + "Text": "44 What is the\nrange of the angles of the incident rays with the axis of the pipe\nfor which total reflections inside the pipe take place, as shown\nin the figure FIGURE 9 28\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n251\n(b) What is the answer if there is no outer covering of the pipe" + }, + { + "Chapter": "9", + "sentence_range": "940-943", + "Text": "What is the\nrange of the angles of the incident rays with the axis of the pipe\nfor which total reflections inside the pipe take place, as shown\nin the figure FIGURE 9 28\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n251\n(b) What is the answer if there is no outer covering of the pipe 9" + }, + { + "Chapter": "9", + "sentence_range": "941-944", + "Text": "FIGURE 9 28\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n251\n(b) What is the answer if there is no outer covering of the pipe 9 18\nThe image of a small electric bulb fixed on the wall of a room is to be\nobtained on the opposite wall 3m away by means of a large convex\nlens" + }, + { + "Chapter": "9", + "sentence_range": "942-945", + "Text": "28\nRationalised 2023-24\nRay Optics and\nOptical Instruments\n251\n(b) What is the answer if there is no outer covering of the pipe 9 18\nThe image of a small electric bulb fixed on the wall of a room is to be\nobtained on the opposite wall 3m away by means of a large convex\nlens What is the maximum possible focal length of the lens required\nfor the purpose" + }, + { + "Chapter": "9", + "sentence_range": "943-946", + "Text": "9 18\nThe image of a small electric bulb fixed on the wall of a room is to be\nobtained on the opposite wall 3m away by means of a large convex\nlens What is the maximum possible focal length of the lens required\nfor the purpose 9" + }, + { + "Chapter": "9", + "sentence_range": "944-947", + "Text": "18\nThe image of a small electric bulb fixed on the wall of a room is to be\nobtained on the opposite wall 3m away by means of a large convex\nlens What is the maximum possible focal length of the lens required\nfor the purpose 9 19\nA screen is placed 90cm from an object" + }, + { + "Chapter": "9", + "sentence_range": "945-948", + "Text": "What is the maximum possible focal length of the lens required\nfor the purpose 9 19\nA screen is placed 90cm from an object The image of the object on\nthe screen is formed by a convex lens at two different locations\nseparated by 20cm" + }, + { + "Chapter": "9", + "sentence_range": "946-949", + "Text": "9 19\nA screen is placed 90cm from an object The image of the object on\nthe screen is formed by a convex lens at two different locations\nseparated by 20cm Determine the focal length of the lens" + }, + { + "Chapter": "9", + "sentence_range": "947-950", + "Text": "19\nA screen is placed 90cm from an object The image of the object on\nthe screen is formed by a convex lens at two different locations\nseparated by 20cm Determine the focal length of the lens 9" + }, + { + "Chapter": "9", + "sentence_range": "948-951", + "Text": "The image of the object on\nthe screen is formed by a convex lens at two different locations\nseparated by 20cm Determine the focal length of the lens 9 20\n(a) Determine the \u2018effective focal length\u2019 of the combination of\nthe two lenses in Exercise 9" + }, + { + "Chapter": "9", + "sentence_range": "949-952", + "Text": "Determine the focal length of the lens 9 20\n(a) Determine the \u2018effective focal length\u2019 of the combination of\nthe two lenses in Exercise 9 10, if they are placed 8" + }, + { + "Chapter": "9", + "sentence_range": "950-953", + "Text": "9 20\n(a) Determine the \u2018effective focal length\u2019 of the combination of\nthe two lenses in Exercise 9 10, if they are placed 8 0cm apart\nwith their principal axes coincident" + }, + { + "Chapter": "9", + "sentence_range": "951-954", + "Text": "20\n(a) Determine the \u2018effective focal length\u2019 of the combination of\nthe two lenses in Exercise 9 10, if they are placed 8 0cm apart\nwith their principal axes coincident Does the answer depend\non which side of the combination a beam of parallel light is\nincident" + }, + { + "Chapter": "9", + "sentence_range": "952-955", + "Text": "10, if they are placed 8 0cm apart\nwith their principal axes coincident Does the answer depend\non which side of the combination a beam of parallel light is\nincident Is the notion of effective focal length of this system\nuseful at all" + }, + { + "Chapter": "9", + "sentence_range": "953-956", + "Text": "0cm apart\nwith their principal axes coincident Does the answer depend\non which side of the combination a beam of parallel light is\nincident Is the notion of effective focal length of this system\nuseful at all (b) An object 1" + }, + { + "Chapter": "9", + "sentence_range": "954-957", + "Text": "Does the answer depend\non which side of the combination a beam of parallel light is\nincident Is the notion of effective focal length of this system\nuseful at all (b) An object 1 5 cm in size is placed on the side of the convex lens\nin the arrangement (a) above" + }, + { + "Chapter": "9", + "sentence_range": "955-958", + "Text": "Is the notion of effective focal length of this system\nuseful at all (b) An object 1 5 cm in size is placed on the side of the convex lens\nin the arrangement (a) above The distance between the object\nand the convex lens is 40 cm" + }, + { + "Chapter": "9", + "sentence_range": "956-959", + "Text": "(b) An object 1 5 cm in size is placed on the side of the convex lens\nin the arrangement (a) above The distance between the object\nand the convex lens is 40 cm Determine the magnification\nproduced by the two-lens system, and the size of the image" + }, + { + "Chapter": "9", + "sentence_range": "957-960", + "Text": "5 cm in size is placed on the side of the convex lens\nin the arrangement (a) above The distance between the object\nand the convex lens is 40 cm Determine the magnification\nproduced by the two-lens system, and the size of the image 9" + }, + { + "Chapter": "9", + "sentence_range": "958-961", + "Text": "The distance between the object\nand the convex lens is 40 cm Determine the magnification\nproduced by the two-lens system, and the size of the image 9 21\nAt what angle should a ray of light be incident on the face of a prism\nof refracting angle 60\u00b0 so that it just suffers total internal reflection\nat the other face" + }, + { + "Chapter": "9", + "sentence_range": "959-962", + "Text": "Determine the magnification\nproduced by the two-lens system, and the size of the image 9 21\nAt what angle should a ray of light be incident on the face of a prism\nof refracting angle 60\u00b0 so that it just suffers total internal reflection\nat the other face The refractive index of the material of the prism is\n1" + }, + { + "Chapter": "9", + "sentence_range": "960-963", + "Text": "9 21\nAt what angle should a ray of light be incident on the face of a prism\nof refracting angle 60\u00b0 so that it just suffers total internal reflection\nat the other face The refractive index of the material of the prism is\n1 524" + }, + { + "Chapter": "9", + "sentence_range": "961-964", + "Text": "21\nAt what angle should a ray of light be incident on the face of a prism\nof refracting angle 60\u00b0 so that it just suffers total internal reflection\nat the other face The refractive index of the material of the prism is\n1 524 9" + }, + { + "Chapter": "9", + "sentence_range": "962-965", + "Text": "The refractive index of the material of the prism is\n1 524 9 22\nA card sheet divided into squares each of size 1 mm2 is being viewed\nat a distance of 9 cm through a magnifying glass (a converging lens\nof focal length 9 cm) held close to the eye" + }, + { + "Chapter": "9", + "sentence_range": "963-966", + "Text": "524 9 22\nA card sheet divided into squares each of size 1 mm2 is being viewed\nat a distance of 9 cm through a magnifying glass (a converging lens\nof focal length 9 cm) held close to the eye (a) What is the magnification produced by the lens" + }, + { + "Chapter": "9", + "sentence_range": "964-967", + "Text": "9 22\nA card sheet divided into squares each of size 1 mm2 is being viewed\nat a distance of 9 cm through a magnifying glass (a converging lens\nof focal length 9 cm) held close to the eye (a) What is the magnification produced by the lens How much is\nthe area of each square in the virtual image" + }, + { + "Chapter": "9", + "sentence_range": "965-968", + "Text": "22\nA card sheet divided into squares each of size 1 mm2 is being viewed\nat a distance of 9 cm through a magnifying glass (a converging lens\nof focal length 9 cm) held close to the eye (a) What is the magnification produced by the lens How much is\nthe area of each square in the virtual image (b) What is the angular magnification (magnifying power) of the\nlens" + }, + { + "Chapter": "9", + "sentence_range": "966-969", + "Text": "(a) What is the magnification produced by the lens How much is\nthe area of each square in the virtual image (b) What is the angular magnification (magnifying power) of the\nlens (c) Is the magnification in (a) equal to the magnifying power in (b)" + }, + { + "Chapter": "9", + "sentence_range": "967-970", + "Text": "How much is\nthe area of each square in the virtual image (b) What is the angular magnification (magnifying power) of the\nlens (c) Is the magnification in (a) equal to the magnifying power in (b) Explain" + }, + { + "Chapter": "9", + "sentence_range": "968-971", + "Text": "(b) What is the angular magnification (magnifying power) of the\nlens (c) Is the magnification in (a) equal to the magnifying power in (b) Explain 9" + }, + { + "Chapter": "9", + "sentence_range": "969-972", + "Text": "(c) Is the magnification in (a) equal to the magnifying power in (b) Explain 9 23\n(a) At what distance should the lens be held from the card sheet in\nExercise 9" + }, + { + "Chapter": "9", + "sentence_range": "970-973", + "Text": "Explain 9 23\n(a) At what distance should the lens be held from the card sheet in\nExercise 9 22 in order to view the squares distinctly with the\nmaximum possible magnifying power" + }, + { + "Chapter": "9", + "sentence_range": "971-974", + "Text": "9 23\n(a) At what distance should the lens be held from the card sheet in\nExercise 9 22 in order to view the squares distinctly with the\nmaximum possible magnifying power (b) What is the magnification in this case" + }, + { + "Chapter": "9", + "sentence_range": "972-975", + "Text": "23\n(a) At what distance should the lens be held from the card sheet in\nExercise 9 22 in order to view the squares distinctly with the\nmaximum possible magnifying power (b) What is the magnification in this case (c) Is the magnification equal to the magnifying power in this case" + }, + { + "Chapter": "9", + "sentence_range": "973-976", + "Text": "22 in order to view the squares distinctly with the\nmaximum possible magnifying power (b) What is the magnification in this case (c) Is the magnification equal to the magnifying power in this case Explain" + }, + { + "Chapter": "9", + "sentence_range": "974-977", + "Text": "(b) What is the magnification in this case (c) Is the magnification equal to the magnifying power in this case Explain 9" + }, + { + "Chapter": "9", + "sentence_range": "975-978", + "Text": "(c) Is the magnification equal to the magnifying power in this case Explain 9 24\nWhat should be the distance between the object in Exercise 9" + }, + { + "Chapter": "9", + "sentence_range": "976-979", + "Text": "Explain 9 24\nWhat should be the distance between the object in Exercise 9 23\nand the magnifying glass if the virtual image of each square in\nthe figure is to have an area of 6" + }, + { + "Chapter": "9", + "sentence_range": "977-980", + "Text": "9 24\nWhat should be the distance between the object in Exercise 9 23\nand the magnifying glass if the virtual image of each square in\nthe figure is to have an area of 6 25 mm2" + }, + { + "Chapter": "9", + "sentence_range": "978-981", + "Text": "24\nWhat should be the distance between the object in Exercise 9 23\nand the magnifying glass if the virtual image of each square in\nthe figure is to have an area of 6 25 mm2 Would you be able to\nsee the squares distinctly with your eyes very close to the\nmagnifier" + }, + { + "Chapter": "9", + "sentence_range": "979-982", + "Text": "23\nand the magnifying glass if the virtual image of each square in\nthe figure is to have an area of 6 25 mm2 Would you be able to\nsee the squares distinctly with your eyes very close to the\nmagnifier [Note: Exercises 9" + }, + { + "Chapter": "9", + "sentence_range": "980-983", + "Text": "25 mm2 Would you be able to\nsee the squares distinctly with your eyes very close to the\nmagnifier [Note: Exercises 9 22 to 9" + }, + { + "Chapter": "9", + "sentence_range": "981-984", + "Text": "Would you be able to\nsee the squares distinctly with your eyes very close to the\nmagnifier [Note: Exercises 9 22 to 9 24 will help you clearly understand the\ndifference between magnification in absolute size and the angular\nmagnification (or magnifying power) of an instrument" + }, + { + "Chapter": "9", + "sentence_range": "982-985", + "Text": "[Note: Exercises 9 22 to 9 24 will help you clearly understand the\ndifference between magnification in absolute size and the angular\nmagnification (or magnifying power) of an instrument ]\nRationalised 2023-24\nPhysics\n252\n9" + }, + { + "Chapter": "9", + "sentence_range": "983-986", + "Text": "22 to 9 24 will help you clearly understand the\ndifference between magnification in absolute size and the angular\nmagnification (or magnifying power) of an instrument ]\nRationalised 2023-24\nPhysics\n252\n9 25\nAnswer the following questions:\n(a) The angle subtended at the eye by an object is equal to the\nangle subtended at the eye by the virtual image produced by a\nmagnifying glass" + }, + { + "Chapter": "9", + "sentence_range": "984-987", + "Text": "24 will help you clearly understand the\ndifference between magnification in absolute size and the angular\nmagnification (or magnifying power) of an instrument ]\nRationalised 2023-24\nPhysics\n252\n9 25\nAnswer the following questions:\n(a) The angle subtended at the eye by an object is equal to the\nangle subtended at the eye by the virtual image produced by a\nmagnifying glass In what sense then does a magnifying glass\nprovide angular magnification" + }, + { + "Chapter": "9", + "sentence_range": "985-988", + "Text": "]\nRationalised 2023-24\nPhysics\n252\n9 25\nAnswer the following questions:\n(a) The angle subtended at the eye by an object is equal to the\nangle subtended at the eye by the virtual image produced by a\nmagnifying glass In what sense then does a magnifying glass\nprovide angular magnification (b) In viewing through a magnifying glass, one usually positions\none\u2019s eyes very close to the lens" + }, + { + "Chapter": "9", + "sentence_range": "986-989", + "Text": "25\nAnswer the following questions:\n(a) The angle subtended at the eye by an object is equal to the\nangle subtended at the eye by the virtual image produced by a\nmagnifying glass In what sense then does a magnifying glass\nprovide angular magnification (b) In viewing through a magnifying glass, one usually positions\none\u2019s eyes very close to the lens Does angular magnification\nchange if the eye is moved back" + }, + { + "Chapter": "9", + "sentence_range": "987-990", + "Text": "In what sense then does a magnifying glass\nprovide angular magnification (b) In viewing through a magnifying glass, one usually positions\none\u2019s eyes very close to the lens Does angular magnification\nchange if the eye is moved back (c) Magnifying power of a simple microscope is inversely proportional\nto the focal length of the lens" + }, + { + "Chapter": "9", + "sentence_range": "988-991", + "Text": "(b) In viewing through a magnifying glass, one usually positions\none\u2019s eyes very close to the lens Does angular magnification\nchange if the eye is moved back (c) Magnifying power of a simple microscope is inversely proportional\nto the focal length of the lens What then stops us from using a\nconvex lens of smaller and smaller focal length and achieving\ngreater and greater magnifying power" + }, + { + "Chapter": "9", + "sentence_range": "989-992", + "Text": "Does angular magnification\nchange if the eye is moved back (c) Magnifying power of a simple microscope is inversely proportional\nto the focal length of the lens What then stops us from using a\nconvex lens of smaller and smaller focal length and achieving\ngreater and greater magnifying power (d) Why must both the objective and the eyepiece of a compound\nmicroscope have short focal lengths" + }, + { + "Chapter": "9", + "sentence_range": "990-993", + "Text": "(c) Magnifying power of a simple microscope is inversely proportional\nto the focal length of the lens What then stops us from using a\nconvex lens of smaller and smaller focal length and achieving\ngreater and greater magnifying power (d) Why must both the objective and the eyepiece of a compound\nmicroscope have short focal lengths (e) When viewing through a compound microscope, our eyes should\nbe positioned not on the eyepiece but a short distance away\nfrom it for best viewing" + }, + { + "Chapter": "9", + "sentence_range": "991-994", + "Text": "What then stops us from using a\nconvex lens of smaller and smaller focal length and achieving\ngreater and greater magnifying power (d) Why must both the objective and the eyepiece of a compound\nmicroscope have short focal lengths (e) When viewing through a compound microscope, our eyes should\nbe positioned not on the eyepiece but a short distance away\nfrom it for best viewing Why" + }, + { + "Chapter": "9", + "sentence_range": "992-995", + "Text": "(d) Why must both the objective and the eyepiece of a compound\nmicroscope have short focal lengths (e) When viewing through a compound microscope, our eyes should\nbe positioned not on the eyepiece but a short distance away\nfrom it for best viewing Why How much should be that short\ndistance between the eye and eyepiece" + }, + { + "Chapter": "9", + "sentence_range": "993-996", + "Text": "(e) When viewing through a compound microscope, our eyes should\nbe positioned not on the eyepiece but a short distance away\nfrom it for best viewing Why How much should be that short\ndistance between the eye and eyepiece 9" + }, + { + "Chapter": "9", + "sentence_range": "994-997", + "Text": "Why How much should be that short\ndistance between the eye and eyepiece 9 26\nAn angular magnification (magnifying power) of 30X is desired using\nan objective of focal length 1" + }, + { + "Chapter": "9", + "sentence_range": "995-998", + "Text": "How much should be that short\ndistance between the eye and eyepiece 9 26\nAn angular magnification (magnifying power) of 30X is desired using\nan objective of focal length 1 25cm and an eyepiece of focal length\n5cm" + }, + { + "Chapter": "9", + "sentence_range": "996-999", + "Text": "9 26\nAn angular magnification (magnifying power) of 30X is desired using\nan objective of focal length 1 25cm and an eyepiece of focal length\n5cm How will you set up the compound microscope" + }, + { + "Chapter": "9", + "sentence_range": "997-1000", + "Text": "26\nAn angular magnification (magnifying power) of 30X is desired using\nan objective of focal length 1 25cm and an eyepiece of focal length\n5cm How will you set up the compound microscope 9" + }, + { + "Chapter": "9", + "sentence_range": "998-1001", + "Text": "25cm and an eyepiece of focal length\n5cm How will you set up the compound microscope 9 27\nA small telescope has an objective lens of focal length 140cm and\nan eyepiece of focal length 5" + }, + { + "Chapter": "9", + "sentence_range": "999-1002", + "Text": "How will you set up the compound microscope 9 27\nA small telescope has an objective lens of focal length 140cm and\nan eyepiece of focal length 5 0cm" + }, + { + "Chapter": "9", + "sentence_range": "1000-1003", + "Text": "9 27\nA small telescope has an objective lens of focal length 140cm and\nan eyepiece of focal length 5 0cm What is the magnifying power of\nthe telescope for viewing distant objects when\n(a) the telescope is in normal adjustment (i" + }, + { + "Chapter": "9", + "sentence_range": "1001-1004", + "Text": "27\nA small telescope has an objective lens of focal length 140cm and\nan eyepiece of focal length 5 0cm What is the magnifying power of\nthe telescope for viewing distant objects when\n(a) the telescope is in normal adjustment (i e" + }, + { + "Chapter": "9", + "sentence_range": "1002-1005", + "Text": "0cm What is the magnifying power of\nthe telescope for viewing distant objects when\n(a) the telescope is in normal adjustment (i e , when the final image\nis at infinity)" + }, + { + "Chapter": "9", + "sentence_range": "1003-1006", + "Text": "What is the magnifying power of\nthe telescope for viewing distant objects when\n(a) the telescope is in normal adjustment (i e , when the final image\nis at infinity) (b) the final image is formed at the least distance of distinct vision\n(25cm)" + }, + { + "Chapter": "9", + "sentence_range": "1004-1007", + "Text": "e , when the final image\nis at infinity) (b) the final image is formed at the least distance of distinct vision\n(25cm) 9" + }, + { + "Chapter": "9", + "sentence_range": "1005-1008", + "Text": ", when the final image\nis at infinity) (b) the final image is formed at the least distance of distinct vision\n(25cm) 9 28\n(a) For the telescope described in Exercise 9" + }, + { + "Chapter": "9", + "sentence_range": "1006-1009", + "Text": "(b) the final image is formed at the least distance of distinct vision\n(25cm) 9 28\n(a) For the telescope described in Exercise 9 27 (a), what is the\nseparation between the objective lens and the eyepiece" + }, + { + "Chapter": "9", + "sentence_range": "1007-1010", + "Text": "9 28\n(a) For the telescope described in Exercise 9 27 (a), what is the\nseparation between the objective lens and the eyepiece (b) If this telescope is used to view a 100 m tall tower 3 km away,\nwhat is the height of the image of the tower formed by the objective\nlens" + }, + { + "Chapter": "9", + "sentence_range": "1008-1011", + "Text": "28\n(a) For the telescope described in Exercise 9 27 (a), what is the\nseparation between the objective lens and the eyepiece (b) If this telescope is used to view a 100 m tall tower 3 km away,\nwhat is the height of the image of the tower formed by the objective\nlens (c) What is the height of the final image of the tower if it is formed at\n25cm" + }, + { + "Chapter": "9", + "sentence_range": "1009-1012", + "Text": "27 (a), what is the\nseparation between the objective lens and the eyepiece (b) If this telescope is used to view a 100 m tall tower 3 km away,\nwhat is the height of the image of the tower formed by the objective\nlens (c) What is the height of the final image of the tower if it is formed at\n25cm 9" + }, + { + "Chapter": "9", + "sentence_range": "1010-1013", + "Text": "(b) If this telescope is used to view a 100 m tall tower 3 km away,\nwhat is the height of the image of the tower formed by the objective\nlens (c) What is the height of the final image of the tower if it is formed at\n25cm 9 29\nA Cassegrain telescope uses two mirrors as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1011-1014", + "Text": "(c) What is the height of the final image of the tower if it is formed at\n25cm 9 29\nA Cassegrain telescope uses two mirrors as shown in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "1012-1015", + "Text": "9 29\nA Cassegrain telescope uses two mirrors as shown in Fig 9 26" + }, + { + "Chapter": "9", + "sentence_range": "1013-1016", + "Text": "29\nA Cassegrain telescope uses two mirrors as shown in Fig 9 26 Such\na telescope is built with the mirrors 20mm apart" + }, + { + "Chapter": "9", + "sentence_range": "1014-1017", + "Text": "9 26 Such\na telescope is built with the mirrors 20mm apart If the radius of\ncurvature of the large mirror is 220mm and the small mirror is\n140mm, where will the final image of an object at infinity be" + }, + { + "Chapter": "9", + "sentence_range": "1015-1018", + "Text": "26 Such\na telescope is built with the mirrors 20mm apart If the radius of\ncurvature of the large mirror is 220mm and the small mirror is\n140mm, where will the final image of an object at infinity be 9" + }, + { + "Chapter": "9", + "sentence_range": "1016-1019", + "Text": "Such\na telescope is built with the mirrors 20mm apart If the radius of\ncurvature of the large mirror is 220mm and the small mirror is\n140mm, where will the final image of an object at infinity be 9 30\nLight incident normally on a plane mirror attached to a galvanometer\ncoil retraces backwards as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1017-1020", + "Text": "If the radius of\ncurvature of the large mirror is 220mm and the small mirror is\n140mm, where will the final image of an object at infinity be 9 30\nLight incident normally on a plane mirror attached to a galvanometer\ncoil retraces backwards as shown in Fig 9" + }, + { + "Chapter": "9", + "sentence_range": "1018-1021", + "Text": "9 30\nLight incident normally on a plane mirror attached to a galvanometer\ncoil retraces backwards as shown in Fig 9 29" + }, + { + "Chapter": "9", + "sentence_range": "1019-1022", + "Text": "30\nLight incident normally on a plane mirror attached to a galvanometer\ncoil retraces backwards as shown in Fig 9 29 A current in the coil\nproduces a deflection of 3" + }, + { + "Chapter": "9", + "sentence_range": "1020-1023", + "Text": "9 29 A current in the coil\nproduces a deflection of 3 5o of the mirror" + }, + { + "Chapter": "9", + "sentence_range": "1021-1024", + "Text": "29 A current in the coil\nproduces a deflection of 3 5o of the mirror What is the displacement\nof the reflected spot of light on a screen placed 1" + }, + { + "Chapter": "9", + "sentence_range": "1022-1025", + "Text": "A current in the coil\nproduces a deflection of 3 5o of the mirror What is the displacement\nof the reflected spot of light on a screen placed 1 5 m away" + }, + { + "Chapter": "9", + "sentence_range": "1023-1026", + "Text": "5o of the mirror What is the displacement\nof the reflected spot of light on a screen placed 1 5 m away Rationalised 2023-24\nRay Optics and\nOptical Instruments\n253\nFIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "1024-1027", + "Text": "What is the displacement\nof the reflected spot of light on a screen placed 1 5 m away Rationalised 2023-24\nRay Optics and\nOptical Instruments\n253\nFIGURE 9 29\n9" + }, + { + "Chapter": "9", + "sentence_range": "1025-1028", + "Text": "5 m away Rationalised 2023-24\nRay Optics and\nOptical Instruments\n253\nFIGURE 9 29\n9 31\nFigure 9" + }, + { + "Chapter": "9", + "sentence_range": "1026-1029", + "Text": "Rationalised 2023-24\nRay Optics and\nOptical Instruments\n253\nFIGURE 9 29\n9 31\nFigure 9 30 shows an equiconvex lens (of refractive index 1" + }, + { + "Chapter": "9", + "sentence_range": "1027-1030", + "Text": "29\n9 31\nFigure 9 30 shows an equiconvex lens (of refractive index 1 50) in\ncontact with a liquid layer on top of a plane mirror" + }, + { + "Chapter": "9", + "sentence_range": "1028-1031", + "Text": "31\nFigure 9 30 shows an equiconvex lens (of refractive index 1 50) in\ncontact with a liquid layer on top of a plane mirror A small needle\nwith its tip on the principal axis is moved along the axis until its\ninverted image is found at the position of the needle" + }, + { + "Chapter": "9", + "sentence_range": "1029-1032", + "Text": "30 shows an equiconvex lens (of refractive index 1 50) in\ncontact with a liquid layer on top of a plane mirror A small needle\nwith its tip on the principal axis is moved along the axis until its\ninverted image is found at the position of the needle The distance of\nthe needle from the lens is measured to be 45" + }, + { + "Chapter": "9", + "sentence_range": "1030-1033", + "Text": "50) in\ncontact with a liquid layer on top of a plane mirror A small needle\nwith its tip on the principal axis is moved along the axis until its\ninverted image is found at the position of the needle The distance of\nthe needle from the lens is measured to be 45 0cm" + }, + { + "Chapter": "9", + "sentence_range": "1031-1034", + "Text": "A small needle\nwith its tip on the principal axis is moved along the axis until its\ninverted image is found at the position of the needle The distance of\nthe needle from the lens is measured to be 45 0cm The liquid is\nremoved and the experiment is repeated" + }, + { + "Chapter": "9", + "sentence_range": "1032-1035", + "Text": "The distance of\nthe needle from the lens is measured to be 45 0cm The liquid is\nremoved and the experiment is repeated The new distance is\nmeasured to be 30" + }, + { + "Chapter": "9", + "sentence_range": "1033-1036", + "Text": "0cm The liquid is\nremoved and the experiment is repeated The new distance is\nmeasured to be 30 0cm" + }, + { + "Chapter": "9", + "sentence_range": "1034-1037", + "Text": "The liquid is\nremoved and the experiment is repeated The new distance is\nmeasured to be 30 0cm What is the refractive index of the liquid" + }, + { + "Chapter": "9", + "sentence_range": "1035-1038", + "Text": "The new distance is\nmeasured to be 30 0cm What is the refractive index of the liquid FIGURE 9" + }, + { + "Chapter": "9", + "sentence_range": "1036-1039", + "Text": "0cm What is the refractive index of the liquid FIGURE 9 30\nRationalised 2023-24\nPhysics\n254\nNotes\nRationalised 2023-24\n255\nWave Optics\nChapter Ten\nWAVE OPTICS\n10" + }, + { + "Chapter": "9", + "sentence_range": "1037-1040", + "Text": "What is the refractive index of the liquid FIGURE 9 30\nRationalised 2023-24\nPhysics\n254\nNotes\nRationalised 2023-24\n255\nWave Optics\nChapter Ten\nWAVE OPTICS\n10 1 INTRODUCTION\nIn 1637 Descartes gave the corpuscular model of light and derived Snell\u2019s\nlaw" + }, + { + "Chapter": "9", + "sentence_range": "1038-1041", + "Text": "FIGURE 9 30\nRationalised 2023-24\nPhysics\n254\nNotes\nRationalised 2023-24\n255\nWave Optics\nChapter Ten\nWAVE OPTICS\n10 1 INTRODUCTION\nIn 1637 Descartes gave the corpuscular model of light and derived Snell\u2019s\nlaw It explained the laws of reflection and refraction of light at an interface" + }, + { + "Chapter": "9", + "sentence_range": "1039-1042", + "Text": "30\nRationalised 2023-24\nPhysics\n254\nNotes\nRationalised 2023-24\n255\nWave Optics\nChapter Ten\nWAVE OPTICS\n10 1 INTRODUCTION\nIn 1637 Descartes gave the corpuscular model of light and derived Snell\u2019s\nlaw It explained the laws of reflection and refraction of light at an interface The corpuscular model predicted that if the ray of light (on refraction)\nbends towards the normal then the speed of light would be greater in the\nsecond medium" + }, + { + "Chapter": "9", + "sentence_range": "1040-1043", + "Text": "1 INTRODUCTION\nIn 1637 Descartes gave the corpuscular model of light and derived Snell\u2019s\nlaw It explained the laws of reflection and refraction of light at an interface The corpuscular model predicted that if the ray of light (on refraction)\nbends towards the normal then the speed of light would be greater in the\nsecond medium This corpuscular model of light was further developed\nby Isaac Newton in his famous book entitled OPTICKS and because of\nthe tremendous popularity of this book, the corpuscular model is very\noften attributed to Newton" + }, + { + "Chapter": "9", + "sentence_range": "1041-1044", + "Text": "It explained the laws of reflection and refraction of light at an interface The corpuscular model predicted that if the ray of light (on refraction)\nbends towards the normal then the speed of light would be greater in the\nsecond medium This corpuscular model of light was further developed\nby Isaac Newton in his famous book entitled OPTICKS and because of\nthe tremendous popularity of this book, the corpuscular model is very\noften attributed to Newton In 1678, the Dutch physicist Christiaan Huygens put forward the\nwave theory of light \u2013 it is this wave model of light that we will discuss in\nthis chapter" + }, + { + "Chapter": "9", + "sentence_range": "1042-1045", + "Text": "The corpuscular model predicted that if the ray of light (on refraction)\nbends towards the normal then the speed of light would be greater in the\nsecond medium This corpuscular model of light was further developed\nby Isaac Newton in his famous book entitled OPTICKS and because of\nthe tremendous popularity of this book, the corpuscular model is very\noften attributed to Newton In 1678, the Dutch physicist Christiaan Huygens put forward the\nwave theory of light \u2013 it is this wave model of light that we will discuss in\nthis chapter As we will see, the wave model could satisfactorily explain\nthe phenomena of reflection and refraction; however, it predicted that on\nrefraction if the wave bends towards the normal then the speed of light\nwould be less in the second medium" + }, + { + "Chapter": "9", + "sentence_range": "1043-1046", + "Text": "This corpuscular model of light was further developed\nby Isaac Newton in his famous book entitled OPTICKS and because of\nthe tremendous popularity of this book, the corpuscular model is very\noften attributed to Newton In 1678, the Dutch physicist Christiaan Huygens put forward the\nwave theory of light \u2013 it is this wave model of light that we will discuss in\nthis chapter As we will see, the wave model could satisfactorily explain\nthe phenomena of reflection and refraction; however, it predicted that on\nrefraction if the wave bends towards the normal then the speed of light\nwould be less in the second medium This is in contradiction to the\nprediction made by using the corpuscular model of light" + }, + { + "Chapter": "9", + "sentence_range": "1044-1047", + "Text": "In 1678, the Dutch physicist Christiaan Huygens put forward the\nwave theory of light \u2013 it is this wave model of light that we will discuss in\nthis chapter As we will see, the wave model could satisfactorily explain\nthe phenomena of reflection and refraction; however, it predicted that on\nrefraction if the wave bends towards the normal then the speed of light\nwould be less in the second medium This is in contradiction to the\nprediction made by using the corpuscular model of light It was much\nlater confirmed by experiments where it was shown that the speed of\nlight in water is less than the speed in air confirming the prediction of the\nwave model; Foucault carried out this experiment in 1850" + }, + { + "Chapter": "9", + "sentence_range": "1045-1048", + "Text": "As we will see, the wave model could satisfactorily explain\nthe phenomena of reflection and refraction; however, it predicted that on\nrefraction if the wave bends towards the normal then the speed of light\nwould be less in the second medium This is in contradiction to the\nprediction made by using the corpuscular model of light It was much\nlater confirmed by experiments where it was shown that the speed of\nlight in water is less than the speed in air confirming the prediction of the\nwave model; Foucault carried out this experiment in 1850 The wave theory was not readily accepted primarily because of\nNewton\u2019s authority and also because light could travel through vacuum\nRationalised 2023-24\nPhysics\n256\nand it was felt that a wave would always require a medium to propagate\nfrom one point to the other" + }, + { + "Chapter": "9", + "sentence_range": "1046-1049", + "Text": "This is in contradiction to the\nprediction made by using the corpuscular model of light It was much\nlater confirmed by experiments where it was shown that the speed of\nlight in water is less than the speed in air confirming the prediction of the\nwave model; Foucault carried out this experiment in 1850 The wave theory was not readily accepted primarily because of\nNewton\u2019s authority and also because light could travel through vacuum\nRationalised 2023-24\nPhysics\n256\nand it was felt that a wave would always require a medium to propagate\nfrom one point to the other However, when Thomas Young performed\nhis famous interference experiment in 1801, it was firmly established\nthat light is indeed a wave phenomenon" + }, + { + "Chapter": "9", + "sentence_range": "1047-1050", + "Text": "It was much\nlater confirmed by experiments where it was shown that the speed of\nlight in water is less than the speed in air confirming the prediction of the\nwave model; Foucault carried out this experiment in 1850 The wave theory was not readily accepted primarily because of\nNewton\u2019s authority and also because light could travel through vacuum\nRationalised 2023-24\nPhysics\n256\nand it was felt that a wave would always require a medium to propagate\nfrom one point to the other However, when Thomas Young performed\nhis famous interference experiment in 1801, it was firmly established\nthat light is indeed a wave phenomenon The wavelength of visible\nlight was measured and found to be extremely small; for example, the\nwavelength of yellow light is about 0" + }, + { + "Chapter": "9", + "sentence_range": "1048-1051", + "Text": "The wave theory was not readily accepted primarily because of\nNewton\u2019s authority and also because light could travel through vacuum\nRationalised 2023-24\nPhysics\n256\nand it was felt that a wave would always require a medium to propagate\nfrom one point to the other However, when Thomas Young performed\nhis famous interference experiment in 1801, it was firmly established\nthat light is indeed a wave phenomenon The wavelength of visible\nlight was measured and found to be extremely small; for example, the\nwavelength of yellow light is about 0 6 mm" + }, + { + "Chapter": "9", + "sentence_range": "1049-1052", + "Text": "However, when Thomas Young performed\nhis famous interference experiment in 1801, it was firmly established\nthat light is indeed a wave phenomenon The wavelength of visible\nlight was measured and found to be extremely small; for example, the\nwavelength of yellow light is about 0 6 mm Because of the smallness\nof the wavelength of visible light (in comparison to the dimensions of\ntypical mirrors and lenses), light can be assumed to approximately\ntravel in straight lines" + }, + { + "Chapter": "9", + "sentence_range": "1050-1053", + "Text": "The wavelength of visible\nlight was measured and found to be extremely small; for example, the\nwavelength of yellow light is about 0 6 mm Because of the smallness\nof the wavelength of visible light (in comparison to the dimensions of\ntypical mirrors and lenses), light can be assumed to approximately\ntravel in straight lines This is the field of geometrical optics, which we\nhad discussed in the previous chapter" + }, + { + "Chapter": "9", + "sentence_range": "1051-1054", + "Text": "6 mm Because of the smallness\nof the wavelength of visible light (in comparison to the dimensions of\ntypical mirrors and lenses), light can be assumed to approximately\ntravel in straight lines This is the field of geometrical optics, which we\nhad discussed in the previous chapter Indeed, the branch of optics in\nwhich one completely neglects the finiteness of the wavelength is called\ngeometrical optics and a ray is defined as the path of energy\npropagation in the limit of wavelength tending to zero" + }, + { + "Chapter": "9", + "sentence_range": "1052-1055", + "Text": "Because of the smallness\nof the wavelength of visible light (in comparison to the dimensions of\ntypical mirrors and lenses), light can be assumed to approximately\ntravel in straight lines This is the field of geometrical optics, which we\nhad discussed in the previous chapter Indeed, the branch of optics in\nwhich one completely neglects the finiteness of the wavelength is called\ngeometrical optics and a ray is defined as the path of energy\npropagation in the limit of wavelength tending to zero After the interference experiment of Young in 1801, for the next 40\nyears or so, many experiments were carried out involving the\ninterference and diffraction of lightwaves; these experiments could only\nbe satisfactorily explained by assuming a wave model of light" + }, + { + "Chapter": "9", + "sentence_range": "1053-1056", + "Text": "This is the field of geometrical optics, which we\nhad discussed in the previous chapter Indeed, the branch of optics in\nwhich one completely neglects the finiteness of the wavelength is called\ngeometrical optics and a ray is defined as the path of energy\npropagation in the limit of wavelength tending to zero After the interference experiment of Young in 1801, for the next 40\nyears or so, many experiments were carried out involving the\ninterference and diffraction of lightwaves; these experiments could only\nbe satisfactorily explained by assuming a wave model of light Thus,\naround the middle of the nineteenth century, the wave theory seemed\nto be very well established" + }, + { + "Chapter": "9", + "sentence_range": "1054-1057", + "Text": "Indeed, the branch of optics in\nwhich one completely neglects the finiteness of the wavelength is called\ngeometrical optics and a ray is defined as the path of energy\npropagation in the limit of wavelength tending to zero After the interference experiment of Young in 1801, for the next 40\nyears or so, many experiments were carried out involving the\ninterference and diffraction of lightwaves; these experiments could only\nbe satisfactorily explained by assuming a wave model of light Thus,\naround the middle of the nineteenth century, the wave theory seemed\nto be very well established The only major difficulty was that since it\nwas thought that a wave required a medium for its propagation, how\ncould light waves propagate through vacuum" + }, + { + "Chapter": "9", + "sentence_range": "1055-1058", + "Text": "After the interference experiment of Young in 1801, for the next 40\nyears or so, many experiments were carried out involving the\ninterference and diffraction of lightwaves; these experiments could only\nbe satisfactorily explained by assuming a wave model of light Thus,\naround the middle of the nineteenth century, the wave theory seemed\nto be very well established The only major difficulty was that since it\nwas thought that a wave required a medium for its propagation, how\ncould light waves propagate through vacuum This was explained\nwhen Maxwell put forward his famous electromagnetic theory of light" + }, + { + "Chapter": "9", + "sentence_range": "1056-1059", + "Text": "Thus,\naround the middle of the nineteenth century, the wave theory seemed\nto be very well established The only major difficulty was that since it\nwas thought that a wave required a medium for its propagation, how\ncould light waves propagate through vacuum This was explained\nwhen Maxwell put forward his famous electromagnetic theory of light Maxwell had developed a set of equations describing the laws of\nelectricity and magnetism and using these equations he derived what\nis known as the wave equation from which he predicted the existence\nof electromagnetic waves*" + }, + { + "Chapter": "9", + "sentence_range": "1057-1060", + "Text": "The only major difficulty was that since it\nwas thought that a wave required a medium for its propagation, how\ncould light waves propagate through vacuum This was explained\nwhen Maxwell put forward his famous electromagnetic theory of light Maxwell had developed a set of equations describing the laws of\nelectricity and magnetism and using these equations he derived what\nis known as the wave equation from which he predicted the existence\nof electromagnetic waves* From the wave equation, Maxwell could\ncalculate the speed of electromagnetic waves in free space and he found\nthat the theoretical value was very close to the measured value of speed\nof light" + }, + { + "Chapter": "9", + "sentence_range": "1058-1061", + "Text": "This was explained\nwhen Maxwell put forward his famous electromagnetic theory of light Maxwell had developed a set of equations describing the laws of\nelectricity and magnetism and using these equations he derived what\nis known as the wave equation from which he predicted the existence\nof electromagnetic waves* From the wave equation, Maxwell could\ncalculate the speed of electromagnetic waves in free space and he found\nthat the theoretical value was very close to the measured value of speed\nof light From this, he propounded that light must be an\nelectromagnetic wave" + }, + { + "Chapter": "9", + "sentence_range": "1059-1062", + "Text": "Maxwell had developed a set of equations describing the laws of\nelectricity and magnetism and using these equations he derived what\nis known as the wave equation from which he predicted the existence\nof electromagnetic waves* From the wave equation, Maxwell could\ncalculate the speed of electromagnetic waves in free space and he found\nthat the theoretical value was very close to the measured value of speed\nof light From this, he propounded that light must be an\nelectromagnetic wave Thus, according to Maxwell, light waves are\nassociated with changing electric and magnetic fields; changing electric\nfield produces a time and space varying magnetic field and a changing\nmagnetic field produces a time and space varying electric field" + }, + { + "Chapter": "9", + "sentence_range": "1060-1063", + "Text": "From the wave equation, Maxwell could\ncalculate the speed of electromagnetic waves in free space and he found\nthat the theoretical value was very close to the measured value of speed\nof light From this, he propounded that light must be an\nelectromagnetic wave Thus, according to Maxwell, light waves are\nassociated with changing electric and magnetic fields; changing electric\nfield produces a time and space varying magnetic field and a changing\nmagnetic field produces a time and space varying electric field The\nchanging electric and magnetic fields result in the propagation of\nelectromagnetic waves (or light waves) even in vacuum" + }, + { + "Chapter": "9", + "sentence_range": "1061-1064", + "Text": "From this, he propounded that light must be an\nelectromagnetic wave Thus, according to Maxwell, light waves are\nassociated with changing electric and magnetic fields; changing electric\nfield produces a time and space varying magnetic field and a changing\nmagnetic field produces a time and space varying electric field The\nchanging electric and magnetic fields result in the propagation of\nelectromagnetic waves (or light waves) even in vacuum In this chapter we will first discuss the original formulation of the\nHuygens principle and derive the laws of reflection and refraction" + }, + { + "Chapter": "9", + "sentence_range": "1062-1065", + "Text": "Thus, according to Maxwell, light waves are\nassociated with changing electric and magnetic fields; changing electric\nfield produces a time and space varying magnetic field and a changing\nmagnetic field produces a time and space varying electric field The\nchanging electric and magnetic fields result in the propagation of\nelectromagnetic waves (or light waves) even in vacuum In this chapter we will first discuss the original formulation of the\nHuygens principle and derive the laws of reflection and refraction In\nSections 10" + }, + { + "Chapter": "9", + "sentence_range": "1063-1066", + "Text": "The\nchanging electric and magnetic fields result in the propagation of\nelectromagnetic waves (or light waves) even in vacuum In this chapter we will first discuss the original formulation of the\nHuygens principle and derive the laws of reflection and refraction In\nSections 10 4 and 10" + }, + { + "Chapter": "9", + "sentence_range": "1064-1067", + "Text": "In this chapter we will first discuss the original formulation of the\nHuygens principle and derive the laws of reflection and refraction In\nSections 10 4 and 10 5, we will discuss the phenomenon of interference\nwhich is based on the principle of superposition" + }, + { + "Chapter": "9", + "sentence_range": "1065-1068", + "Text": "In\nSections 10 4 and 10 5, we will discuss the phenomenon of interference\nwhich is based on the principle of superposition In Section 10" + }, + { + "Chapter": "9", + "sentence_range": "1066-1069", + "Text": "4 and 10 5, we will discuss the phenomenon of interference\nwhich is based on the principle of superposition In Section 10 6 we\nwill discuss the phenomenon of diffraction which is based on Huygens-\nFresnel principle" + }, + { + "Chapter": "9", + "sentence_range": "1067-1070", + "Text": "5, we will discuss the phenomenon of interference\nwhich is based on the principle of superposition In Section 10 6 we\nwill discuss the phenomenon of diffraction which is based on Huygens-\nFresnel principle Finally in Section 10" + }, + { + "Chapter": "9", + "sentence_range": "1068-1071", + "Text": "In Section 10 6 we\nwill discuss the phenomenon of diffraction which is based on Huygens-\nFresnel principle Finally in Section 10 7 we will discuss the\nphenomenon of polarisation which is based on the fact that the light\nwaves are transverse electromagnetic waves" + }, + { + "Chapter": "9", + "sentence_range": "1069-1072", + "Text": "6 we\nwill discuss the phenomenon of diffraction which is based on Huygens-\nFresnel principle Finally in Section 10 7 we will discuss the\nphenomenon of polarisation which is based on the fact that the light\nwaves are transverse electromagnetic waves *\nMaxwell had predicted the existence of electromagnetic waves around 1855; it\nwas much later (around 1890) that Heinrich Hertz produced radiowaves in the\nlaboratory" + }, + { + "Chapter": "9", + "sentence_range": "1070-1073", + "Text": "Finally in Section 10 7 we will discuss the\nphenomenon of polarisation which is based on the fact that the light\nwaves are transverse electromagnetic waves *\nMaxwell had predicted the existence of electromagnetic waves around 1855; it\nwas much later (around 1890) that Heinrich Hertz produced radiowaves in the\nlaboratory J" + }, + { + "Chapter": "9", + "sentence_range": "1071-1074", + "Text": "7 we will discuss the\nphenomenon of polarisation which is based on the fact that the light\nwaves are transverse electromagnetic waves *\nMaxwell had predicted the existence of electromagnetic waves around 1855; it\nwas much later (around 1890) that Heinrich Hertz produced radiowaves in the\nlaboratory J C" + }, + { + "Chapter": "9", + "sentence_range": "1072-1075", + "Text": "*\nMaxwell had predicted the existence of electromagnetic waves around 1855; it\nwas much later (around 1890) that Heinrich Hertz produced radiowaves in the\nlaboratory J C Bose and G" + }, + { + "Chapter": "9", + "sentence_range": "1073-1076", + "Text": "J C Bose and G Marconi made practical applications of the Hertzian\nwaves\nRationalised 2023-24\n257\nWave Optics\n10" + }, + { + "Chapter": "9", + "sentence_range": "1074-1077", + "Text": "C Bose and G Marconi made practical applications of the Hertzian\nwaves\nRationalised 2023-24\n257\nWave Optics\n10 2 HUYGENS PRINCIPLE\nWe would first define a wavefront: when we drop a small stone on a\ncalm pool of water, waves spread out from the point of impact" + }, + { + "Chapter": "9", + "sentence_range": "1075-1078", + "Text": "Bose and G Marconi made practical applications of the Hertzian\nwaves\nRationalised 2023-24\n257\nWave Optics\n10 2 HUYGENS PRINCIPLE\nWe would first define a wavefront: when we drop a small stone on a\ncalm pool of water, waves spread out from the point of impact Every\npoint on the surface starts oscillating with time" + }, + { + "Chapter": "9", + "sentence_range": "1076-1079", + "Text": "Marconi made practical applications of the Hertzian\nwaves\nRationalised 2023-24\n257\nWave Optics\n10 2 HUYGENS PRINCIPLE\nWe would first define a wavefront: when we drop a small stone on a\ncalm pool of water, waves spread out from the point of impact Every\npoint on the surface starts oscillating with time At any instant, a\nphotograph of the surface would show circular rings on which the\ndisturbance is maximum" + }, + { + "Chapter": "9", + "sentence_range": "1077-1080", + "Text": "2 HUYGENS PRINCIPLE\nWe would first define a wavefront: when we drop a small stone on a\ncalm pool of water, waves spread out from the point of impact Every\npoint on the surface starts oscillating with time At any instant, a\nphotograph of the surface would show circular rings on which the\ndisturbance is maximum Clearly, all points on such a circle are\noscillating in phase because they are at the same distance from the\nsource" + }, + { + "Chapter": "9", + "sentence_range": "1078-1081", + "Text": "Every\npoint on the surface starts oscillating with time At any instant, a\nphotograph of the surface would show circular rings on which the\ndisturbance is maximum Clearly, all points on such a circle are\noscillating in phase because they are at the same distance from the\nsource Such a locus of points, which oscillate in phase is called a\nwavefront; thus a wavefront is defined as a surface of constant\nphase" + }, + { + "Chapter": "9", + "sentence_range": "1079-1082", + "Text": "At any instant, a\nphotograph of the surface would show circular rings on which the\ndisturbance is maximum Clearly, all points on such a circle are\noscillating in phase because they are at the same distance from the\nsource Such a locus of points, which oscillate in phase is called a\nwavefront; thus a wavefront is defined as a surface of constant\nphase The speed with which the wavefront moves outwards from the\nsource is called the speed of the wave" + }, + { + "Chapter": "9", + "sentence_range": "1080-1083", + "Text": "Clearly, all points on such a circle are\noscillating in phase because they are at the same distance from the\nsource Such a locus of points, which oscillate in phase is called a\nwavefront; thus a wavefront is defined as a surface of constant\nphase The speed with which the wavefront moves outwards from the\nsource is called the speed of the wave The energy of the wave travels\nin a direction perpendicular to the wavefront" + }, + { + "Chapter": "9", + "sentence_range": "1081-1084", + "Text": "Such a locus of points, which oscillate in phase is called a\nwavefront; thus a wavefront is defined as a surface of constant\nphase The speed with which the wavefront moves outwards from the\nsource is called the speed of the wave The energy of the wave travels\nin a direction perpendicular to the wavefront If we have a point source emitting waves uniformly in all directions,\nthen the locus of points which have the same amplitude and vibrate in\nthe same phase are spheres and we have what is known as a spherical\nwave as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1082-1085", + "Text": "The speed with which the wavefront moves outwards from the\nsource is called the speed of the wave The energy of the wave travels\nin a direction perpendicular to the wavefront If we have a point source emitting waves uniformly in all directions,\nthen the locus of points which have the same amplitude and vibrate in\nthe same phase are spheres and we have what is known as a spherical\nwave as shown in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1083-1086", + "Text": "The energy of the wave travels\nin a direction perpendicular to the wavefront If we have a point source emitting waves uniformly in all directions,\nthen the locus of points which have the same amplitude and vibrate in\nthe same phase are spheres and we have what is known as a spherical\nwave as shown in Fig 10 1(a)" + }, + { + "Chapter": "9", + "sentence_range": "1084-1087", + "Text": "If we have a point source emitting waves uniformly in all directions,\nthen the locus of points which have the same amplitude and vibrate in\nthe same phase are spheres and we have what is known as a spherical\nwave as shown in Fig 10 1(a) At a large distance from the source, a\nsmall portion of the sphere can be considered as a plane and we have\nwhat is known as a plane wave [Fig" + }, + { + "Chapter": "9", + "sentence_range": "1085-1088", + "Text": "10 1(a) At a large distance from the source, a\nsmall portion of the sphere can be considered as a plane and we have\nwhat is known as a plane wave [Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1086-1089", + "Text": "1(a) At a large distance from the source, a\nsmall portion of the sphere can be considered as a plane and we have\nwhat is known as a plane wave [Fig 10 1(b)]" + }, + { + "Chapter": "9", + "sentence_range": "1087-1090", + "Text": "At a large distance from the source, a\nsmall portion of the sphere can be considered as a plane and we have\nwhat is known as a plane wave [Fig 10 1(b)] Now, if we know the shape of the wavefront at t = 0, then Huygens\nprinciple allows us to determine the shape of the wavefront at a later\ntime t" + }, + { + "Chapter": "9", + "sentence_range": "1088-1091", + "Text": "10 1(b)] Now, if we know the shape of the wavefront at t = 0, then Huygens\nprinciple allows us to determine the shape of the wavefront at a later\ntime t Thus, Huygens principle is essentially a geometrical construction,\nwhich given the shape of the wafefront at any time allows us to determine\nthe shape of the wavefront at a later time" + }, + { + "Chapter": "9", + "sentence_range": "1089-1092", + "Text": "1(b)] Now, if we know the shape of the wavefront at t = 0, then Huygens\nprinciple allows us to determine the shape of the wavefront at a later\ntime t Thus, Huygens principle is essentially a geometrical construction,\nwhich given the shape of the wafefront at any time allows us to determine\nthe shape of the wavefront at a later time Let us consider a diverging\nwave and let F1F2 represent a portion of the spherical wavefront at t = 0\n(Fig" + }, + { + "Chapter": "9", + "sentence_range": "1090-1093", + "Text": "Now, if we know the shape of the wavefront at t = 0, then Huygens\nprinciple allows us to determine the shape of the wavefront at a later\ntime t Thus, Huygens principle is essentially a geometrical construction,\nwhich given the shape of the wafefront at any time allows us to determine\nthe shape of the wavefront at a later time Let us consider a diverging\nwave and let F1F2 represent a portion of the spherical wavefront at t = 0\n(Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1091-1094", + "Text": "Thus, Huygens principle is essentially a geometrical construction,\nwhich given the shape of the wafefront at any time allows us to determine\nthe shape of the wavefront at a later time Let us consider a diverging\nwave and let F1F2 represent a portion of the spherical wavefront at t = 0\n(Fig 10 2)" + }, + { + "Chapter": "9", + "sentence_range": "1092-1095", + "Text": "Let us consider a diverging\nwave and let F1F2 represent a portion of the spherical wavefront at t = 0\n(Fig 10 2) Now, according to Huygens principle, each point of the\nwavefront is the source of a secondary disturbance and the wavelets\nemanating from these points spread out in all directions with the speed\nof the wave" + }, + { + "Chapter": "9", + "sentence_range": "1093-1096", + "Text": "10 2) Now, according to Huygens principle, each point of the\nwavefront is the source of a secondary disturbance and the wavelets\nemanating from these points spread out in all directions with the speed\nof the wave These wavelets emanating from the wavefront are usually\nreferred to as secondary wavelets and if we draw a common tangent\nto all these spheres, we obtain the new position of the wavefront at a\nlater time" + }, + { + "Chapter": "9", + "sentence_range": "1094-1097", + "Text": "2) Now, according to Huygens principle, each point of the\nwavefront is the source of a secondary disturbance and the wavelets\nemanating from these points spread out in all directions with the speed\nof the wave These wavelets emanating from the wavefront are usually\nreferred to as secondary wavelets and if we draw a common tangent\nto all these spheres, we obtain the new position of the wavefront at a\nlater time FIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1095-1098", + "Text": "Now, according to Huygens principle, each point of the\nwavefront is the source of a secondary disturbance and the wavelets\nemanating from these points spread out in all directions with the speed\nof the wave These wavelets emanating from the wavefront are usually\nreferred to as secondary wavelets and if we draw a common tangent\nto all these spheres, we obtain the new position of the wavefront at a\nlater time FIGURE 10 1 (a) A\ndiverging spherical\nwave emanating from\na point source" + }, + { + "Chapter": "9", + "sentence_range": "1096-1099", + "Text": "These wavelets emanating from the wavefront are usually\nreferred to as secondary wavelets and if we draw a common tangent\nto all these spheres, we obtain the new position of the wavefront at a\nlater time FIGURE 10 1 (a) A\ndiverging spherical\nwave emanating from\na point source The\nwavefronts are\nspherical" + }, + { + "Chapter": "9", + "sentence_range": "1097-1100", + "Text": "FIGURE 10 1 (a) A\ndiverging spherical\nwave emanating from\na point source The\nwavefronts are\nspherical FIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1098-1101", + "Text": "1 (a) A\ndiverging spherical\nwave emanating from\na point source The\nwavefronts are\nspherical FIGURE 10 2 F1F2 represents the spherical wavefront (with O as\ncentre) at t = 0" + }, + { + "Chapter": "9", + "sentence_range": "1099-1102", + "Text": "The\nwavefronts are\nspherical FIGURE 10 2 F1F2 represents the spherical wavefront (with O as\ncentre) at t = 0 The envelope of the secondary wavelets\nemanating from F1F2 produces the forward moving wavefront G1G2" + }, + { + "Chapter": "9", + "sentence_range": "1100-1103", + "Text": "FIGURE 10 2 F1F2 represents the spherical wavefront (with O as\ncentre) at t = 0 The envelope of the secondary wavelets\nemanating from F1F2 produces the forward moving wavefront G1G2 The backwave D1D2 does not exist" + }, + { + "Chapter": "9", + "sentence_range": "1101-1104", + "Text": "2 F1F2 represents the spherical wavefront (with O as\ncentre) at t = 0 The envelope of the secondary wavelets\nemanating from F1F2 produces the forward moving wavefront G1G2 The backwave D1D2 does not exist FIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1102-1105", + "Text": "The envelope of the secondary wavelets\nemanating from F1F2 produces the forward moving wavefront G1G2 The backwave D1D2 does not exist FIGURE 10 1 (b) At a\nlarge distance from\nthe source, a small\nportion of the\nspherical wave can\nbe approximated by a\nplane wave" + }, + { + "Chapter": "9", + "sentence_range": "1103-1106", + "Text": "The backwave D1D2 does not exist FIGURE 10 1 (b) At a\nlarge distance from\nthe source, a small\nportion of the\nspherical wave can\nbe approximated by a\nplane wave Rationalised 2023-24\nPhysics\n258\nThus, if we wish to determine the shape of the wavefront at t = t, we\ndraw spheres of radius vt from each point on the spherical wavefront\nwhere v represents the speed of the waves in the medium" + }, + { + "Chapter": "9", + "sentence_range": "1104-1107", + "Text": "FIGURE 10 1 (b) At a\nlarge distance from\nthe source, a small\nportion of the\nspherical wave can\nbe approximated by a\nplane wave Rationalised 2023-24\nPhysics\n258\nThus, if we wish to determine the shape of the wavefront at t = t, we\ndraw spheres of radius vt from each point on the spherical wavefront\nwhere v represents the speed of the waves in the medium If we now draw\na common tangent to all these spheres, we obtain the new position of the\nwavefront at t = t" + }, + { + "Chapter": "9", + "sentence_range": "1105-1108", + "Text": "1 (b) At a\nlarge distance from\nthe source, a small\nportion of the\nspherical wave can\nbe approximated by a\nplane wave Rationalised 2023-24\nPhysics\n258\nThus, if we wish to determine the shape of the wavefront at t = t, we\ndraw spheres of radius vt from each point on the spherical wavefront\nwhere v represents the speed of the waves in the medium If we now draw\na common tangent to all these spheres, we obtain the new position of the\nwavefront at t = t The new wavefront shown as G1G2 in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1106-1109", + "Text": "Rationalised 2023-24\nPhysics\n258\nThus, if we wish to determine the shape of the wavefront at t = t, we\ndraw spheres of radius vt from each point on the spherical wavefront\nwhere v represents the speed of the waves in the medium If we now draw\na common tangent to all these spheres, we obtain the new position of the\nwavefront at t = t The new wavefront shown as G1G2 in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1107-1110", + "Text": "If we now draw\na common tangent to all these spheres, we obtain the new position of the\nwavefront at t = t The new wavefront shown as G1G2 in Fig 10 2 is again\nspherical with point O as the centre" + }, + { + "Chapter": "9", + "sentence_range": "1108-1111", + "Text": "The new wavefront shown as G1G2 in Fig 10 2 is again\nspherical with point O as the centre The above model has one shortcoming: we also have a backwave which\nis shown as D1D2 in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1109-1112", + "Text": "10 2 is again\nspherical with point O as the centre The above model has one shortcoming: we also have a backwave which\nis shown as D1D2 in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1110-1113", + "Text": "2 is again\nspherical with point O as the centre The above model has one shortcoming: we also have a backwave which\nis shown as D1D2 in Fig 10 2" + }, + { + "Chapter": "9", + "sentence_range": "1111-1114", + "Text": "The above model has one shortcoming: we also have a backwave which\nis shown as D1D2 in Fig 10 2 Huygens argued that the amplitude of the\nsecondary wavelets is maximum in the forward direction and zero in the\nbackward direction; by making this adhoc assumption, Huygens could\nexplain the absence of the backwave" + }, + { + "Chapter": "9", + "sentence_range": "1112-1115", + "Text": "10 2 Huygens argued that the amplitude of the\nsecondary wavelets is maximum in the forward direction and zero in the\nbackward direction; by making this adhoc assumption, Huygens could\nexplain the absence of the backwave However, this adhoc assumption is\nnot satisfactory and the absence of the backwave is really justified from\nmore rigorous wave theory" + }, + { + "Chapter": "9", + "sentence_range": "1113-1116", + "Text": "2 Huygens argued that the amplitude of the\nsecondary wavelets is maximum in the forward direction and zero in the\nbackward direction; by making this adhoc assumption, Huygens could\nexplain the absence of the backwave However, this adhoc assumption is\nnot satisfactory and the absence of the backwave is really justified from\nmore rigorous wave theory In a similar manner, we can use Huygens principle to determine the\nshape of the wavefront for a plane wave propagating through a medium\n(Fig" + }, + { + "Chapter": "9", + "sentence_range": "1114-1117", + "Text": "Huygens argued that the amplitude of the\nsecondary wavelets is maximum in the forward direction and zero in the\nbackward direction; by making this adhoc assumption, Huygens could\nexplain the absence of the backwave However, this adhoc assumption is\nnot satisfactory and the absence of the backwave is really justified from\nmore rigorous wave theory In a similar manner, we can use Huygens principle to determine the\nshape of the wavefront for a plane wave propagating through a medium\n(Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1115-1118", + "Text": "However, this adhoc assumption is\nnot satisfactory and the absence of the backwave is really justified from\nmore rigorous wave theory In a similar manner, we can use Huygens principle to determine the\nshape of the wavefront for a plane wave propagating through a medium\n(Fig 10 3)" + }, + { + "Chapter": "9", + "sentence_range": "1116-1119", + "Text": "In a similar manner, we can use Huygens principle to determine the\nshape of the wavefront for a plane wave propagating through a medium\n(Fig 10 3) 10" + }, + { + "Chapter": "9", + "sentence_range": "1117-1120", + "Text": "10 3) 10 3 REFRACTION AND REFLECTION OF\nPLANE WAVES USING HUYGENS PRINCIPLE\n10" + }, + { + "Chapter": "9", + "sentence_range": "1118-1121", + "Text": "3) 10 3 REFRACTION AND REFLECTION OF\nPLANE WAVES USING HUYGENS PRINCIPLE\n10 3" + }, + { + "Chapter": "9", + "sentence_range": "1119-1122", + "Text": "10 3 REFRACTION AND REFLECTION OF\nPLANE WAVES USING HUYGENS PRINCIPLE\n10 3 1 Refraction of a plane wave\nWe will now use Huygens principle to derive the laws of refraction" + }, + { + "Chapter": "9", + "sentence_range": "1120-1123", + "Text": "3 REFRACTION AND REFLECTION OF\nPLANE WAVES USING HUYGENS PRINCIPLE\n10 3 1 Refraction of a plane wave\nWe will now use Huygens principle to derive the laws of refraction Let PP\u00a2\nrepresent the surface separating medium 1 and medium 2, as shown in\nFig" + }, + { + "Chapter": "9", + "sentence_range": "1121-1124", + "Text": "3 1 Refraction of a plane wave\nWe will now use Huygens principle to derive the laws of refraction Let PP\u00a2\nrepresent the surface separating medium 1 and medium 2, as shown in\nFig 10" + }, + { + "Chapter": "9", + "sentence_range": "1122-1125", + "Text": "1 Refraction of a plane wave\nWe will now use Huygens principle to derive the laws of refraction Let PP\u00a2\nrepresent the surface separating medium 1 and medium 2, as shown in\nFig 10 4" + }, + { + "Chapter": "9", + "sentence_range": "1123-1126", + "Text": "Let PP\u00a2\nrepresent the surface separating medium 1 and medium 2, as shown in\nFig 10 4 Let v1 and v2 represent the speed of light in medium 1 and\nmedium 2, respectively" + }, + { + "Chapter": "9", + "sentence_range": "1124-1127", + "Text": "10 4 Let v1 and v2 represent the speed of light in medium 1 and\nmedium 2, respectively We assume a plane wavefront AB propagating in\nthe direction A\u00a2A incident on the interface at an angle i as shown in the\nfigure" + }, + { + "Chapter": "9", + "sentence_range": "1125-1128", + "Text": "4 Let v1 and v2 represent the speed of light in medium 1 and\nmedium 2, respectively We assume a plane wavefront AB propagating in\nthe direction A\u00a2A incident on the interface at an angle i as shown in the\nfigure Let t be the time taken by the wavefront to travel the distance BC" + }, + { + "Chapter": "9", + "sentence_range": "1126-1129", + "Text": "Let v1 and v2 represent the speed of light in medium 1 and\nmedium 2, respectively We assume a plane wavefront AB propagating in\nthe direction A\u00a2A incident on the interface at an angle i as shown in the\nfigure Let t be the time taken by the wavefront to travel the distance BC Thus,\nBC = v1 t\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1127-1130", + "Text": "We assume a plane wavefront AB propagating in\nthe direction A\u00a2A incident on the interface at an angle i as shown in the\nfigure Let t be the time taken by the wavefront to travel the distance BC Thus,\nBC = v1 t\nFIGURE 10 3\nHuygens geometrical\nconstruction for a\nplane wave\npropagating to the\nright" + }, + { + "Chapter": "9", + "sentence_range": "1128-1131", + "Text": "Let t be the time taken by the wavefront to travel the distance BC Thus,\nBC = v1 t\nFIGURE 10 3\nHuygens geometrical\nconstruction for a\nplane wave\npropagating to the\nright F1 F2 is the\nplane wavefront at\nt = 0 and G1G2 is the\nwavefront at a later\ntime t" + }, + { + "Chapter": "9", + "sentence_range": "1129-1132", + "Text": "Thus,\nBC = v1 t\nFIGURE 10 3\nHuygens geometrical\nconstruction for a\nplane wave\npropagating to the\nright F1 F2 is the\nplane wavefront at\nt = 0 and G1G2 is the\nwavefront at a later\ntime t The lines A1A2,\nB1B2 \u2026 etc" + }, + { + "Chapter": "9", + "sentence_range": "1130-1133", + "Text": "3\nHuygens geometrical\nconstruction for a\nplane wave\npropagating to the\nright F1 F2 is the\nplane wavefront at\nt = 0 and G1G2 is the\nwavefront at a later\ntime t The lines A1A2,\nB1B2 \u2026 etc , are\nnormal to both F1F2\nand G1G2 and\nrepresent rays" + }, + { + "Chapter": "9", + "sentence_range": "1131-1134", + "Text": "F1 F2 is the\nplane wavefront at\nt = 0 and G1G2 is the\nwavefront at a later\ntime t The lines A1A2,\nB1B2 \u2026 etc , are\nnormal to both F1F2\nand G1G2 and\nrepresent rays FIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1132-1135", + "Text": "The lines A1A2,\nB1B2 \u2026 etc , are\nnormal to both F1F2\nand G1G2 and\nrepresent rays FIGURE 10 4 A plane wave AB is incident at an angle i on the surface\nPP\u00a2 separating medium 1 and medium 2" + }, + { + "Chapter": "9", + "sentence_range": "1133-1136", + "Text": ", are\nnormal to both F1F2\nand G1G2 and\nrepresent rays FIGURE 10 4 A plane wave AB is incident at an angle i on the surface\nPP\u00a2 separating medium 1 and medium 2 The plane wave undergoes\nrefraction and CE represents the refracted wavefront" + }, + { + "Chapter": "9", + "sentence_range": "1134-1137", + "Text": "FIGURE 10 4 A plane wave AB is incident at an angle i on the surface\nPP\u00a2 separating medium 1 and medium 2 The plane wave undergoes\nrefraction and CE represents the refracted wavefront The figure\ncorresponds to v2 < v1 so that the refracted waves bends towards the\nnormal" + }, + { + "Chapter": "9", + "sentence_range": "1135-1138", + "Text": "4 A plane wave AB is incident at an angle i on the surface\nPP\u00a2 separating medium 1 and medium 2 The plane wave undergoes\nrefraction and CE represents the refracted wavefront The figure\ncorresponds to v2 < v1 so that the refracted waves bends towards the\nnormal Rationalised 2023-24\n259\nWave Optics\nIn order to determine the shape of the refracted\nwavefront, we draw a sphere of radius v2t from the point\nA in the second medium (the speed of the wave in the\nsecond medium is v2)" + }, + { + "Chapter": "9", + "sentence_range": "1136-1139", + "Text": "The plane wave undergoes\nrefraction and CE represents the refracted wavefront The figure\ncorresponds to v2 < v1 so that the refracted waves bends towards the\nnormal Rationalised 2023-24\n259\nWave Optics\nIn order to determine the shape of the refracted\nwavefront, we draw a sphere of radius v2t from the point\nA in the second medium (the speed of the wave in the\nsecond medium is v2) Let CE represent a tangent plane\ndrawn from the point C on to the sphere" + }, + { + "Chapter": "9", + "sentence_range": "1137-1140", + "Text": "The figure\ncorresponds to v2 < v1 so that the refracted waves bends towards the\nnormal Rationalised 2023-24\n259\nWave Optics\nIn order to determine the shape of the refracted\nwavefront, we draw a sphere of radius v2t from the point\nA in the second medium (the speed of the wave in the\nsecond medium is v2) Let CE represent a tangent plane\ndrawn from the point C on to the sphere Then, AE = v2 t\nand CE would represent the refracted wavefront" + }, + { + "Chapter": "9", + "sentence_range": "1138-1141", + "Text": "Rationalised 2023-24\n259\nWave Optics\nIn order to determine the shape of the refracted\nwavefront, we draw a sphere of radius v2t from the point\nA in the second medium (the speed of the wave in the\nsecond medium is v2) Let CE represent a tangent plane\ndrawn from the point C on to the sphere Then, AE = v2 t\nand CE would represent the refracted wavefront If we\nnow consider the triangles ABC and AEC, we readily\nobtain\nsin i = \n1\nBC\nAC\nAC\n=v \u03c4\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1139-1142", + "Text": "Let CE represent a tangent plane\ndrawn from the point C on to the sphere Then, AE = v2 t\nand CE would represent the refracted wavefront If we\nnow consider the triangles ABC and AEC, we readily\nobtain\nsin i = \n1\nBC\nAC\nAC\n=v \u03c4\n(10 1)\nand\nsin r = \n2\nAE\nAC\nAC\n=v \u03c4\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1140-1143", + "Text": "Then, AE = v2 t\nand CE would represent the refracted wavefront If we\nnow consider the triangles ABC and AEC, we readily\nobtain\nsin i = \n1\nBC\nAC\nAC\n=v \u03c4\n(10 1)\nand\nsin r = \n2\nAE\nAC\nAC\n=v \u03c4\n(10 2)\nwhere i and r are the angles of incidence and refraction,\nrespectively" + }, + { + "Chapter": "9", + "sentence_range": "1141-1144", + "Text": "If we\nnow consider the triangles ABC and AEC, we readily\nobtain\nsin i = \n1\nBC\nAC\nAC\n=v \u03c4\n(10 1)\nand\nsin r = \n2\nAE\nAC\nAC\n=v \u03c4\n(10 2)\nwhere i and r are the angles of incidence and refraction,\nrespectively Thus we obtain\n1\n2\nsin\nsin\ni\nv\nr\n=v\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1142-1145", + "Text": "1)\nand\nsin r = \n2\nAE\nAC\nAC\n=v \u03c4\n(10 2)\nwhere i and r are the angles of incidence and refraction,\nrespectively Thus we obtain\n1\n2\nsin\nsin\ni\nv\nr\n=v\n(10 3)\nFrom the above equation, we get the important result\nthat if r < i (i" + }, + { + "Chapter": "9", + "sentence_range": "1143-1146", + "Text": "2)\nwhere i and r are the angles of incidence and refraction,\nrespectively Thus we obtain\n1\n2\nsin\nsin\ni\nv\nr\n=v\n(10 3)\nFrom the above equation, we get the important result\nthat if r < i (i e" + }, + { + "Chapter": "9", + "sentence_range": "1144-1147", + "Text": "Thus we obtain\n1\n2\nsin\nsin\ni\nv\nr\n=v\n(10 3)\nFrom the above equation, we get the important result\nthat if r < i (i e , if the ray bends toward the normal), the\nspeed of the light wave in the second medium (v2) will be\nless then the speed of the light wave in the first medium\n(v1)" + }, + { + "Chapter": "9", + "sentence_range": "1145-1148", + "Text": "3)\nFrom the above equation, we get the important result\nthat if r < i (i e , if the ray bends toward the normal), the\nspeed of the light wave in the second medium (v2) will be\nless then the speed of the light wave in the first medium\n(v1) This prediction is opposite to the prediction from\nthe corpuscular model of light and as later experiments\nshowed, the prediction of the wave theory is correct" + }, + { + "Chapter": "9", + "sentence_range": "1146-1149", + "Text": "e , if the ray bends toward the normal), the\nspeed of the light wave in the second medium (v2) will be\nless then the speed of the light wave in the first medium\n(v1) This prediction is opposite to the prediction from\nthe corpuscular model of light and as later experiments\nshowed, the prediction of the wave theory is correct Now,\nif c represents the speed of light in vacuum, then,\n1\n1\nc\nn\n=v\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1147-1150", + "Text": ", if the ray bends toward the normal), the\nspeed of the light wave in the second medium (v2) will be\nless then the speed of the light wave in the first medium\n(v1) This prediction is opposite to the prediction from\nthe corpuscular model of light and as later experiments\nshowed, the prediction of the wave theory is correct Now,\nif c represents the speed of light in vacuum, then,\n1\n1\nc\nn\n=v\n(10 4)\nand\nn2 = \n2\nvc\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1148-1151", + "Text": "This prediction is opposite to the prediction from\nthe corpuscular model of light and as later experiments\nshowed, the prediction of the wave theory is correct Now,\nif c represents the speed of light in vacuum, then,\n1\n1\nc\nn\n=v\n(10 4)\nand\nn2 = \n2\nvc\n(10 5)\nare known as the refractive indices of medium 1 and\nmedium 2, respectively" + }, + { + "Chapter": "9", + "sentence_range": "1149-1152", + "Text": "Now,\nif c represents the speed of light in vacuum, then,\n1\n1\nc\nn\n=v\n(10 4)\nand\nn2 = \n2\nvc\n(10 5)\nare known as the refractive indices of medium 1 and\nmedium 2, respectively In terms of the refractive indices, Eq" + }, + { + "Chapter": "9", + "sentence_range": "1150-1153", + "Text": "4)\nand\nn2 = \n2\nvc\n(10 5)\nare known as the refractive indices of medium 1 and\nmedium 2, respectively In terms of the refractive indices, Eq (10" + }, + { + "Chapter": "9", + "sentence_range": "1151-1154", + "Text": "5)\nare known as the refractive indices of medium 1 and\nmedium 2, respectively In terms of the refractive indices, Eq (10 3) can\nbe written as\nn1 sin i = n2 sin r\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1152-1155", + "Text": "In terms of the refractive indices, Eq (10 3) can\nbe written as\nn1 sin i = n2 sin r\n(10 6)\nThis is the Snell\u2019s law of refraction" + }, + { + "Chapter": "9", + "sentence_range": "1153-1156", + "Text": "(10 3) can\nbe written as\nn1 sin i = n2 sin r\n(10 6)\nThis is the Snell\u2019s law of refraction Further, if l1 and l 2 denote the\nwavelengths of light in medium 1 and medium 2, respectively and if the\ndistance BC is equal to l 1 then the distance AE will be equal to l 2 (because\nif the crest from B has reached C in time t, then the crest from A should\nhave also reached E in time t ); thus,\n1\n1\n2\n2\nBC\nAE\nv\nv\n\u03bb\u03bb\n=\n=\nor\n1\n2\n1\n2\nv\nv\n\u03bb\n=\u03bb\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1154-1157", + "Text": "3) can\nbe written as\nn1 sin i = n2 sin r\n(10 6)\nThis is the Snell\u2019s law of refraction Further, if l1 and l 2 denote the\nwavelengths of light in medium 1 and medium 2, respectively and if the\ndistance BC is equal to l 1 then the distance AE will be equal to l 2 (because\nif the crest from B has reached C in time t, then the crest from A should\nhave also reached E in time t ); thus,\n1\n1\n2\n2\nBC\nAE\nv\nv\n\u03bb\u03bb\n=\n=\nor\n1\n2\n1\n2\nv\nv\n\u03bb\n=\u03bb\n(10 7)\nCHRISTIAAN HUYGENS (1629 \u2013 1695)\nChristiaan Huygens\n(1629 \u2013 1695) Dutch\nphysicist, astronomer,\nmathematician and the\nfounder of the wave\ntheory of light" + }, + { + "Chapter": "9", + "sentence_range": "1155-1158", + "Text": "6)\nThis is the Snell\u2019s law of refraction Further, if l1 and l 2 denote the\nwavelengths of light in medium 1 and medium 2, respectively and if the\ndistance BC is equal to l 1 then the distance AE will be equal to l 2 (because\nif the crest from B has reached C in time t, then the crest from A should\nhave also reached E in time t ); thus,\n1\n1\n2\n2\nBC\nAE\nv\nv\n\u03bb\u03bb\n=\n=\nor\n1\n2\n1\n2\nv\nv\n\u03bb\n=\u03bb\n(10 7)\nCHRISTIAAN HUYGENS (1629 \u2013 1695)\nChristiaan Huygens\n(1629 \u2013 1695) Dutch\nphysicist, astronomer,\nmathematician and the\nfounder of the wave\ntheory of light His book,\nTreatise on light, makes\nfascinating reading even\ntoday" + }, + { + "Chapter": "9", + "sentence_range": "1156-1159", + "Text": "Further, if l1 and l 2 denote the\nwavelengths of light in medium 1 and medium 2, respectively and if the\ndistance BC is equal to l 1 then the distance AE will be equal to l 2 (because\nif the crest from B has reached C in time t, then the crest from A should\nhave also reached E in time t ); thus,\n1\n1\n2\n2\nBC\nAE\nv\nv\n\u03bb\u03bb\n=\n=\nor\n1\n2\n1\n2\nv\nv\n\u03bb\n=\u03bb\n(10 7)\nCHRISTIAAN HUYGENS (1629 \u2013 1695)\nChristiaan Huygens\n(1629 \u2013 1695) Dutch\nphysicist, astronomer,\nmathematician and the\nfounder of the wave\ntheory of light His book,\nTreatise on light, makes\nfascinating reading even\ntoday He brilliantly\nexplained the double\nrefraction shown by the\nmineral calcite in this\nwork in addition to\nreflection and refraction" + }, + { + "Chapter": "9", + "sentence_range": "1157-1160", + "Text": "7)\nCHRISTIAAN HUYGENS (1629 \u2013 1695)\nChristiaan Huygens\n(1629 \u2013 1695) Dutch\nphysicist, astronomer,\nmathematician and the\nfounder of the wave\ntheory of light His book,\nTreatise on light, makes\nfascinating reading even\ntoday He brilliantly\nexplained the double\nrefraction shown by the\nmineral calcite in this\nwork in addition to\nreflection and refraction He was the first to\nanalyse circular and\nsimple harmonic motion\nand designed and built\nimproved clocks and\ntelescopes" + }, + { + "Chapter": "9", + "sentence_range": "1158-1161", + "Text": "His book,\nTreatise on light, makes\nfascinating reading even\ntoday He brilliantly\nexplained the double\nrefraction shown by the\nmineral calcite in this\nwork in addition to\nreflection and refraction He was the first to\nanalyse circular and\nsimple harmonic motion\nand designed and built\nimproved clocks and\ntelescopes He discovered\nthe true geometry of\nSaturn\u2019s rings" + }, + { + "Chapter": "9", + "sentence_range": "1159-1162", + "Text": "He brilliantly\nexplained the double\nrefraction shown by the\nmineral calcite in this\nwork in addition to\nreflection and refraction He was the first to\nanalyse circular and\nsimple harmonic motion\nand designed and built\nimproved clocks and\ntelescopes He discovered\nthe true geometry of\nSaturn\u2019s rings Rationalised 2023-24\nPhysics\n260\nThe above equation implies that when a wave gets refracted into a\ndenser medium (v1 > v2) the wavelength and the speed of propagation\ndecrease but the frequency n (= v/l) remains the same" + }, + { + "Chapter": "9", + "sentence_range": "1160-1163", + "Text": "He was the first to\nanalyse circular and\nsimple harmonic motion\nand designed and built\nimproved clocks and\ntelescopes He discovered\nthe true geometry of\nSaturn\u2019s rings Rationalised 2023-24\nPhysics\n260\nThe above equation implies that when a wave gets refracted into a\ndenser medium (v1 > v2) the wavelength and the speed of propagation\ndecrease but the frequency n (= v/l) remains the same 10" + }, + { + "Chapter": "9", + "sentence_range": "1161-1164", + "Text": "He discovered\nthe true geometry of\nSaturn\u2019s rings Rationalised 2023-24\nPhysics\n260\nThe above equation implies that when a wave gets refracted into a\ndenser medium (v1 > v2) the wavelength and the speed of propagation\ndecrease but the frequency n (= v/l) remains the same 10 3" + }, + { + "Chapter": "9", + "sentence_range": "1162-1165", + "Text": "Rationalised 2023-24\nPhysics\n260\nThe above equation implies that when a wave gets refracted into a\ndenser medium (v1 > v2) the wavelength and the speed of propagation\ndecrease but the frequency n (= v/l) remains the same 10 3 2 Refraction at a rarer medium\nWe now consider refraction of a plane wave at a rarer medium, i" + }, + { + "Chapter": "9", + "sentence_range": "1163-1166", + "Text": "10 3 2 Refraction at a rarer medium\nWe now consider refraction of a plane wave at a rarer medium, i e" + }, + { + "Chapter": "9", + "sentence_range": "1164-1167", + "Text": "3 2 Refraction at a rarer medium\nWe now consider refraction of a plane wave at a rarer medium, i e ,\nv2 > v1" + }, + { + "Chapter": "9", + "sentence_range": "1165-1168", + "Text": "2 Refraction at a rarer medium\nWe now consider refraction of a plane wave at a rarer medium, i e ,\nv2 > v1 Proceeding in an exactly similar manner we can construct a\nrefracted wavefront as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1166-1169", + "Text": "e ,\nv2 > v1 Proceeding in an exactly similar manner we can construct a\nrefracted wavefront as shown in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1167-1170", + "Text": ",\nv2 > v1 Proceeding in an exactly similar manner we can construct a\nrefracted wavefront as shown in Fig 10 5" + }, + { + "Chapter": "9", + "sentence_range": "1168-1171", + "Text": "Proceeding in an exactly similar manner we can construct a\nrefracted wavefront as shown in Fig 10 5 The angle of refraction\nwill now be greater than angle of incidence; however, we will still have\nn1 sin i = n2 sin r" + }, + { + "Chapter": "9", + "sentence_range": "1169-1172", + "Text": "10 5 The angle of refraction\nwill now be greater than angle of incidence; however, we will still have\nn1 sin i = n2 sin r We define an angle ic by the following equation\n2\n1\nsin c\nn\ni\n=n\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1170-1173", + "Text": "5 The angle of refraction\nwill now be greater than angle of incidence; however, we will still have\nn1 sin i = n2 sin r We define an angle ic by the following equation\n2\n1\nsin c\nn\ni\n=n\n(10 8)\nThus, if i = ic then sin r = 1 and r = 90\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "1171-1174", + "Text": "The angle of refraction\nwill now be greater than angle of incidence; however, we will still have\nn1 sin i = n2 sin r We define an angle ic by the following equation\n2\n1\nsin c\nn\ni\n=n\n(10 8)\nThus, if i = ic then sin r = 1 and r = 90\u00b0 Obviously, for i > ic, there can\nnot be any refracted wave" + }, + { + "Chapter": "9", + "sentence_range": "1172-1175", + "Text": "We define an angle ic by the following equation\n2\n1\nsin c\nn\ni\n=n\n(10 8)\nThus, if i = ic then sin r = 1 and r = 90\u00b0 Obviously, for i > ic, there can\nnot be any refracted wave The angle ic is known as the critical angle and\nfor all angles of incidence greater than the critical angle, we will not have\nany refracted wave and the wave will undergo what is known as total\ninternal reflection" + }, + { + "Chapter": "9", + "sentence_range": "1173-1176", + "Text": "8)\nThus, if i = ic then sin r = 1 and r = 90\u00b0 Obviously, for i > ic, there can\nnot be any refracted wave The angle ic is known as the critical angle and\nfor all angles of incidence greater than the critical angle, we will not have\nany refracted wave and the wave will undergo what is known as total\ninternal reflection The phenomenon of total internal reflection and its\napplications was discussed in Section 9" + }, + { + "Chapter": "9", + "sentence_range": "1174-1177", + "Text": "Obviously, for i > ic, there can\nnot be any refracted wave The angle ic is known as the critical angle and\nfor all angles of incidence greater than the critical angle, we will not have\nany refracted wave and the wave will undergo what is known as total\ninternal reflection The phenomenon of total internal reflection and its\napplications was discussed in Section 9 4" + }, + { + "Chapter": "9", + "sentence_range": "1175-1178", + "Text": "The angle ic is known as the critical angle and\nfor all angles of incidence greater than the critical angle, we will not have\nany refracted wave and the wave will undergo what is known as total\ninternal reflection The phenomenon of total internal reflection and its\napplications was discussed in Section 9 4 Demonstration of interference, diffraction, refraction, resonance and Doppler effect\nhttp://www" + }, + { + "Chapter": "9", + "sentence_range": "1176-1179", + "Text": "The phenomenon of total internal reflection and its\napplications was discussed in Section 9 4 Demonstration of interference, diffraction, refraction, resonance and Doppler effect\nhttp://www falstad" + }, + { + "Chapter": "9", + "sentence_range": "1177-1180", + "Text": "4 Demonstration of interference, diffraction, refraction, resonance and Doppler effect\nhttp://www falstad com/ripple/\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1178-1181", + "Text": "Demonstration of interference, diffraction, refraction, resonance and Doppler effect\nhttp://www falstad com/ripple/\nFIGURE 10 5 Refraction of a plane wave incident on a\nrarer medium for which v2 > v1" + }, + { + "Chapter": "9", + "sentence_range": "1179-1182", + "Text": "falstad com/ripple/\nFIGURE 10 5 Refraction of a plane wave incident on a\nrarer medium for which v2 > v1 The plane wave bends\naway from the normal" + }, + { + "Chapter": "9", + "sentence_range": "1180-1183", + "Text": "com/ripple/\nFIGURE 10 5 Refraction of a plane wave incident on a\nrarer medium for which v2 > v1 The plane wave bends\naway from the normal 10" + }, + { + "Chapter": "9", + "sentence_range": "1181-1184", + "Text": "5 Refraction of a plane wave incident on a\nrarer medium for which v2 > v1 The plane wave bends\naway from the normal 10 3" + }, + { + "Chapter": "9", + "sentence_range": "1182-1185", + "Text": "The plane wave bends\naway from the normal 10 3 3 Reflection of a plane wave by a plane surface\nWe next consider a plane wave AB incident at an angle i on a reflecting\nsurface MN" + }, + { + "Chapter": "9", + "sentence_range": "1183-1186", + "Text": "10 3 3 Reflection of a plane wave by a plane surface\nWe next consider a plane wave AB incident at an angle i on a reflecting\nsurface MN If v represents the speed of the wave in the medium and if t\nrepresents the time taken by the wavefront to advance from the point B\nto C then the distance\nBC = vt\nIn order to construct the reflected wavefront we draw a sphere of\nradius vt from the point A as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1184-1187", + "Text": "3 3 Reflection of a plane wave by a plane surface\nWe next consider a plane wave AB incident at an angle i on a reflecting\nsurface MN If v represents the speed of the wave in the medium and if t\nrepresents the time taken by the wavefront to advance from the point B\nto C then the distance\nBC = vt\nIn order to construct the reflected wavefront we draw a sphere of\nradius vt from the point A as shown in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1185-1188", + "Text": "3 Reflection of a plane wave by a plane surface\nWe next consider a plane wave AB incident at an angle i on a reflecting\nsurface MN If v represents the speed of the wave in the medium and if t\nrepresents the time taken by the wavefront to advance from the point B\nto C then the distance\nBC = vt\nIn order to construct the reflected wavefront we draw a sphere of\nradius vt from the point A as shown in Fig 10 6" + }, + { + "Chapter": "9", + "sentence_range": "1186-1189", + "Text": "If v represents the speed of the wave in the medium and if t\nrepresents the time taken by the wavefront to advance from the point B\nto C then the distance\nBC = vt\nIn order to construct the reflected wavefront we draw a sphere of\nradius vt from the point A as shown in Fig 10 6 Let CE represent the\ntangent plane drawn from the point C to this sphere" + }, + { + "Chapter": "9", + "sentence_range": "1187-1190", + "Text": "10 6 Let CE represent the\ntangent plane drawn from the point C to this sphere Obviously\nAE = BC = vt\nRationalised 2023-24\n261\nWave Optics\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1188-1191", + "Text": "6 Let CE represent the\ntangent plane drawn from the point C to this sphere Obviously\nAE = BC = vt\nRationalised 2023-24\n261\nWave Optics\nFIGURE 10 6 Reflection of a plane wave AB by the reflecting surface MN" + }, + { + "Chapter": "9", + "sentence_range": "1189-1192", + "Text": "Let CE represent the\ntangent plane drawn from the point C to this sphere Obviously\nAE = BC = vt\nRationalised 2023-24\n261\nWave Optics\nFIGURE 10 6 Reflection of a plane wave AB by the reflecting surface MN AB and CE represent incident and reflected wavefronts" + }, + { + "Chapter": "9", + "sentence_range": "1190-1193", + "Text": "Obviously\nAE = BC = vt\nRationalised 2023-24\n261\nWave Optics\nFIGURE 10 6 Reflection of a plane wave AB by the reflecting surface MN AB and CE represent incident and reflected wavefronts FIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1191-1194", + "Text": "6 Reflection of a plane wave AB by the reflecting surface MN AB and CE represent incident and reflected wavefronts FIGURE 10 7 Refraction of a plane wave by (a) a thin prism, (b) a convex lens" + }, + { + "Chapter": "9", + "sentence_range": "1192-1195", + "Text": "AB and CE represent incident and reflected wavefronts FIGURE 10 7 Refraction of a plane wave by (a) a thin prism, (b) a convex lens (c) Reflection of a plane wave by a concave mirror" + }, + { + "Chapter": "9", + "sentence_range": "1193-1196", + "Text": "FIGURE 10 7 Refraction of a plane wave by (a) a thin prism, (b) a convex lens (c) Reflection of a plane wave by a concave mirror If we now consider the triangles EAC and BAC we will find that they\nare congruent and therefore, the angles i and r (as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1194-1197", + "Text": "7 Refraction of a plane wave by (a) a thin prism, (b) a convex lens (c) Reflection of a plane wave by a concave mirror If we now consider the triangles EAC and BAC we will find that they\nare congruent and therefore, the angles i and r (as shown in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1195-1198", + "Text": "(c) Reflection of a plane wave by a concave mirror If we now consider the triangles EAC and BAC we will find that they\nare congruent and therefore, the angles i and r (as shown in Fig 10 6)\nwould be equal" + }, + { + "Chapter": "9", + "sentence_range": "1196-1199", + "Text": "If we now consider the triangles EAC and BAC we will find that they\nare congruent and therefore, the angles i and r (as shown in Fig 10 6)\nwould be equal This is the law of reflection" + }, + { + "Chapter": "9", + "sentence_range": "1197-1200", + "Text": "10 6)\nwould be equal This is the law of reflection Once we have the laws of reflection and refraction, the behaviour of\nprisms, lenses, and mirrors can be understood" + }, + { + "Chapter": "9", + "sentence_range": "1198-1201", + "Text": "6)\nwould be equal This is the law of reflection Once we have the laws of reflection and refraction, the behaviour of\nprisms, lenses, and mirrors can be understood These phenomena were\ndiscussed in detail in Chapter 9 on the basis of rectilinear propagation of\nlight" + }, + { + "Chapter": "9", + "sentence_range": "1199-1202", + "Text": "This is the law of reflection Once we have the laws of reflection and refraction, the behaviour of\nprisms, lenses, and mirrors can be understood These phenomena were\ndiscussed in detail in Chapter 9 on the basis of rectilinear propagation of\nlight Here we just describe the behaviour of the wavefronts as they\nundergo reflection or refraction" + }, + { + "Chapter": "9", + "sentence_range": "1200-1203", + "Text": "Once we have the laws of reflection and refraction, the behaviour of\nprisms, lenses, and mirrors can be understood These phenomena were\ndiscussed in detail in Chapter 9 on the basis of rectilinear propagation of\nlight Here we just describe the behaviour of the wavefronts as they\nundergo reflection or refraction In Fig" + }, + { + "Chapter": "9", + "sentence_range": "1201-1204", + "Text": "These phenomena were\ndiscussed in detail in Chapter 9 on the basis of rectilinear propagation of\nlight Here we just describe the behaviour of the wavefronts as they\nundergo reflection or refraction In Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1202-1205", + "Text": "Here we just describe the behaviour of the wavefronts as they\nundergo reflection or refraction In Fig 10 7(a) we consider a plane wave\npassing through a thin prism" + }, + { + "Chapter": "9", + "sentence_range": "1203-1206", + "Text": "In Fig 10 7(a) we consider a plane wave\npassing through a thin prism Clearly, since the speed of light waves is\nless in glass, the lower portion of the incoming wavefront (which travels\nthrough the greatest thickness of glass) will get delayed resulting in a tilt\nin the emerging wavefront as shown in the figure" + }, + { + "Chapter": "9", + "sentence_range": "1204-1207", + "Text": "10 7(a) we consider a plane wave\npassing through a thin prism Clearly, since the speed of light waves is\nless in glass, the lower portion of the incoming wavefront (which travels\nthrough the greatest thickness of glass) will get delayed resulting in a tilt\nin the emerging wavefront as shown in the figure In Fig" + }, + { + "Chapter": "9", + "sentence_range": "1205-1208", + "Text": "7(a) we consider a plane wave\npassing through a thin prism Clearly, since the speed of light waves is\nless in glass, the lower portion of the incoming wavefront (which travels\nthrough the greatest thickness of glass) will get delayed resulting in a tilt\nin the emerging wavefront as shown in the figure In Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1206-1209", + "Text": "Clearly, since the speed of light waves is\nless in glass, the lower portion of the incoming wavefront (which travels\nthrough the greatest thickness of glass) will get delayed resulting in a tilt\nin the emerging wavefront as shown in the figure In Fig 10 7(b) we\nconsider a plane wave incident on a thin convex lens; the central part of\nthe incident plane wave traverses the thickest portion of the lens and is\ndelayed the most" + }, + { + "Chapter": "9", + "sentence_range": "1207-1210", + "Text": "In Fig 10 7(b) we\nconsider a plane wave incident on a thin convex lens; the central part of\nthe incident plane wave traverses the thickest portion of the lens and is\ndelayed the most The emerging wavefront has a depression at the centre\nand therefore the wavefront becomes spherical and converges to the point\nF which is known as the focus" + }, + { + "Chapter": "9", + "sentence_range": "1208-1211", + "Text": "10 7(b) we\nconsider a plane wave incident on a thin convex lens; the central part of\nthe incident plane wave traverses the thickest portion of the lens and is\ndelayed the most The emerging wavefront has a depression at the centre\nand therefore the wavefront becomes spherical and converges to the point\nF which is known as the focus In Fig" + }, + { + "Chapter": "9", + "sentence_range": "1209-1212", + "Text": "7(b) we\nconsider a plane wave incident on a thin convex lens; the central part of\nthe incident plane wave traverses the thickest portion of the lens and is\ndelayed the most The emerging wavefront has a depression at the centre\nand therefore the wavefront becomes spherical and converges to the point\nF which is known as the focus In Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1210-1213", + "Text": "The emerging wavefront has a depression at the centre\nand therefore the wavefront becomes spherical and converges to the point\nF which is known as the focus In Fig 10 7(c) a plane wave is incident on\na concave mirror and on reflection we have a spherical wave converging\nto the focal point F" + }, + { + "Chapter": "9", + "sentence_range": "1211-1214", + "Text": "In Fig 10 7(c) a plane wave is incident on\na concave mirror and on reflection we have a spherical wave converging\nto the focal point F In a similar manner, we can understand refraction\nand reflection by concave lenses and convex mirrors" + }, + { + "Chapter": "9", + "sentence_range": "1212-1215", + "Text": "10 7(c) a plane wave is incident on\na concave mirror and on reflection we have a spherical wave converging\nto the focal point F In a similar manner, we can understand refraction\nand reflection by concave lenses and convex mirrors From the above discussion it follows that the total time taken from a\npoint on the object to the corresponding point on the image is the same\nmeasured along any ray" + }, + { + "Chapter": "9", + "sentence_range": "1213-1216", + "Text": "7(c) a plane wave is incident on\na concave mirror and on reflection we have a spherical wave converging\nto the focal point F In a similar manner, we can understand refraction\nand reflection by concave lenses and convex mirrors From the above discussion it follows that the total time taken from a\npoint on the object to the corresponding point on the image is the same\nmeasured along any ray For example, when a convex lens focusses light\nto form a real image, although the ray going through the centre traverses\na shorter path, but because of the slower speed in glass, the time taken\nis the same as for rays travelling near the edge of the lens" + }, + { + "Chapter": "9", + "sentence_range": "1214-1217", + "Text": "In a similar manner, we can understand refraction\nand reflection by concave lenses and convex mirrors From the above discussion it follows that the total time taken from a\npoint on the object to the corresponding point on the image is the same\nmeasured along any ray For example, when a convex lens focusses light\nto form a real image, although the ray going through the centre traverses\na shorter path, but because of the slower speed in glass, the time taken\nis the same as for rays travelling near the edge of the lens Rationalised 2023-24\nPhysics\n262\n10" + }, + { + "Chapter": "9", + "sentence_range": "1215-1218", + "Text": "From the above discussion it follows that the total time taken from a\npoint on the object to the corresponding point on the image is the same\nmeasured along any ray For example, when a convex lens focusses light\nto form a real image, although the ray going through the centre traverses\na shorter path, but because of the slower speed in glass, the time taken\nis the same as for rays travelling near the edge of the lens Rationalised 2023-24\nPhysics\n262\n10 4 COHERENT AND INCOHERENT\nADDITION OF WAVES\nIn this section we will discuss the\ninterference pattern produced by the\nsuperposition of two waves" + }, + { + "Chapter": "9", + "sentence_range": "1216-1219", + "Text": "For example, when a convex lens focusses light\nto form a real image, although the ray going through the centre traverses\na shorter path, but because of the slower speed in glass, the time taken\nis the same as for rays travelling near the edge of the lens Rationalised 2023-24\nPhysics\n262\n10 4 COHERENT AND INCOHERENT\nADDITION OF WAVES\nIn this section we will discuss the\ninterference pattern produced by the\nsuperposition of two waves You may recall\nthat we had discussed the superposition\nprinciple in Chapter 14 of your Class XI\ntextbook" + }, + { + "Chapter": "9", + "sentence_range": "1217-1220", + "Text": "Rationalised 2023-24\nPhysics\n262\n10 4 COHERENT AND INCOHERENT\nADDITION OF WAVES\nIn this section we will discuss the\ninterference pattern produced by the\nsuperposition of two waves You may recall\nthat we had discussed the superposition\nprinciple in Chapter 14 of your Class XI\ntextbook Indeed the entire field of\ninterference is based on the superposition\nprinciple according to which at a particular\npoint in the medium, the resultant\ndisplacement produced by a number of\nwaves is the vector sum of the displace-\nments produced by each of the waves" + }, + { + "Chapter": "9", + "sentence_range": "1218-1221", + "Text": "4 COHERENT AND INCOHERENT\nADDITION OF WAVES\nIn this section we will discuss the\ninterference pattern produced by the\nsuperposition of two waves You may recall\nthat we had discussed the superposition\nprinciple in Chapter 14 of your Class XI\ntextbook Indeed the entire field of\ninterference is based on the superposition\nprinciple according to which at a particular\npoint in the medium, the resultant\ndisplacement produced by a number of\nwaves is the vector sum of the displace-\nments produced by each of the waves Consider two needles S1 and S2 moving\nperiodically up and down in an identical\nfashion in a trough of water [Fig" + }, + { + "Chapter": "9", + "sentence_range": "1219-1222", + "Text": "You may recall\nthat we had discussed the superposition\nprinciple in Chapter 14 of your Class XI\ntextbook Indeed the entire field of\ninterference is based on the superposition\nprinciple according to which at a particular\npoint in the medium, the resultant\ndisplacement produced by a number of\nwaves is the vector sum of the displace-\nments produced by each of the waves Consider two needles S1 and S2 moving\nperiodically up and down in an identical\nfashion in a trough of water [Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1220-1223", + "Text": "Indeed the entire field of\ninterference is based on the superposition\nprinciple according to which at a particular\npoint in the medium, the resultant\ndisplacement produced by a number of\nwaves is the vector sum of the displace-\nments produced by each of the waves Consider two needles S1 and S2 moving\nperiodically up and down in an identical\nfashion in a trough of water [Fig 10 8(a)]" + }, + { + "Chapter": "9", + "sentence_range": "1221-1224", + "Text": "Consider two needles S1 and S2 moving\nperiodically up and down in an identical\nfashion in a trough of water [Fig 10 8(a)] They produce two water waves,\nand at a particular point, the phase difference between the displacements\nproduced by each of the waves does not change with time; when this\nhappens the two sources are said to be coherent" + }, + { + "Chapter": "9", + "sentence_range": "1222-1225", + "Text": "10 8(a)] They produce two water waves,\nand at a particular point, the phase difference between the displacements\nproduced by each of the waves does not change with time; when this\nhappens the two sources are said to be coherent Figure 10" + }, + { + "Chapter": "9", + "sentence_range": "1223-1226", + "Text": "8(a)] They produce two water waves,\nand at a particular point, the phase difference between the displacements\nproduced by each of the waves does not change with time; when this\nhappens the two sources are said to be coherent Figure 10 8(b) shows\nthe position of crests (solid circles) and troughs (dashed circles) at a given\ninstant of time" + }, + { + "Chapter": "9", + "sentence_range": "1224-1227", + "Text": "They produce two water waves,\nand at a particular point, the phase difference between the displacements\nproduced by each of the waves does not change with time; when this\nhappens the two sources are said to be coherent Figure 10 8(b) shows\nthe position of crests (solid circles) and troughs (dashed circles) at a given\ninstant of time Consider a point P for which\nS1 P = S2 P\nEXAMPLE 10" + }, + { + "Chapter": "9", + "sentence_range": "1225-1228", + "Text": "Figure 10 8(b) shows\nthe position of crests (solid circles) and troughs (dashed circles) at a given\ninstant of time Consider a point P for which\nS1 P = S2 P\nEXAMPLE 10 1\nExample 10" + }, + { + "Chapter": "9", + "sentence_range": "1226-1229", + "Text": "8(b) shows\nthe position of crests (solid circles) and troughs (dashed circles) at a given\ninstant of time Consider a point P for which\nS1 P = S2 P\nEXAMPLE 10 1\nExample 10 1\n(a)\nWhen monochromatic light is incident on a surface separating\ntwo media, the reflected and refracted light both have the same\nfrequency as the incident frequency" + }, + { + "Chapter": "9", + "sentence_range": "1227-1230", + "Text": "Consider a point P for which\nS1 P = S2 P\nEXAMPLE 10 1\nExample 10 1\n(a)\nWhen monochromatic light is incident on a surface separating\ntwo media, the reflected and refracted light both have the same\nfrequency as the incident frequency Explain why" + }, + { + "Chapter": "9", + "sentence_range": "1228-1231", + "Text": "1\nExample 10 1\n(a)\nWhen monochromatic light is incident on a surface separating\ntwo media, the reflected and refracted light both have the same\nfrequency as the incident frequency Explain why (b)\nWhen light travels from a rarer to a denser medium, the speed\ndecreases" + }, + { + "Chapter": "9", + "sentence_range": "1229-1232", + "Text": "1\n(a)\nWhen monochromatic light is incident on a surface separating\ntwo media, the reflected and refracted light both have the same\nfrequency as the incident frequency Explain why (b)\nWhen light travels from a rarer to a denser medium, the speed\ndecreases Does the reduction in speed imply a reduction in the\nenergy carried by the light wave" + }, + { + "Chapter": "9", + "sentence_range": "1230-1233", + "Text": "Explain why (b)\nWhen light travels from a rarer to a denser medium, the speed\ndecreases Does the reduction in speed imply a reduction in the\nenergy carried by the light wave (c)\nIn the wave picture of light, intensity of light is determined by the\nsquare of the amplitude of the wave" + }, + { + "Chapter": "9", + "sentence_range": "1231-1234", + "Text": "(b)\nWhen light travels from a rarer to a denser medium, the speed\ndecreases Does the reduction in speed imply a reduction in the\nenergy carried by the light wave (c)\nIn the wave picture of light, intensity of light is determined by the\nsquare of the amplitude of the wave What determines the intensity\nof light in the photon picture of light" + }, + { + "Chapter": "9", + "sentence_range": "1232-1235", + "Text": "Does the reduction in speed imply a reduction in the\nenergy carried by the light wave (c)\nIn the wave picture of light, intensity of light is determined by the\nsquare of the amplitude of the wave What determines the intensity\nof light in the photon picture of light Solution\n(a)\nReflection and refraction arise through interaction of incident light\nwith the atomic constituents of matter" + }, + { + "Chapter": "9", + "sentence_range": "1233-1236", + "Text": "(c)\nIn the wave picture of light, intensity of light is determined by the\nsquare of the amplitude of the wave What determines the intensity\nof light in the photon picture of light Solution\n(a)\nReflection and refraction arise through interaction of incident light\nwith the atomic constituents of matter Atoms may be viewed as\noscillators, which take up the frequency of the external agency\n(light) causing forced oscillations" + }, + { + "Chapter": "9", + "sentence_range": "1234-1237", + "Text": "What determines the intensity\nof light in the photon picture of light Solution\n(a)\nReflection and refraction arise through interaction of incident light\nwith the atomic constituents of matter Atoms may be viewed as\noscillators, which take up the frequency of the external agency\n(light) causing forced oscillations The frequency of light emitted by\na charged oscillator equals its frequency of oscillation" + }, + { + "Chapter": "9", + "sentence_range": "1235-1238", + "Text": "Solution\n(a)\nReflection and refraction arise through interaction of incident light\nwith the atomic constituents of matter Atoms may be viewed as\noscillators, which take up the frequency of the external agency\n(light) causing forced oscillations The frequency of light emitted by\na charged oscillator equals its frequency of oscillation Thus, the\nfrequency of scattered light equals the frequency of incident light" + }, + { + "Chapter": "9", + "sentence_range": "1236-1239", + "Text": "Atoms may be viewed as\noscillators, which take up the frequency of the external agency\n(light) causing forced oscillations The frequency of light emitted by\na charged oscillator equals its frequency of oscillation Thus, the\nfrequency of scattered light equals the frequency of incident light (b)\nNo" + }, + { + "Chapter": "9", + "sentence_range": "1237-1240", + "Text": "The frequency of light emitted by\na charged oscillator equals its frequency of oscillation Thus, the\nfrequency of scattered light equals the frequency of incident light (b)\nNo Energy carried by a wave depends on the amplitude of the\nwave, not on the speed of wave propagation" + }, + { + "Chapter": "9", + "sentence_range": "1238-1241", + "Text": "Thus, the\nfrequency of scattered light equals the frequency of incident light (b)\nNo Energy carried by a wave depends on the amplitude of the\nwave, not on the speed of wave propagation (c)\nFor a given frequency, intensity of light in the photon picture is\ndetermined by the number of photons crossing an unit area per\nunit time" + }, + { + "Chapter": "9", + "sentence_range": "1239-1242", + "Text": "(b)\nNo Energy carried by a wave depends on the amplitude of the\nwave, not on the speed of wave propagation (c)\nFor a given frequency, intensity of light in the photon picture is\ndetermined by the number of photons crossing an unit area per\nunit time (a)\n(b)\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1240-1243", + "Text": "Energy carried by a wave depends on the amplitude of the\nwave, not on the speed of wave propagation (c)\nFor a given frequency, intensity of light in the photon picture is\ndetermined by the number of photons crossing an unit area per\nunit time (a)\n(b)\nFIGURE 10 8 (a) Two needles oscillating in\nphase in water represent two coherent sources" + }, + { + "Chapter": "9", + "sentence_range": "1241-1244", + "Text": "(c)\nFor a given frequency, intensity of light in the photon picture is\ndetermined by the number of photons crossing an unit area per\nunit time (a)\n(b)\nFIGURE 10 8 (a) Two needles oscillating in\nphase in water represent two coherent sources (b) The pattern of displacement of water\nmolecules at an instant on the surface of water\nshowing nodal N (no displacement) and\nantinodal A (maximum displacement) lines" + }, + { + "Chapter": "9", + "sentence_range": "1242-1245", + "Text": "(a)\n(b)\nFIGURE 10 8 (a) Two needles oscillating in\nphase in water represent two coherent sources (b) The pattern of displacement of water\nmolecules at an instant on the surface of water\nshowing nodal N (no displacement) and\nantinodal A (maximum displacement) lines Rationalised 2023-24\n263\nWave Optics\nSince the distances S1 P and S2 P are equal, waves from S1 and S2 will\ntake the same time to travel to the point P and waves that emanate from\nS1 and S2 in phase will also arrive, at the point P, in phase" + }, + { + "Chapter": "9", + "sentence_range": "1243-1246", + "Text": "8 (a) Two needles oscillating in\nphase in water represent two coherent sources (b) The pattern of displacement of water\nmolecules at an instant on the surface of water\nshowing nodal N (no displacement) and\nantinodal A (maximum displacement) lines Rationalised 2023-24\n263\nWave Optics\nSince the distances S1 P and S2 P are equal, waves from S1 and S2 will\ntake the same time to travel to the point P and waves that emanate from\nS1 and S2 in phase will also arrive, at the point P, in phase Thus, if the displacement produced by the source S1 at the point P is\ngiven by\ny1 = a cos wt\nthen, the displacement produced by the source S2 (at the point P) will\nalso be given by\ny2 = a cos wt\nThus, the resultant of displacement at P would be given by\ny = y1 + y2 = 2 a cos wt\nSince the intensity is proportional to the square of the amplitude, the\nresultant intensity will be given by\nI = 4 I0\nwhere I0 represents the intensity produced by each one of the individual\nsources; I0 is proportional to a2" + }, + { + "Chapter": "9", + "sentence_range": "1244-1247", + "Text": "(b) The pattern of displacement of water\nmolecules at an instant on the surface of water\nshowing nodal N (no displacement) and\nantinodal A (maximum displacement) lines Rationalised 2023-24\n263\nWave Optics\nSince the distances S1 P and S2 P are equal, waves from S1 and S2 will\ntake the same time to travel to the point P and waves that emanate from\nS1 and S2 in phase will also arrive, at the point P, in phase Thus, if the displacement produced by the source S1 at the point P is\ngiven by\ny1 = a cos wt\nthen, the displacement produced by the source S2 (at the point P) will\nalso be given by\ny2 = a cos wt\nThus, the resultant of displacement at P would be given by\ny = y1 + y2 = 2 a cos wt\nSince the intensity is proportional to the square of the amplitude, the\nresultant intensity will be given by\nI = 4 I0\nwhere I0 represents the intensity produced by each one of the individual\nsources; I0 is proportional to a2 In fact at any point on the perpendicular\nbisector of S1S2, the intensity will be 4I0" + }, + { + "Chapter": "9", + "sentence_range": "1245-1248", + "Text": "Rationalised 2023-24\n263\nWave Optics\nSince the distances S1 P and S2 P are equal, waves from S1 and S2 will\ntake the same time to travel to the point P and waves that emanate from\nS1 and S2 in phase will also arrive, at the point P, in phase Thus, if the displacement produced by the source S1 at the point P is\ngiven by\ny1 = a cos wt\nthen, the displacement produced by the source S2 (at the point P) will\nalso be given by\ny2 = a cos wt\nThus, the resultant of displacement at P would be given by\ny = y1 + y2 = 2 a cos wt\nSince the intensity is proportional to the square of the amplitude, the\nresultant intensity will be given by\nI = 4 I0\nwhere I0 represents the intensity produced by each one of the individual\nsources; I0 is proportional to a2 In fact at any point on the perpendicular\nbisector of S1S2, the intensity will be 4I0 The two sources are said to\ninterfere constructively and we have what is referred to as constructive\ninterference" + }, + { + "Chapter": "9", + "sentence_range": "1246-1249", + "Text": "Thus, if the displacement produced by the source S1 at the point P is\ngiven by\ny1 = a cos wt\nthen, the displacement produced by the source S2 (at the point P) will\nalso be given by\ny2 = a cos wt\nThus, the resultant of displacement at P would be given by\ny = y1 + y2 = 2 a cos wt\nSince the intensity is proportional to the square of the amplitude, the\nresultant intensity will be given by\nI = 4 I0\nwhere I0 represents the intensity produced by each one of the individual\nsources; I0 is proportional to a2 In fact at any point on the perpendicular\nbisector of S1S2, the intensity will be 4I0 The two sources are said to\ninterfere constructively and we have what is referred to as constructive\ninterference We next consider a point Q [Fig" + }, + { + "Chapter": "9", + "sentence_range": "1247-1250", + "Text": "In fact at any point on the perpendicular\nbisector of S1S2, the intensity will be 4I0 The two sources are said to\ninterfere constructively and we have what is referred to as constructive\ninterference We next consider a point Q [Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1248-1251", + "Text": "The two sources are said to\ninterfere constructively and we have what is referred to as constructive\ninterference We next consider a point Q [Fig 10 9(a)]\nfor which\nS2Q \u2013S1Q = 2l\nThe waves emanating from S1 will arrive exactly two cycles earlier\nthan the waves from S2 and will again be in phase [Fig" + }, + { + "Chapter": "9", + "sentence_range": "1249-1252", + "Text": "We next consider a point Q [Fig 10 9(a)]\nfor which\nS2Q \u2013S1Q = 2l\nThe waves emanating from S1 will arrive exactly two cycles earlier\nthan the waves from S2 and will again be in phase [Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1250-1253", + "Text": "10 9(a)]\nfor which\nS2Q \u2013S1Q = 2l\nThe waves emanating from S1 will arrive exactly two cycles earlier\nthan the waves from S2 and will again be in phase [Fig 10 9(a)]" + }, + { + "Chapter": "9", + "sentence_range": "1251-1254", + "Text": "9(a)]\nfor which\nS2Q \u2013S1Q = 2l\nThe waves emanating from S1 will arrive exactly two cycles earlier\nthan the waves from S2 and will again be in phase [Fig 10 9(a)] Thus, if\nthe displacement produced by S1 is given by\ny1 = a cos wt\nthen the displacement produced by S2 will be given by\ny2 = a cos (wt \u2013 4p) = a cos wt\nwhere we have used the fact that a path difference of 2l corresponds to a\nphase difference of 4p" + }, + { + "Chapter": "9", + "sentence_range": "1252-1255", + "Text": "10 9(a)] Thus, if\nthe displacement produced by S1 is given by\ny1 = a cos wt\nthen the displacement produced by S2 will be given by\ny2 = a cos (wt \u2013 4p) = a cos wt\nwhere we have used the fact that a path difference of 2l corresponds to a\nphase difference of 4p The two displacements are once again in phase\nand the intensity will again be 4 I0 giving rise to constructive interference" + }, + { + "Chapter": "9", + "sentence_range": "1253-1256", + "Text": "9(a)] Thus, if\nthe displacement produced by S1 is given by\ny1 = a cos wt\nthen the displacement produced by S2 will be given by\ny2 = a cos (wt \u2013 4p) = a cos wt\nwhere we have used the fact that a path difference of 2l corresponds to a\nphase difference of 4p The two displacements are once again in phase\nand the intensity will again be 4 I0 giving rise to constructive interference In the above analysis we have assumed that the distances S1Q and S2Q\nare much greater than d (which represents the distance between S1 and\nS2) so that although S1Q and S2Q are not equal, the amplitudes of the\ndisplacement produced by each wave are very nearly the same" + }, + { + "Chapter": "9", + "sentence_range": "1254-1257", + "Text": "Thus, if\nthe displacement produced by S1 is given by\ny1 = a cos wt\nthen the displacement produced by S2 will be given by\ny2 = a cos (wt \u2013 4p) = a cos wt\nwhere we have used the fact that a path difference of 2l corresponds to a\nphase difference of 4p The two displacements are once again in phase\nand the intensity will again be 4 I0 giving rise to constructive interference In the above analysis we have assumed that the distances S1Q and S2Q\nare much greater than d (which represents the distance between S1 and\nS2) so that although S1Q and S2Q are not equal, the amplitudes of the\ndisplacement produced by each wave are very nearly the same We next consider a point R [Fig" + }, + { + "Chapter": "9", + "sentence_range": "1255-1258", + "Text": "The two displacements are once again in phase\nand the intensity will again be 4 I0 giving rise to constructive interference In the above analysis we have assumed that the distances S1Q and S2Q\nare much greater than d (which represents the distance between S1 and\nS2) so that although S1Q and S2Q are not equal, the amplitudes of the\ndisplacement produced by each wave are very nearly the same We next consider a point R [Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1256-1259", + "Text": "In the above analysis we have assumed that the distances S1Q and S2Q\nare much greater than d (which represents the distance between S1 and\nS2) so that although S1Q and S2Q are not equal, the amplitudes of the\ndisplacement produced by each wave are very nearly the same We next consider a point R [Fig 10 9(b)] for which\nS2R \u2013 S1R = \u20132" + }, + { + "Chapter": "9", + "sentence_range": "1257-1260", + "Text": "We next consider a point R [Fig 10 9(b)] for which\nS2R \u2013 S1R = \u20132 5l\nThe waves emanating from S1 will arrive exactly two and a half cycles\nlater than the waves from S2 [Fig" + }, + { + "Chapter": "9", + "sentence_range": "1258-1261", + "Text": "10 9(b)] for which\nS2R \u2013 S1R = \u20132 5l\nThe waves emanating from S1 will arrive exactly two and a half cycles\nlater than the waves from S2 [Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1259-1262", + "Text": "9(b)] for which\nS2R \u2013 S1R = \u20132 5l\nThe waves emanating from S1 will arrive exactly two and a half cycles\nlater than the waves from S2 [Fig 10 10(b)]" + }, + { + "Chapter": "9", + "sentence_range": "1260-1263", + "Text": "5l\nThe waves emanating from S1 will arrive exactly two and a half cycles\nlater than the waves from S2 [Fig 10 10(b)] Thus if the displacement\nproduced by S1 is given by\ny1 = a cos wt\nthen the displacement produced by S2 will be given by\ny2 = a cos (wt + 5p) = \u2013 a cos wt\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1261-1264", + "Text": "10 10(b)] Thus if the displacement\nproduced by S1 is given by\ny1 = a cos wt\nthen the displacement produced by S2 will be given by\ny2 = a cos (wt + 5p) = \u2013 a cos wt\nFIGURE 10 9\n(a) Constructive\ninterference at a\npoint Q for which the\npath difference is 2l" + }, + { + "Chapter": "9", + "sentence_range": "1262-1265", + "Text": "10(b)] Thus if the displacement\nproduced by S1 is given by\ny1 = a cos wt\nthen the displacement produced by S2 will be given by\ny2 = a cos (wt + 5p) = \u2013 a cos wt\nFIGURE 10 9\n(a) Constructive\ninterference at a\npoint Q for which the\npath difference is 2l (b) Destructive\ninterference at a\npoint R for which the\npath difference is\n2" + }, + { + "Chapter": "9", + "sentence_range": "1263-1266", + "Text": "Thus if the displacement\nproduced by S1 is given by\ny1 = a cos wt\nthen the displacement produced by S2 will be given by\ny2 = a cos (wt + 5p) = \u2013 a cos wt\nFIGURE 10 9\n(a) Constructive\ninterference at a\npoint Q for which the\npath difference is 2l (b) Destructive\ninterference at a\npoint R for which the\npath difference is\n2 5 l" + }, + { + "Chapter": "9", + "sentence_range": "1264-1267", + "Text": "9\n(a) Constructive\ninterference at a\npoint Q for which the\npath difference is 2l (b) Destructive\ninterference at a\npoint R for which the\npath difference is\n2 5 l FIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1265-1268", + "Text": "(b) Destructive\ninterference at a\npoint R for which the\npath difference is\n2 5 l FIGURE 10 10 Locus\nof points for which\nS1P \u2013 S2P is equal to\nzero, \u00b1l, \u00b1 2l, \u00b1 3l" + }, + { + "Chapter": "9", + "sentence_range": "1266-1269", + "Text": "5 l FIGURE 10 10 Locus\nof points for which\nS1P \u2013 S2P is equal to\nzero, \u00b1l, \u00b1 2l, \u00b1 3l Rationalised 2023-24\nPhysics\n264\nwhere we have used the fact that a path difference of 2" + }, + { + "Chapter": "9", + "sentence_range": "1267-1270", + "Text": "FIGURE 10 10 Locus\nof points for which\nS1P \u2013 S2P is equal to\nzero, \u00b1l, \u00b1 2l, \u00b1 3l Rationalised 2023-24\nPhysics\n264\nwhere we have used the fact that a path difference of 2 5l corresponds to\na phase difference of 5p" + }, + { + "Chapter": "9", + "sentence_range": "1268-1271", + "Text": "10 Locus\nof points for which\nS1P \u2013 S2P is equal to\nzero, \u00b1l, \u00b1 2l, \u00b1 3l Rationalised 2023-24\nPhysics\n264\nwhere we have used the fact that a path difference of 2 5l corresponds to\na phase difference of 5p The two displacements are now out of phase\nand the two displacements will cancel out to give zero intensity" + }, + { + "Chapter": "9", + "sentence_range": "1269-1272", + "Text": "Rationalised 2023-24\nPhysics\n264\nwhere we have used the fact that a path difference of 2 5l corresponds to\na phase difference of 5p The two displacements are now out of phase\nand the two displacements will cancel out to give zero intensity This is\nreferred to as destructive interference" + }, + { + "Chapter": "9", + "sentence_range": "1270-1273", + "Text": "5l corresponds to\na phase difference of 5p The two displacements are now out of phase\nand the two displacements will cancel out to give zero intensity This is\nreferred to as destructive interference To summarise: If we have two coherent sources S1 and S2 vibrating\nin phase, then for an arbitrary point P whenever the path difference,\nS1P ~ S2P = nl (n = 0, 1, 2, 3," + }, + { + "Chapter": "9", + "sentence_range": "1271-1274", + "Text": "The two displacements are now out of phase\nand the two displacements will cancel out to give zero intensity This is\nreferred to as destructive interference To summarise: If we have two coherent sources S1 and S2 vibrating\nin phase, then for an arbitrary point P whenever the path difference,\nS1P ~ S2P = nl (n = 0, 1, 2, 3, )\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1272-1275", + "Text": "This is\nreferred to as destructive interference To summarise: If we have two coherent sources S1 and S2 vibrating\nin phase, then for an arbitrary point P whenever the path difference,\nS1P ~ S2P = nl (n = 0, 1, 2, 3, )\n(10 9)\nwe will have constructive interference and the resultant intensity will be\n4I0; the sign ~ between S1P and S2 P represents the difference between\nS1P and S2 P" + }, + { + "Chapter": "9", + "sentence_range": "1273-1276", + "Text": "To summarise: If we have two coherent sources S1 and S2 vibrating\nin phase, then for an arbitrary point P whenever the path difference,\nS1P ~ S2P = nl (n = 0, 1, 2, 3, )\n(10 9)\nwe will have constructive interference and the resultant intensity will be\n4I0; the sign ~ between S1P and S2 P represents the difference between\nS1P and S2 P On the other hand, if the point P is such that the path\ndifference,\nS1P ~ S2P = (n+ 1\n2 ) l (n = 0, 1, 2, 3," + }, + { + "Chapter": "9", + "sentence_range": "1274-1277", + "Text": ")\n(10 9)\nwe will have constructive interference and the resultant intensity will be\n4I0; the sign ~ between S1P and S2 P represents the difference between\nS1P and S2 P On the other hand, if the point P is such that the path\ndifference,\nS1P ~ S2P = (n+ 1\n2 ) l (n = 0, 1, 2, 3, )\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1275-1278", + "Text": "9)\nwe will have constructive interference and the resultant intensity will be\n4I0; the sign ~ between S1P and S2 P represents the difference between\nS1P and S2 P On the other hand, if the point P is such that the path\ndifference,\nS1P ~ S2P = (n+ 1\n2 ) l (n = 0, 1, 2, 3, )\n(10 10)\nwe will have destructive interference and the resultant intensity will be\nzero" + }, + { + "Chapter": "9", + "sentence_range": "1276-1279", + "Text": "On the other hand, if the point P is such that the path\ndifference,\nS1P ~ S2P = (n+ 1\n2 ) l (n = 0, 1, 2, 3, )\n(10 10)\nwe will have destructive interference and the resultant intensity will be\nzero Now, for any other arbitrary point G (Fig" + }, + { + "Chapter": "9", + "sentence_range": "1277-1280", + "Text": ")\n(10 10)\nwe will have destructive interference and the resultant intensity will be\nzero Now, for any other arbitrary point G (Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1278-1281", + "Text": "10)\nwe will have destructive interference and the resultant intensity will be\nzero Now, for any other arbitrary point G (Fig 10 10) let the phase\ndifference between the two displacements be f" + }, + { + "Chapter": "9", + "sentence_range": "1279-1282", + "Text": "Now, for any other arbitrary point G (Fig 10 10) let the phase\ndifference between the two displacements be f Thus, if the displacement\nproduced by S1 is given by\ny1 = a cos wt\nthen, the displacement produced by S2 would be\ny2 = a cos (wt + f)\nand the resultant displacement will be given by\ny = y1 + y2\n = a [cos wt + cos (wt +f)]\n = 2 a cos (f/2) cos (wt + f/2)\nThe amplitude of the resultant displacement is 2a cos (f/2) and\ntherefore the intensity at that point will be\nI = 4 I0 cos2 (f/2)\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1280-1283", + "Text": "10 10) let the phase\ndifference between the two displacements be f Thus, if the displacement\nproduced by S1 is given by\ny1 = a cos wt\nthen, the displacement produced by S2 would be\ny2 = a cos (wt + f)\nand the resultant displacement will be given by\ny = y1 + y2\n = a [cos wt + cos (wt +f)]\n = 2 a cos (f/2) cos (wt + f/2)\nThe amplitude of the resultant displacement is 2a cos (f/2) and\ntherefore the intensity at that point will be\nI = 4 I0 cos2 (f/2)\n(10 11)\nIf f = 0, \u00b1 2 p, \u00b1 4 p,\u2026 which corresponds to the condition given by\nEq" + }, + { + "Chapter": "9", + "sentence_range": "1281-1284", + "Text": "10) let the phase\ndifference between the two displacements be f Thus, if the displacement\nproduced by S1 is given by\ny1 = a cos wt\nthen, the displacement produced by S2 would be\ny2 = a cos (wt + f)\nand the resultant displacement will be given by\ny = y1 + y2\n = a [cos wt + cos (wt +f)]\n = 2 a cos (f/2) cos (wt + f/2)\nThe amplitude of the resultant displacement is 2a cos (f/2) and\ntherefore the intensity at that point will be\nI = 4 I0 cos2 (f/2)\n(10 11)\nIf f = 0, \u00b1 2 p, \u00b1 4 p,\u2026 which corresponds to the condition given by\nEq (10" + }, + { + "Chapter": "9", + "sentence_range": "1282-1285", + "Text": "Thus, if the displacement\nproduced by S1 is given by\ny1 = a cos wt\nthen, the displacement produced by S2 would be\ny2 = a cos (wt + f)\nand the resultant displacement will be given by\ny = y1 + y2\n = a [cos wt + cos (wt +f)]\n = 2 a cos (f/2) cos (wt + f/2)\nThe amplitude of the resultant displacement is 2a cos (f/2) and\ntherefore the intensity at that point will be\nI = 4 I0 cos2 (f/2)\n(10 11)\nIf f = 0, \u00b1 2 p, \u00b1 4 p,\u2026 which corresponds to the condition given by\nEq (10 9) we will have constructive interference leading to maximum\nintensity" + }, + { + "Chapter": "9", + "sentence_range": "1283-1286", + "Text": "11)\nIf f = 0, \u00b1 2 p, \u00b1 4 p,\u2026 which corresponds to the condition given by\nEq (10 9) we will have constructive interference leading to maximum\nintensity On the other hand, if f = \u00b1 p, \u00b1 3p, \u00b1 5p \u2026 [which corresponds to\nthe condition given by Eq" + }, + { + "Chapter": "9", + "sentence_range": "1284-1287", + "Text": "(10 9) we will have constructive interference leading to maximum\nintensity On the other hand, if f = \u00b1 p, \u00b1 3p, \u00b1 5p \u2026 [which corresponds to\nthe condition given by Eq (10" + }, + { + "Chapter": "9", + "sentence_range": "1285-1288", + "Text": "9) we will have constructive interference leading to maximum\nintensity On the other hand, if f = \u00b1 p, \u00b1 3p, \u00b1 5p \u2026 [which corresponds to\nthe condition given by Eq (10 10)] we will have destructive interference\nleading to zero intensity" + }, + { + "Chapter": "9", + "sentence_range": "1286-1289", + "Text": "On the other hand, if f = \u00b1 p, \u00b1 3p, \u00b1 5p \u2026 [which corresponds to\nthe condition given by Eq (10 10)] we will have destructive interference\nleading to zero intensity Now if the two sources are coherent (i" + }, + { + "Chapter": "9", + "sentence_range": "1287-1290", + "Text": "(10 10)] we will have destructive interference\nleading to zero intensity Now if the two sources are coherent (i e" + }, + { + "Chapter": "9", + "sentence_range": "1288-1291", + "Text": "10)] we will have destructive interference\nleading to zero intensity Now if the two sources are coherent (i e , if the two needles are going\nup and down regularly) then the phase difference f at any point will not\nchange with time and we will have a stable interference pattern; i" + }, + { + "Chapter": "9", + "sentence_range": "1289-1292", + "Text": "Now if the two sources are coherent (i e , if the two needles are going\nup and down regularly) then the phase difference f at any point will not\nchange with time and we will have a stable interference pattern; i e" + }, + { + "Chapter": "9", + "sentence_range": "1290-1293", + "Text": "e , if the two needles are going\nup and down regularly) then the phase difference f at any point will not\nchange with time and we will have a stable interference pattern; i e , the\npositions of maxima and minima will not change with time" + }, + { + "Chapter": "9", + "sentence_range": "1291-1294", + "Text": ", if the two needles are going\nup and down regularly) then the phase difference f at any point will not\nchange with time and we will have a stable interference pattern; i e , the\npositions of maxima and minima will not change with time However, if\nthe two needles do not maintain a constant phase difference, then the\ninterference pattern will also change with time and, if the phase difference\nchanges very rapidly with time, the positions of maxima and minima will\nalso vary rapidly with time and we will see a \u201ctime-averaged\u201d intensity\ndistribution" + }, + { + "Chapter": "9", + "sentence_range": "1292-1295", + "Text": "e , the\npositions of maxima and minima will not change with time However, if\nthe two needles do not maintain a constant phase difference, then the\ninterference pattern will also change with time and, if the phase difference\nchanges very rapidly with time, the positions of maxima and minima will\nalso vary rapidly with time and we will see a \u201ctime-averaged\u201d intensity\ndistribution When this happens, we will observe an average intensity\nthat will be given by\nI = 2 I0\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1293-1296", + "Text": ", the\npositions of maxima and minima will not change with time However, if\nthe two needles do not maintain a constant phase difference, then the\ninterference pattern will also change with time and, if the phase difference\nchanges very rapidly with time, the positions of maxima and minima will\nalso vary rapidly with time and we will see a \u201ctime-averaged\u201d intensity\ndistribution When this happens, we will observe an average intensity\nthat will be given by\nI = 2 I0\n(10 12)\nat all points" + }, + { + "Chapter": "9", + "sentence_range": "1294-1297", + "Text": "However, if\nthe two needles do not maintain a constant phase difference, then the\ninterference pattern will also change with time and, if the phase difference\nchanges very rapidly with time, the positions of maxima and minima will\nalso vary rapidly with time and we will see a \u201ctime-averaged\u201d intensity\ndistribution When this happens, we will observe an average intensity\nthat will be given by\nI = 2 I0\n(10 12)\nat all points Ripple Tank experiments on wave interference\nhttp://phet" + }, + { + "Chapter": "9", + "sentence_range": "1295-1298", + "Text": "When this happens, we will observe an average intensity\nthat will be given by\nI = 2 I0\n(10 12)\nat all points Ripple Tank experiments on wave interference\nhttp://phet colorado" + }, + { + "Chapter": "9", + "sentence_range": "1296-1299", + "Text": "12)\nat all points Ripple Tank experiments on wave interference\nhttp://phet colorado edu/en/simulation/legacy/wave-interference\nRationalised 2023-24\n265\nWave Optics\nWhen the phase difference between the two vibrating sources changes\nrapidly with time, we say that the two sources are incoherent and when\nthis happens the intensities just add up" + }, + { + "Chapter": "9", + "sentence_range": "1297-1300", + "Text": "Ripple Tank experiments on wave interference\nhttp://phet colorado edu/en/simulation/legacy/wave-interference\nRationalised 2023-24\n265\nWave Optics\nWhen the phase difference between the two vibrating sources changes\nrapidly with time, we say that the two sources are incoherent and when\nthis happens the intensities just add up This is indeed what happens\nwhen two separate light sources illuminate a wall" + }, + { + "Chapter": "9", + "sentence_range": "1298-1301", + "Text": "colorado edu/en/simulation/legacy/wave-interference\nRationalised 2023-24\n265\nWave Optics\nWhen the phase difference between the two vibrating sources changes\nrapidly with time, we say that the two sources are incoherent and when\nthis happens the intensities just add up This is indeed what happens\nwhen two separate light sources illuminate a wall 10" + }, + { + "Chapter": "9", + "sentence_range": "1299-1302", + "Text": "edu/en/simulation/legacy/wave-interference\nRationalised 2023-24\n265\nWave Optics\nWhen the phase difference between the two vibrating sources changes\nrapidly with time, we say that the two sources are incoherent and when\nthis happens the intensities just add up This is indeed what happens\nwhen two separate light sources illuminate a wall 10 5 INTERFERENCE OF LIGHT WAVES AND YOUNG\u2019S\nEXPERIMENT\nWe will now discuss interference using light waves" + }, + { + "Chapter": "9", + "sentence_range": "1300-1303", + "Text": "This is indeed what happens\nwhen two separate light sources illuminate a wall 10 5 INTERFERENCE OF LIGHT WAVES AND YOUNG\u2019S\nEXPERIMENT\nWe will now discuss interference using light waves If\nwe use two sodium lamps illuminating two pinholes\n(Fig" + }, + { + "Chapter": "9", + "sentence_range": "1301-1304", + "Text": "10 5 INTERFERENCE OF LIGHT WAVES AND YOUNG\u2019S\nEXPERIMENT\nWe will now discuss interference using light waves If\nwe use two sodium lamps illuminating two pinholes\n(Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1302-1305", + "Text": "5 INTERFERENCE OF LIGHT WAVES AND YOUNG\u2019S\nEXPERIMENT\nWe will now discuss interference using light waves If\nwe use two sodium lamps illuminating two pinholes\n(Fig 10 11) we will not observe any interference fringes" + }, + { + "Chapter": "9", + "sentence_range": "1303-1306", + "Text": "If\nwe use two sodium lamps illuminating two pinholes\n(Fig 10 11) we will not observe any interference fringes This is because of the fact that the light wave emitted\nfrom an ordinary source (like a sodium lamp) undergoes\nabrupt phase changes in times of the order of 10\u201310\nseconds" + }, + { + "Chapter": "9", + "sentence_range": "1304-1307", + "Text": "10 11) we will not observe any interference fringes This is because of the fact that the light wave emitted\nfrom an ordinary source (like a sodium lamp) undergoes\nabrupt phase changes in times of the order of 10\u201310\nseconds Thus the light waves coming out from two\nindependent sources of light will not have any fixed\nphase relationship and would be incoherent, when this\nhappens, as discussed in the previous section, the\nintensities on the screen will add up" + }, + { + "Chapter": "9", + "sentence_range": "1305-1308", + "Text": "11) we will not observe any interference fringes This is because of the fact that the light wave emitted\nfrom an ordinary source (like a sodium lamp) undergoes\nabrupt phase changes in times of the order of 10\u201310\nseconds Thus the light waves coming out from two\nindependent sources of light will not have any fixed\nphase relationship and would be incoherent, when this\nhappens, as discussed in the previous section, the\nintensities on the screen will add up The British physicist Thomas Young used an\ningenious technique to \u201clock\u201d the phases of the waves\nemanating from S1 and S2" + }, + { + "Chapter": "9", + "sentence_range": "1306-1309", + "Text": "This is because of the fact that the light wave emitted\nfrom an ordinary source (like a sodium lamp) undergoes\nabrupt phase changes in times of the order of 10\u201310\nseconds Thus the light waves coming out from two\nindependent sources of light will not have any fixed\nphase relationship and would be incoherent, when this\nhappens, as discussed in the previous section, the\nintensities on the screen will add up The British physicist Thomas Young used an\ningenious technique to \u201clock\u201d the phases of the waves\nemanating from S1 and S2 He made two pinholes S1\nand S2 (very close to each other) on an opaque screen [Fig" + }, + { + "Chapter": "9", + "sentence_range": "1307-1310", + "Text": "Thus the light waves coming out from two\nindependent sources of light will not have any fixed\nphase relationship and would be incoherent, when this\nhappens, as discussed in the previous section, the\nintensities on the screen will add up The British physicist Thomas Young used an\ningenious technique to \u201clock\u201d the phases of the waves\nemanating from S1 and S2 He made two pinholes S1\nand S2 (very close to each other) on an opaque screen [Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1308-1311", + "Text": "The British physicist Thomas Young used an\ningenious technique to \u201clock\u201d the phases of the waves\nemanating from S1 and S2 He made two pinholes S1\nand S2 (very close to each other) on an opaque screen [Fig 10 12(a)]" + }, + { + "Chapter": "9", + "sentence_range": "1309-1312", + "Text": "He made two pinholes S1\nand S2 (very close to each other) on an opaque screen [Fig 10 12(a)] These were illuminated by another pinholes that was in turn, lit by a\nbright source" + }, + { + "Chapter": "9", + "sentence_range": "1310-1313", + "Text": "10 12(a)] These were illuminated by another pinholes that was in turn, lit by a\nbright source Light waves spread out from S and fall on both S1 and S2" + }, + { + "Chapter": "9", + "sentence_range": "1311-1314", + "Text": "12(a)] These were illuminated by another pinholes that was in turn, lit by a\nbright source Light waves spread out from S and fall on both S1 and S2 S1 and S2 then behave like two coherent sources because light waves\ncoming out from S1 and S2 are derived from the same original source\nand any abrupt phase change in S will manifest in exactly similar phase\nchanges in the light coming out from S1 and S2" + }, + { + "Chapter": "9", + "sentence_range": "1312-1315", + "Text": "These were illuminated by another pinholes that was in turn, lit by a\nbright source Light waves spread out from S and fall on both S1 and S2 S1 and S2 then behave like two coherent sources because light waves\ncoming out from S1 and S2 are derived from the same original source\nand any abrupt phase change in S will manifest in exactly similar phase\nchanges in the light coming out from S1 and S2 Thus, the two sources S1\nand S2 will be locked in phase; i" + }, + { + "Chapter": "9", + "sentence_range": "1313-1316", + "Text": "Light waves spread out from S and fall on both S1 and S2 S1 and S2 then behave like two coherent sources because light waves\ncoming out from S1 and S2 are derived from the same original source\nand any abrupt phase change in S will manifest in exactly similar phase\nchanges in the light coming out from S1 and S2 Thus, the two sources S1\nand S2 will be locked in phase; i e" + }, + { + "Chapter": "9", + "sentence_range": "1314-1317", + "Text": "S1 and S2 then behave like two coherent sources because light waves\ncoming out from S1 and S2 are derived from the same original source\nand any abrupt phase change in S will manifest in exactly similar phase\nchanges in the light coming out from S1 and S2 Thus, the two sources S1\nand S2 will be locked in phase; i e , they will be coherent like the two\nvibrating needle in our water wave example [Fig" + }, + { + "Chapter": "9", + "sentence_range": "1315-1318", + "Text": "Thus, the two sources S1\nand S2 will be locked in phase; i e , they will be coherent like the two\nvibrating needle in our water wave example [Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1316-1319", + "Text": "e , they will be coherent like the two\nvibrating needle in our water wave example [Fig 10 8(a)]" + }, + { + "Chapter": "9", + "sentence_range": "1317-1320", + "Text": ", they will be coherent like the two\nvibrating needle in our water wave example [Fig 10 8(a)] The spherical waves emanating from S1 and S2 will produce\ninterference fringes on the screen GG\u00a2, as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1318-1321", + "Text": "10 8(a)] The spherical waves emanating from S1 and S2 will produce\ninterference fringes on the screen GG\u00a2, as shown in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1319-1322", + "Text": "8(a)] The spherical waves emanating from S1 and S2 will produce\ninterference fringes on the screen GG\u00a2, as shown in Fig 10 12(b)" + }, + { + "Chapter": "9", + "sentence_range": "1320-1323", + "Text": "The spherical waves emanating from S1 and S2 will produce\ninterference fringes on the screen GG\u00a2, as shown in Fig 10 12(b) The\npositions of maximum and minimum intensities can be calculated by\nusing the analysis given in Section 10" + }, + { + "Chapter": "9", + "sentence_range": "1321-1324", + "Text": "10 12(b) The\npositions of maximum and minimum intensities can be calculated by\nusing the analysis given in Section 10 4" + }, + { + "Chapter": "9", + "sentence_range": "1322-1325", + "Text": "12(b) The\npositions of maximum and minimum intensities can be calculated by\nusing the analysis given in Section 10 4 (a)\n(b)\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1323-1326", + "Text": "The\npositions of maximum and minimum intensities can be calculated by\nusing the analysis given in Section 10 4 (a)\n(b)\nFIGURE 10 12 Young\u2019s arrangement to produce interference pattern" + }, + { + "Chapter": "9", + "sentence_range": "1324-1327", + "Text": "4 (a)\n(b)\nFIGURE 10 12 Young\u2019s arrangement to produce interference pattern FIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1325-1328", + "Text": "(a)\n(b)\nFIGURE 10 12 Young\u2019s arrangement to produce interference pattern FIGURE 10 11 If two sodium\nlamps illuminate two pinholes\nS1 and S2, the intensities will add\nup and no interference fringes will\nbe observed on the screen" + }, + { + "Chapter": "9", + "sentence_range": "1326-1329", + "Text": "12 Young\u2019s arrangement to produce interference pattern FIGURE 10 11 If two sodium\nlamps illuminate two pinholes\nS1 and S2, the intensities will add\nup and no interference fringes will\nbe observed on the screen Rationalised 2023-24\nPhysics\n266\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1327-1330", + "Text": "FIGURE 10 11 If two sodium\nlamps illuminate two pinholes\nS1 and S2, the intensities will add\nup and no interference fringes will\nbe observed on the screen Rationalised 2023-24\nPhysics\n266\nFIGURE 10 13 Computer generated fringe pattern produced by two point\nsource S1 and S2 on the screen GG\u00a2 (Fig" + }, + { + "Chapter": "9", + "sentence_range": "1328-1331", + "Text": "11 If two sodium\nlamps illuminate two pinholes\nS1 and S2, the intensities will add\nup and no interference fringes will\nbe observed on the screen Rationalised 2023-24\nPhysics\n266\nFIGURE 10 13 Computer generated fringe pattern produced by two point\nsource S1 and S2 on the screen GG\u00a2 (Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1329-1332", + "Text": "Rationalised 2023-24\nPhysics\n266\nFIGURE 10 13 Computer generated fringe pattern produced by two point\nsource S1 and S2 on the screen GG\u00a2 (Fig 10 12); correspond to d = 0" + }, + { + "Chapter": "9", + "sentence_range": "1330-1333", + "Text": "13 Computer generated fringe pattern produced by two point\nsource S1 and S2 on the screen GG\u00a2 (Fig 10 12); correspond to d = 0 025\nmm, D = 5 cm and l = 5 \u00d7 10\u20135 cm" + }, + { + "Chapter": "9", + "sentence_range": "1331-1334", + "Text": "10 12); correspond to d = 0 025\nmm, D = 5 cm and l = 5 \u00d7 10\u20135 cm ) (Adopted from OPTICS by A" + }, + { + "Chapter": "9", + "sentence_range": "1332-1335", + "Text": "12); correspond to d = 0 025\nmm, D = 5 cm and l = 5 \u00d7 10\u20135 cm ) (Adopted from OPTICS by A Ghatak,\nTata McGraw Hill Publishing Co" + }, + { + "Chapter": "9", + "sentence_range": "1333-1336", + "Text": "025\nmm, D = 5 cm and l = 5 \u00d7 10\u20135 cm ) (Adopted from OPTICS by A Ghatak,\nTata McGraw Hill Publishing Co Ltd" + }, + { + "Chapter": "9", + "sentence_range": "1334-1337", + "Text": ") (Adopted from OPTICS by A Ghatak,\nTata McGraw Hill Publishing Co Ltd , New Delhi, 2000" + }, + { + "Chapter": "9", + "sentence_range": "1335-1338", + "Text": "Ghatak,\nTata McGraw Hill Publishing Co Ltd , New Delhi, 2000 )\nThomas \nYoung\n(1773 \u2013 1829) English\nphysicist, physician and\nEgyptologist" + }, + { + "Chapter": "9", + "sentence_range": "1336-1339", + "Text": "Ltd , New Delhi, 2000 )\nThomas \nYoung\n(1773 \u2013 1829) English\nphysicist, physician and\nEgyptologist Young worked\non a wide variety of\nscientific problems, ranging\nfrom the structure of the eye\nand the mechanism of\nvision to the decipherment\nof the Rosetta stone" + }, + { + "Chapter": "9", + "sentence_range": "1337-1340", + "Text": ", New Delhi, 2000 )\nThomas \nYoung\n(1773 \u2013 1829) English\nphysicist, physician and\nEgyptologist Young worked\non a wide variety of\nscientific problems, ranging\nfrom the structure of the eye\nand the mechanism of\nvision to the decipherment\nof the Rosetta stone He\nrevived the wave theory of\nlight and recognised that\ninterference phenomena\nprovide proof of the wave\nproperties of light" + }, + { + "Chapter": "9", + "sentence_range": "1338-1341", + "Text": ")\nThomas \nYoung\n(1773 \u2013 1829) English\nphysicist, physician and\nEgyptologist Young worked\non a wide variety of\nscientific problems, ranging\nfrom the structure of the eye\nand the mechanism of\nvision to the decipherment\nof the Rosetta stone He\nrevived the wave theory of\nlight and recognised that\ninterference phenomena\nprovide proof of the wave\nproperties of light THOMAS YOUNG (1773 \u2013 1829)\nWe will have constructive interference resulting in a bright\nregion when xd\nD\n = nl" + }, + { + "Chapter": "9", + "sentence_range": "1339-1342", + "Text": "Young worked\non a wide variety of\nscientific problems, ranging\nfrom the structure of the eye\nand the mechanism of\nvision to the decipherment\nof the Rosetta stone He\nrevived the wave theory of\nlight and recognised that\ninterference phenomena\nprovide proof of the wave\nproperties of light THOMAS YOUNG (1773 \u2013 1829)\nWe will have constructive interference resulting in a bright\nregion when xd\nD\n = nl That is,\nx = xn = n D\n\u03bbd\n; n = 0, \u00b1 1, \u00b1 2," + }, + { + "Chapter": "9", + "sentence_range": "1340-1343", + "Text": "He\nrevived the wave theory of\nlight and recognised that\ninterference phenomena\nprovide proof of the wave\nproperties of light THOMAS YOUNG (1773 \u2013 1829)\nWe will have constructive interference resulting in a bright\nregion when xd\nD\n = nl That is,\nx = xn = n D\n\u03bbd\n; n = 0, \u00b1 1, \u00b1 2, (10" + }, + { + "Chapter": "9", + "sentence_range": "1341-1344", + "Text": "THOMAS YOUNG (1773 \u2013 1829)\nWe will have constructive interference resulting in a bright\nregion when xd\nD\n = nl That is,\nx = xn = n D\n\u03bbd\n; n = 0, \u00b1 1, \u00b1 2, (10 13)\nOn the other hand, we will have destructive\ninterference resulting in a dark region when xd\nD\n= (n+\n1\n2 ) l\nthat is\nx = xn = (n+\n1\n2 ) \n;\n0, 1,\n2\nD\nn\n\uf06cd\n\uf03d\n\uf0b1\n\uf0b1\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1342-1345", + "Text": "That is,\nx = xn = n D\n\u03bbd\n; n = 0, \u00b1 1, \u00b1 2, (10 13)\nOn the other hand, we will have destructive\ninterference resulting in a dark region when xd\nD\n= (n+\n1\n2 ) l\nthat is\nx = xn = (n+\n1\n2 ) \n;\n0, 1,\n2\nD\nn\n\uf06cd\n\uf03d\n\uf0b1\n\uf0b1\n(10 14)\nThus dark and bright bands appear on the screen,\nas shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1343-1346", + "Text": "(10 13)\nOn the other hand, we will have destructive\ninterference resulting in a dark region when xd\nD\n= (n+\n1\n2 ) l\nthat is\nx = xn = (n+\n1\n2 ) \n;\n0, 1,\n2\nD\nn\n\uf06cd\n\uf03d\n\uf0b1\n\uf0b1\n(10 14)\nThus dark and bright bands appear on the screen,\nas shown in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1344-1347", + "Text": "13)\nOn the other hand, we will have destructive\ninterference resulting in a dark region when xd\nD\n= (n+\n1\n2 ) l\nthat is\nx = xn = (n+\n1\n2 ) \n;\n0, 1,\n2\nD\nn\n\uf06cd\n\uf03d\n\uf0b1\n\uf0b1\n(10 14)\nThus dark and bright bands appear on the screen,\nas shown in Fig 10 13" + }, + { + "Chapter": "9", + "sentence_range": "1345-1348", + "Text": "14)\nThus dark and bright bands appear on the screen,\nas shown in Fig 10 13 Such bands are called fringes" + }, + { + "Chapter": "9", + "sentence_range": "1346-1349", + "Text": "10 13 Such bands are called fringes Equations (10" + }, + { + "Chapter": "9", + "sentence_range": "1347-1350", + "Text": "13 Such bands are called fringes Equations (10 13) and (10" + }, + { + "Chapter": "9", + "sentence_range": "1348-1351", + "Text": "Such bands are called fringes Equations (10 13) and (10 14) show that dark and\nbright fringes are equally spaced" + }, + { + "Chapter": "9", + "sentence_range": "1349-1352", + "Text": "Equations (10 13) and (10 14) show that dark and\nbright fringes are equally spaced 10" + }, + { + "Chapter": "9", + "sentence_range": "1350-1353", + "Text": "13) and (10 14) show that dark and\nbright fringes are equally spaced 10 6 DIFFRACTION\nIf we look clearly at the shadow cast by an opaque object, close to the\nregion of geometrical shadow, there are alternate dark and bright regions\njust like in interference" + }, + { + "Chapter": "9", + "sentence_range": "1351-1354", + "Text": "14) show that dark and\nbright fringes are equally spaced 10 6 DIFFRACTION\nIf we look clearly at the shadow cast by an opaque object, close to the\nregion of geometrical shadow, there are alternate dark and bright regions\njust like in interference This happens due to the phenomenon of\ndiffraction" + }, + { + "Chapter": "9", + "sentence_range": "1352-1355", + "Text": "10 6 DIFFRACTION\nIf we look clearly at the shadow cast by an opaque object, close to the\nregion of geometrical shadow, there are alternate dark and bright regions\njust like in interference This happens due to the phenomenon of\ndiffraction Diffraction is a general characteristic exhibited by all types of\nwaves, be it sound waves, light waves, water waves or matter waves" + }, + { + "Chapter": "9", + "sentence_range": "1353-1356", + "Text": "6 DIFFRACTION\nIf we look clearly at the shadow cast by an opaque object, close to the\nregion of geometrical shadow, there are alternate dark and bright regions\njust like in interference This happens due to the phenomenon of\ndiffraction Diffraction is a general characteristic exhibited by all types of\nwaves, be it sound waves, light waves, water waves or matter waves Since\nthe wavelength of light is much smaller than the dimensions of most\nobstacles; we do not encounter diffraction effects of light in everyday\nRationalised 2023-24\n267\nWave Optics\nobservations" + }, + { + "Chapter": "9", + "sentence_range": "1354-1357", + "Text": "This happens due to the phenomenon of\ndiffraction Diffraction is a general characteristic exhibited by all types of\nwaves, be it sound waves, light waves, water waves or matter waves Since\nthe wavelength of light is much smaller than the dimensions of most\nobstacles; we do not encounter diffraction effects of light in everyday\nRationalised 2023-24\n267\nWave Optics\nobservations However, the finite resolution of our eye or of optical\ninstruments such as telescopes or microscopes is limited due to the\nphenomenon of diffraction" + }, + { + "Chapter": "9", + "sentence_range": "1355-1358", + "Text": "Diffraction is a general characteristic exhibited by all types of\nwaves, be it sound waves, light waves, water waves or matter waves Since\nthe wavelength of light is much smaller than the dimensions of most\nobstacles; we do not encounter diffraction effects of light in everyday\nRationalised 2023-24\n267\nWave Optics\nobservations However, the finite resolution of our eye or of optical\ninstruments such as telescopes or microscopes is limited due to the\nphenomenon of diffraction Indeed the colours that you see when a CD is\nviewed is due to diffraction effects" + }, + { + "Chapter": "9", + "sentence_range": "1356-1359", + "Text": "Since\nthe wavelength of light is much smaller than the dimensions of most\nobstacles; we do not encounter diffraction effects of light in everyday\nRationalised 2023-24\n267\nWave Optics\nobservations However, the finite resolution of our eye or of optical\ninstruments such as telescopes or microscopes is limited due to the\nphenomenon of diffraction Indeed the colours that you see when a CD is\nviewed is due to diffraction effects We will now discuss the phenomenon\nof diffraction" + }, + { + "Chapter": "9", + "sentence_range": "1357-1360", + "Text": "However, the finite resolution of our eye or of optical\ninstruments such as telescopes or microscopes is limited due to the\nphenomenon of diffraction Indeed the colours that you see when a CD is\nviewed is due to diffraction effects We will now discuss the phenomenon\nof diffraction 10" + }, + { + "Chapter": "9", + "sentence_range": "1358-1361", + "Text": "Indeed the colours that you see when a CD is\nviewed is due to diffraction effects We will now discuss the phenomenon\nof diffraction 10 6" + }, + { + "Chapter": "9", + "sentence_range": "1359-1362", + "Text": "We will now discuss the phenomenon\nof diffraction 10 6 1 The single slit\nIn the discussion of Young\u2019s experiment, we stated that a single narrow\nslit acts as a new source from which light spreads out" + }, + { + "Chapter": "9", + "sentence_range": "1360-1363", + "Text": "10 6 1 The single slit\nIn the discussion of Young\u2019s experiment, we stated that a single narrow\nslit acts as a new source from which light spreads out Even before Young,\nearly experimenters \u2013 including Newton \u2013 had noticed that light spreads\nout from narrow holes and slits" + }, + { + "Chapter": "9", + "sentence_range": "1361-1364", + "Text": "6 1 The single slit\nIn the discussion of Young\u2019s experiment, we stated that a single narrow\nslit acts as a new source from which light spreads out Even before Young,\nearly experimenters \u2013 including Newton \u2013 had noticed that light spreads\nout from narrow holes and slits It seems to turn around corners and\nenter regions where we would expect a shadow" + }, + { + "Chapter": "9", + "sentence_range": "1362-1365", + "Text": "1 The single slit\nIn the discussion of Young\u2019s experiment, we stated that a single narrow\nslit acts as a new source from which light spreads out Even before Young,\nearly experimenters \u2013 including Newton \u2013 had noticed that light spreads\nout from narrow holes and slits It seems to turn around corners and\nenter regions where we would expect a shadow These effects, known as\ndiffraction, can only be properly understood using wave ideas" + }, + { + "Chapter": "9", + "sentence_range": "1363-1366", + "Text": "Even before Young,\nearly experimenters \u2013 including Newton \u2013 had noticed that light spreads\nout from narrow holes and slits It seems to turn around corners and\nenter regions where we would expect a shadow These effects, known as\ndiffraction, can only be properly understood using wave ideas After all,\nyou are hardly surprised to hear sound\nwaves from someone talking around a corner" + }, + { + "Chapter": "9", + "sentence_range": "1364-1367", + "Text": "It seems to turn around corners and\nenter regions where we would expect a shadow These effects, known as\ndiffraction, can only be properly understood using wave ideas After all,\nyou are hardly surprised to hear sound\nwaves from someone talking around a corner When the double slit in Young\u2019s\nexperiment is replaced by a single narrow\nslit (illuminated by a monochromatic\nsource), a broad pattern with a central bright\nregion is seen" + }, + { + "Chapter": "9", + "sentence_range": "1365-1368", + "Text": "These effects, known as\ndiffraction, can only be properly understood using wave ideas After all,\nyou are hardly surprised to hear sound\nwaves from someone talking around a corner When the double slit in Young\u2019s\nexperiment is replaced by a single narrow\nslit (illuminated by a monochromatic\nsource), a broad pattern with a central bright\nregion is seen On both sides, there are\nalternate dark and bright regions, the\nintensity becoming weaker away from the\ncentre (Fig" + }, + { + "Chapter": "9", + "sentence_range": "1366-1369", + "Text": "After all,\nyou are hardly surprised to hear sound\nwaves from someone talking around a corner When the double slit in Young\u2019s\nexperiment is replaced by a single narrow\nslit (illuminated by a monochromatic\nsource), a broad pattern with a central bright\nregion is seen On both sides, there are\nalternate dark and bright regions, the\nintensity becoming weaker away from the\ncentre (Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1367-1370", + "Text": "When the double slit in Young\u2019s\nexperiment is replaced by a single narrow\nslit (illuminated by a monochromatic\nsource), a broad pattern with a central bright\nregion is seen On both sides, there are\nalternate dark and bright regions, the\nintensity becoming weaker away from the\ncentre (Fig 10 15)" + }, + { + "Chapter": "9", + "sentence_range": "1368-1371", + "Text": "On both sides, there are\nalternate dark and bright regions, the\nintensity becoming weaker away from the\ncentre (Fig 10 15) To understand this, go\nto Fig" + }, + { + "Chapter": "9", + "sentence_range": "1369-1372", + "Text": "10 15) To understand this, go\nto Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1370-1373", + "Text": "15) To understand this, go\nto Fig 10 14, which shows a parallel beam\nof light falling normally on a single slit LN of\nwidth a" + }, + { + "Chapter": "9", + "sentence_range": "1371-1374", + "Text": "To understand this, go\nto Fig 10 14, which shows a parallel beam\nof light falling normally on a single slit LN of\nwidth a The diffracted light goes on to meet\na screen" + }, + { + "Chapter": "9", + "sentence_range": "1372-1375", + "Text": "10 14, which shows a parallel beam\nof light falling normally on a single slit LN of\nwidth a The diffracted light goes on to meet\na screen The midpoint of the slit is M" + }, + { + "Chapter": "9", + "sentence_range": "1373-1376", + "Text": "14, which shows a parallel beam\nof light falling normally on a single slit LN of\nwidth a The diffracted light goes on to meet\na screen The midpoint of the slit is M A straight line through M perpendicular\nto the slit plane meets the screen at C" + }, + { + "Chapter": "9", + "sentence_range": "1374-1377", + "Text": "The diffracted light goes on to meet\na screen The midpoint of the slit is M A straight line through M perpendicular\nto the slit plane meets the screen at C We want the\nintensity at any point P on the screen" + }, + { + "Chapter": "9", + "sentence_range": "1375-1378", + "Text": "The midpoint of the slit is M A straight line through M perpendicular\nto the slit plane meets the screen at C We want the\nintensity at any point P on the screen As before, straight\nlines joining P to the different points L,M,N, etc" + }, + { + "Chapter": "9", + "sentence_range": "1376-1379", + "Text": "A straight line through M perpendicular\nto the slit plane meets the screen at C We want the\nintensity at any point P on the screen As before, straight\nlines joining P to the different points L,M,N, etc , can be\ntreated as parallel, making an angle q with the\nnormal MC" + }, + { + "Chapter": "9", + "sentence_range": "1377-1380", + "Text": "We want the\nintensity at any point P on the screen As before, straight\nlines joining P to the different points L,M,N, etc , can be\ntreated as parallel, making an angle q with the\nnormal MC The basic idea is to divide the slit into much smaller\nparts, and add their contributions at P with the proper\nphase differences" + }, + { + "Chapter": "9", + "sentence_range": "1378-1381", + "Text": "As before, straight\nlines joining P to the different points L,M,N, etc , can be\ntreated as parallel, making an angle q with the\nnormal MC The basic idea is to divide the slit into much smaller\nparts, and add their contributions at P with the proper\nphase differences We are treating different parts of the\nwavefront at the slit as secondary sources" + }, + { + "Chapter": "9", + "sentence_range": "1379-1382", + "Text": ", can be\ntreated as parallel, making an angle q with the\nnormal MC The basic idea is to divide the slit into much smaller\nparts, and add their contributions at P with the proper\nphase differences We are treating different parts of the\nwavefront at the slit as secondary sources Because the\nincoming wavefront is parallel to the plane of the slit, these\nsources are in phase" + }, + { + "Chapter": "9", + "sentence_range": "1380-1383", + "Text": "The basic idea is to divide the slit into much smaller\nparts, and add their contributions at P with the proper\nphase differences We are treating different parts of the\nwavefront at the slit as secondary sources Because the\nincoming wavefront is parallel to the plane of the slit, these\nsources are in phase It is observed that the intensity has a central\nmaximum at q = 0 and other secondary maxima at q l\n(n+1/2) l/a, which go on becoming weaker and weaker\nwith increasing n" + }, + { + "Chapter": "9", + "sentence_range": "1381-1384", + "Text": "We are treating different parts of the\nwavefront at the slit as secondary sources Because the\nincoming wavefront is parallel to the plane of the slit, these\nsources are in phase It is observed that the intensity has a central\nmaximum at q = 0 and other secondary maxima at q l\n(n+1/2) l/a, which go on becoming weaker and weaker\nwith increasing n The minima (zero intensity) are at q l\nnl/a, n = \u00b11, \u00b12, \u00b13," + }, + { + "Chapter": "9", + "sentence_range": "1382-1385", + "Text": "Because the\nincoming wavefront is parallel to the plane of the slit, these\nsources are in phase It is observed that the intensity has a central\nmaximum at q = 0 and other secondary maxima at q l\n(n+1/2) l/a, which go on becoming weaker and weaker\nwith increasing n The minima (zero intensity) are at q l\nnl/a, n = \u00b11, \u00b12, \u00b13, The photograph and intensity pattern corresponding\nto it is shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1383-1386", + "Text": "It is observed that the intensity has a central\nmaximum at q = 0 and other secondary maxima at q l\n(n+1/2) l/a, which go on becoming weaker and weaker\nwith increasing n The minima (zero intensity) are at q l\nnl/a, n = \u00b11, \u00b12, \u00b13, The photograph and intensity pattern corresponding\nto it is shown in Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1384-1387", + "Text": "The minima (zero intensity) are at q l\nnl/a, n = \u00b11, \u00b12, \u00b13, The photograph and intensity pattern corresponding\nto it is shown in Fig 10 15" + }, + { + "Chapter": "9", + "sentence_range": "1385-1388", + "Text": "The photograph and intensity pattern corresponding\nto it is shown in Fig 10 15 There has been prolonged discussion about\ndifference between intereference and diffraction among\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1386-1389", + "Text": "10 15 There has been prolonged discussion about\ndifference between intereference and diffraction among\nFIGURE 10 14 The geometry of path\ndifferences for diffraction by a single slit" + }, + { + "Chapter": "9", + "sentence_range": "1387-1390", + "Text": "15 There has been prolonged discussion about\ndifference between intereference and diffraction among\nFIGURE 10 14 The geometry of path\ndifferences for diffraction by a single slit FIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1388-1391", + "Text": "There has been prolonged discussion about\ndifference between intereference and diffraction among\nFIGURE 10 14 The geometry of path\ndifferences for diffraction by a single slit FIGURE 10 15 Intensity\ndistribution and photograph of\nfringes due to diffraction\nat single slit" + }, + { + "Chapter": "9", + "sentence_range": "1389-1392", + "Text": "14 The geometry of path\ndifferences for diffraction by a single slit FIGURE 10 15 Intensity\ndistribution and photograph of\nfringes due to diffraction\nat single slit Rationalised 2023-24\nPhysics\n268\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1390-1393", + "Text": "FIGURE 10 15 Intensity\ndistribution and photograph of\nfringes due to diffraction\nat single slit Rationalised 2023-24\nPhysics\n268\nFIGURE 10 16\nHolding two blades to\nform a single slit" + }, + { + "Chapter": "9", + "sentence_range": "1391-1394", + "Text": "15 Intensity\ndistribution and photograph of\nfringes due to diffraction\nat single slit Rationalised 2023-24\nPhysics\n268\nFIGURE 10 16\nHolding two blades to\nform a single slit A\nbulb filament viewed\nthrough this shows\nclear diffraction\nbands" + }, + { + "Chapter": "9", + "sentence_range": "1392-1395", + "Text": "Rationalised 2023-24\nPhysics\n268\nFIGURE 10 16\nHolding two blades to\nform a single slit A\nbulb filament viewed\nthrough this shows\nclear diffraction\nbands scientists since the discovery of these phenomena" + }, + { + "Chapter": "9", + "sentence_range": "1393-1396", + "Text": "16\nHolding two blades to\nform a single slit A\nbulb filament viewed\nthrough this shows\nclear diffraction\nbands scientists since the discovery of these phenomena In this context, it is\ninteresting to note what Richard Feynman* has said in his famous\nFeynman Lectures on Physics:\nNo one has ever been able to define the difference between\ninterference and diffraction satisfactorily" + }, + { + "Chapter": "9", + "sentence_range": "1394-1397", + "Text": "A\nbulb filament viewed\nthrough this shows\nclear diffraction\nbands scientists since the discovery of these phenomena In this context, it is\ninteresting to note what Richard Feynman* has said in his famous\nFeynman Lectures on Physics:\nNo one has ever been able to define the difference between\ninterference and diffraction satisfactorily It is just a question\nof usage, and there is no specific, important physical difference\nbetween them" + }, + { + "Chapter": "9", + "sentence_range": "1395-1398", + "Text": "scientists since the discovery of these phenomena In this context, it is\ninteresting to note what Richard Feynman* has said in his famous\nFeynman Lectures on Physics:\nNo one has ever been able to define the difference between\ninterference and diffraction satisfactorily It is just a question\nof usage, and there is no specific, important physical difference\nbetween them The best we can do is, roughly speaking, is to\nsay that when there are only a few sources, say two interfering\nsources, then the result is usually called interference, but if there\nis a large number of them, it seems that the word diffraction is\nmore often used" + }, + { + "Chapter": "9", + "sentence_range": "1396-1399", + "Text": "In this context, it is\ninteresting to note what Richard Feynman* has said in his famous\nFeynman Lectures on Physics:\nNo one has ever been able to define the difference between\ninterference and diffraction satisfactorily It is just a question\nof usage, and there is no specific, important physical difference\nbetween them The best we can do is, roughly speaking, is to\nsay that when there are only a few sources, say two interfering\nsources, then the result is usually called interference, but if there\nis a large number of them, it seems that the word diffraction is\nmore often used In the double-slit experiment, we must note that the pattern on the\nscreen is actually a superposition of single-slit diffraction from each slit\nor hole, and the double-slit interference pattern" + }, + { + "Chapter": "9", + "sentence_range": "1397-1400", + "Text": "It is just a question\nof usage, and there is no specific, important physical difference\nbetween them The best we can do is, roughly speaking, is to\nsay that when there are only a few sources, say two interfering\nsources, then the result is usually called interference, but if there\nis a large number of them, it seems that the word diffraction is\nmore often used In the double-slit experiment, we must note that the pattern on the\nscreen is actually a superposition of single-slit diffraction from each slit\nor hole, and the double-slit interference pattern 10" + }, + { + "Chapter": "9", + "sentence_range": "1398-1401", + "Text": "The best we can do is, roughly speaking, is to\nsay that when there are only a few sources, say two interfering\nsources, then the result is usually called interference, but if there\nis a large number of them, it seems that the word diffraction is\nmore often used In the double-slit experiment, we must note that the pattern on the\nscreen is actually a superposition of single-slit diffraction from each slit\nor hole, and the double-slit interference pattern 10 6" + }, + { + "Chapter": "9", + "sentence_range": "1399-1402", + "Text": "In the double-slit experiment, we must note that the pattern on the\nscreen is actually a superposition of single-slit diffraction from each slit\nor hole, and the double-slit interference pattern 10 6 2 Seeing the single slit diffraction pattern\nIt is surprisingly easy to see the single-slit diffraction pattern for oneself" + }, + { + "Chapter": "9", + "sentence_range": "1400-1403", + "Text": "10 6 2 Seeing the single slit diffraction pattern\nIt is surprisingly easy to see the single-slit diffraction pattern for oneself The equipment needed can be found in most homes \u2013\u2013 two razor blades\nand one clear glass electric bulb preferably with a straight filament" + }, + { + "Chapter": "9", + "sentence_range": "1401-1404", + "Text": "6 2 Seeing the single slit diffraction pattern\nIt is surprisingly easy to see the single-slit diffraction pattern for oneself The equipment needed can be found in most homes \u2013\u2013 two razor blades\nand one clear glass electric bulb preferably with a straight filament One\nhas to hold the two blades so that the edges are parallel and have a\nnarrow slit in between" + }, + { + "Chapter": "9", + "sentence_range": "1402-1405", + "Text": "2 Seeing the single slit diffraction pattern\nIt is surprisingly easy to see the single-slit diffraction pattern for oneself The equipment needed can be found in most homes \u2013\u2013 two razor blades\nand one clear glass electric bulb preferably with a straight filament One\nhas to hold the two blades so that the edges are parallel and have a\nnarrow slit in between This is easily done with the thumb and forefingers\n(Fig" + }, + { + "Chapter": "9", + "sentence_range": "1403-1406", + "Text": "The equipment needed can be found in most homes \u2013\u2013 two razor blades\nand one clear glass electric bulb preferably with a straight filament One\nhas to hold the two blades so that the edges are parallel and have a\nnarrow slit in between This is easily done with the thumb and forefingers\n(Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1404-1407", + "Text": "One\nhas to hold the two blades so that the edges are parallel and have a\nnarrow slit in between This is easily done with the thumb and forefingers\n(Fig 10 16)" + }, + { + "Chapter": "9", + "sentence_range": "1405-1408", + "Text": "This is easily done with the thumb and forefingers\n(Fig 10 16) Keep the slit parallel to the filament, right in front of the eye" + }, + { + "Chapter": "9", + "sentence_range": "1406-1409", + "Text": "10 16) Keep the slit parallel to the filament, right in front of the eye Use\nspectacles if you normally do" + }, + { + "Chapter": "9", + "sentence_range": "1407-1410", + "Text": "16) Keep the slit parallel to the filament, right in front of the eye Use\nspectacles if you normally do With slight adjustment of the width of\nthe slit and the parallelism of the edges, the pattern should be seen\nwith its bright and dark bands" + }, + { + "Chapter": "9", + "sentence_range": "1408-1411", + "Text": "Keep the slit parallel to the filament, right in front of the eye Use\nspectacles if you normally do With slight adjustment of the width of\nthe slit and the parallelism of the edges, the pattern should be seen\nwith its bright and dark bands Since the position of all the bands\n(except the central one) depends on wavelength, they will show some\ncolours" + }, + { + "Chapter": "9", + "sentence_range": "1409-1412", + "Text": "Use\nspectacles if you normally do With slight adjustment of the width of\nthe slit and the parallelism of the edges, the pattern should be seen\nwith its bright and dark bands Since the position of all the bands\n(except the central one) depends on wavelength, they will show some\ncolours Using a filter for red or blue will make the fringes clearer" + }, + { + "Chapter": "9", + "sentence_range": "1410-1413", + "Text": "With slight adjustment of the width of\nthe slit and the parallelism of the edges, the pattern should be seen\nwith its bright and dark bands Since the position of all the bands\n(except the central one) depends on wavelength, they will show some\ncolours Using a filter for red or blue will make the fringes clearer With both filters available, the wider fringes for red compared to blue\ncan be seen" + }, + { + "Chapter": "9", + "sentence_range": "1411-1414", + "Text": "Since the position of all the bands\n(except the central one) depends on wavelength, they will show some\ncolours Using a filter for red or blue will make the fringes clearer With both filters available, the wider fringes for red compared to blue\ncan be seen In this experiment, the filament plays the role of the first slit S in\nFig" + }, + { + "Chapter": "9", + "sentence_range": "1412-1415", + "Text": "Using a filter for red or blue will make the fringes clearer With both filters available, the wider fringes for red compared to blue\ncan be seen In this experiment, the filament plays the role of the first slit S in\nFig 10" + }, + { + "Chapter": "9", + "sentence_range": "1413-1416", + "Text": "With both filters available, the wider fringes for red compared to blue\ncan be seen In this experiment, the filament plays the role of the first slit S in\nFig 10 15" + }, + { + "Chapter": "9", + "sentence_range": "1414-1417", + "Text": "In this experiment, the filament plays the role of the first slit S in\nFig 10 15 The lens of the eye focuses the pattern on the screen (the\nretina of the eye)" + }, + { + "Chapter": "9", + "sentence_range": "1415-1418", + "Text": "10 15 The lens of the eye focuses the pattern on the screen (the\nretina of the eye) With some effort, one can cut a double slit in an aluminium foil with\na blade" + }, + { + "Chapter": "9", + "sentence_range": "1416-1419", + "Text": "15 The lens of the eye focuses the pattern on the screen (the\nretina of the eye) With some effort, one can cut a double slit in an aluminium foil with\na blade The bulb filament can be viewed as before to repeat Young\u2019s\nexperiment" + }, + { + "Chapter": "9", + "sentence_range": "1417-1420", + "Text": "The lens of the eye focuses the pattern on the screen (the\nretina of the eye) With some effort, one can cut a double slit in an aluminium foil with\na blade The bulb filament can be viewed as before to repeat Young\u2019s\nexperiment In daytime, there is another suitable bright source subtending\na small angle at the eye" + }, + { + "Chapter": "9", + "sentence_range": "1418-1421", + "Text": "With some effort, one can cut a double slit in an aluminium foil with\na blade The bulb filament can be viewed as before to repeat Young\u2019s\nexperiment In daytime, there is another suitable bright source subtending\na small angle at the eye This is the reflection of the Sun in any shiny\nconvex surface (e" + }, + { + "Chapter": "9", + "sentence_range": "1419-1422", + "Text": "The bulb filament can be viewed as before to repeat Young\u2019s\nexperiment In daytime, there is another suitable bright source subtending\na small angle at the eye This is the reflection of the Sun in any shiny\nconvex surface (e g" + }, + { + "Chapter": "9", + "sentence_range": "1420-1423", + "Text": "In daytime, there is another suitable bright source subtending\na small angle at the eye This is the reflection of the Sun in any shiny\nconvex surface (e g , a cycle bell)" + }, + { + "Chapter": "9", + "sentence_range": "1421-1424", + "Text": "This is the reflection of the Sun in any shiny\nconvex surface (e g , a cycle bell) Do not try direct sunlight \u2013 it can damage\nthe eye and will not give fringes anyway as the Sun subtends an angle\nof (1/2)\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "1422-1425", + "Text": "g , a cycle bell) Do not try direct sunlight \u2013 it can damage\nthe eye and will not give fringes anyway as the Sun subtends an angle\nof (1/2)\u00b0 In interference and diffraction, light energy is redistributed" + }, + { + "Chapter": "9", + "sentence_range": "1423-1426", + "Text": ", a cycle bell) Do not try direct sunlight \u2013 it can damage\nthe eye and will not give fringes anyway as the Sun subtends an angle\nof (1/2)\u00b0 In interference and diffraction, light energy is redistributed If it\nreduces in one region, producing a dark fringe, it increases in another\nregion, producing a bright fringe" + }, + { + "Chapter": "9", + "sentence_range": "1424-1427", + "Text": "Do not try direct sunlight \u2013 it can damage\nthe eye and will not give fringes anyway as the Sun subtends an angle\nof (1/2)\u00b0 In interference and diffraction, light energy is redistributed If it\nreduces in one region, producing a dark fringe, it increases in another\nregion, producing a bright fringe There is no gain or loss of energy,\nwhich is consistent with the principle of conservation of energy" + }, + { + "Chapter": "9", + "sentence_range": "1425-1428", + "Text": "In interference and diffraction, light energy is redistributed If it\nreduces in one region, producing a dark fringe, it increases in another\nregion, producing a bright fringe There is no gain or loss of energy,\nwhich is consistent with the principle of conservation of energy *\nRichand Feynman was one of the recipients of the 1965 Nobel Prize in Physics\nfor his fundamental work in quantum electrodynamics" + }, + { + "Chapter": "9", + "sentence_range": "1426-1429", + "Text": "If it\nreduces in one region, producing a dark fringe, it increases in another\nregion, producing a bright fringe There is no gain or loss of energy,\nwhich is consistent with the principle of conservation of energy *\nRichand Feynman was one of the recipients of the 1965 Nobel Prize in Physics\nfor his fundamental work in quantum electrodynamics Rationalised 2023-24\n269\nWave Optics\n10" + }, + { + "Chapter": "9", + "sentence_range": "1427-1430", + "Text": "There is no gain or loss of energy,\nwhich is consistent with the principle of conservation of energy *\nRichand Feynman was one of the recipients of the 1965 Nobel Prize in Physics\nfor his fundamental work in quantum electrodynamics Rationalised 2023-24\n269\nWave Optics\n10 7 POLARISATION\nConsider holding a long string that is held horizontally, the other end of\nwhich is assumed to be fixed" + }, + { + "Chapter": "9", + "sentence_range": "1428-1431", + "Text": "*\nRichand Feynman was one of the recipients of the 1965 Nobel Prize in Physics\nfor his fundamental work in quantum electrodynamics Rationalised 2023-24\n269\nWave Optics\n10 7 POLARISATION\nConsider holding a long string that is held horizontally, the other end of\nwhich is assumed to be fixed If we move the end of the string up and\ndown in a periodic manner, we will generate a wave propagating in the\n+x direction (Fig" + }, + { + "Chapter": "9", + "sentence_range": "1429-1432", + "Text": "Rationalised 2023-24\n269\nWave Optics\n10 7 POLARISATION\nConsider holding a long string that is held horizontally, the other end of\nwhich is assumed to be fixed If we move the end of the string up and\ndown in a periodic manner, we will generate a wave propagating in the\n+x direction (Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1430-1433", + "Text": "7 POLARISATION\nConsider holding a long string that is held horizontally, the other end of\nwhich is assumed to be fixed If we move the end of the string up and\ndown in a periodic manner, we will generate a wave propagating in the\n+x direction (Fig 10 17)" + }, + { + "Chapter": "9", + "sentence_range": "1431-1434", + "Text": "If we move the end of the string up and\ndown in a periodic manner, we will generate a wave propagating in the\n+x direction (Fig 10 17) Such a wave could be described by the following\nequation\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1432-1435", + "Text": "10 17) Such a wave could be described by the following\nequation\nFIGURE 10 17 (a) The curves represent the displacement of a string at\nt = 0 and at t = Dt, respectively when a sinusoidal wave is propagating\nin the +x-direction" + }, + { + "Chapter": "9", + "sentence_range": "1433-1436", + "Text": "17) Such a wave could be described by the following\nequation\nFIGURE 10 17 (a) The curves represent the displacement of a string at\nt = 0 and at t = Dt, respectively when a sinusoidal wave is propagating\nin the +x-direction (b) The curve represents the time variation\nof the displacement at x = 0 when a sinusoidal wave is propagating\nin the +x-direction" + }, + { + "Chapter": "9", + "sentence_range": "1434-1437", + "Text": "Such a wave could be described by the following\nequation\nFIGURE 10 17 (a) The curves represent the displacement of a string at\nt = 0 and at t = Dt, respectively when a sinusoidal wave is propagating\nin the +x-direction (b) The curve represents the time variation\nof the displacement at x = 0 when a sinusoidal wave is propagating\nin the +x-direction At x = Dx, the time variation of the\ndisplacement will be slightly displaced to the right" + }, + { + "Chapter": "9", + "sentence_range": "1435-1438", + "Text": "17 (a) The curves represent the displacement of a string at\nt = 0 and at t = Dt, respectively when a sinusoidal wave is propagating\nin the +x-direction (b) The curve represents the time variation\nof the displacement at x = 0 when a sinusoidal wave is propagating\nin the +x-direction At x = Dx, the time variation of the\ndisplacement will be slightly displaced to the right y (x,t) = a sin (kx \u2013 wt)\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1436-1439", + "Text": "(b) The curve represents the time variation\nof the displacement at x = 0 when a sinusoidal wave is propagating\nin the +x-direction At x = Dx, the time variation of the\ndisplacement will be slightly displaced to the right y (x,t) = a sin (kx \u2013 wt)\n(10 15)\nwhere a and w (= 2pn) represent the amplitude and the angular frequency\nof the wave, respectively; further,\n2\nk\n\u03bb\n\u03c0\n=\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1437-1440", + "Text": "At x = Dx, the time variation of the\ndisplacement will be slightly displaced to the right y (x,t) = a sin (kx \u2013 wt)\n(10 15)\nwhere a and w (= 2pn) represent the amplitude and the angular frequency\nof the wave, respectively; further,\n2\nk\n\u03bb\n\u03c0\n=\n(10 16)\nrepresents the wavelength associated with the wave" + }, + { + "Chapter": "9", + "sentence_range": "1438-1441", + "Text": "y (x,t) = a sin (kx \u2013 wt)\n(10 15)\nwhere a and w (= 2pn) represent the amplitude and the angular frequency\nof the wave, respectively; further,\n2\nk\n\u03bb\n\u03c0\n=\n(10 16)\nrepresents the wavelength associated with the wave We had discussed\npropagation of such waves in Chapter 14 of Class XI textbook" + }, + { + "Chapter": "9", + "sentence_range": "1439-1442", + "Text": "15)\nwhere a and w (= 2pn) represent the amplitude and the angular frequency\nof the wave, respectively; further,\n2\nk\n\u03bb\n\u03c0\n=\n(10 16)\nrepresents the wavelength associated with the wave We had discussed\npropagation of such waves in Chapter 14 of Class XI textbook Since the\ndisplacement (which is along the y direction) is at right angles to the\ndirection of propagation of the wave, we have what is known as a\ntransverse wave" + }, + { + "Chapter": "9", + "sentence_range": "1440-1443", + "Text": "16)\nrepresents the wavelength associated with the wave We had discussed\npropagation of such waves in Chapter 14 of Class XI textbook Since the\ndisplacement (which is along the y direction) is at right angles to the\ndirection of propagation of the wave, we have what is known as a\ntransverse wave Also, since the displacement is in the y direction, it is\noften referred to as a y-polarised wave" + }, + { + "Chapter": "9", + "sentence_range": "1441-1444", + "Text": "We had discussed\npropagation of such waves in Chapter 14 of Class XI textbook Since the\ndisplacement (which is along the y direction) is at right angles to the\ndirection of propagation of the wave, we have what is known as a\ntransverse wave Also, since the displacement is in the y direction, it is\noften referred to as a y-polarised wave Since each point on the string\nmoves on a straight line, the wave is also referred to as a linearly polarised\nRationalised 2023-24\nPhysics\n270\nwave" + }, + { + "Chapter": "9", + "sentence_range": "1442-1445", + "Text": "Since the\ndisplacement (which is along the y direction) is at right angles to the\ndirection of propagation of the wave, we have what is known as a\ntransverse wave Also, since the displacement is in the y direction, it is\noften referred to as a y-polarised wave Since each point on the string\nmoves on a straight line, the wave is also referred to as a linearly polarised\nRationalised 2023-24\nPhysics\n270\nwave Further, the string always remains confined to the x-y plane and\ntherefore it is also referred to as a plane polarised wave" + }, + { + "Chapter": "9", + "sentence_range": "1443-1446", + "Text": "Also, since the displacement is in the y direction, it is\noften referred to as a y-polarised wave Since each point on the string\nmoves on a straight line, the wave is also referred to as a linearly polarised\nRationalised 2023-24\nPhysics\n270\nwave Further, the string always remains confined to the x-y plane and\ntherefore it is also referred to as a plane polarised wave In a similar manner we can consider the vibration of the string in the\nx-z plane generating a z-polarised wave whose displacement will be given\nby\nz (x,t) = a sin (kx \u2013 wt)\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1444-1447", + "Text": "Since each point on the string\nmoves on a straight line, the wave is also referred to as a linearly polarised\nRationalised 2023-24\nPhysics\n270\nwave Further, the string always remains confined to the x-y plane and\ntherefore it is also referred to as a plane polarised wave In a similar manner we can consider the vibration of the string in the\nx-z plane generating a z-polarised wave whose displacement will be given\nby\nz (x,t) = a sin (kx \u2013 wt)\n(10 17)\nIt should be mentioned that the linearly polarised waves [described\nby Eqs" + }, + { + "Chapter": "9", + "sentence_range": "1445-1448", + "Text": "Further, the string always remains confined to the x-y plane and\ntherefore it is also referred to as a plane polarised wave In a similar manner we can consider the vibration of the string in the\nx-z plane generating a z-polarised wave whose displacement will be given\nby\nz (x,t) = a sin (kx \u2013 wt)\n(10 17)\nIt should be mentioned that the linearly polarised waves [described\nby Eqs (10" + }, + { + "Chapter": "9", + "sentence_range": "1446-1449", + "Text": "In a similar manner we can consider the vibration of the string in the\nx-z plane generating a z-polarised wave whose displacement will be given\nby\nz (x,t) = a sin (kx \u2013 wt)\n(10 17)\nIt should be mentioned that the linearly polarised waves [described\nby Eqs (10 15) and (10" + }, + { + "Chapter": "9", + "sentence_range": "1447-1450", + "Text": "17)\nIt should be mentioned that the linearly polarised waves [described\nby Eqs (10 15) and (10 17)] are all transverse waves; i" + }, + { + "Chapter": "9", + "sentence_range": "1448-1451", + "Text": "(10 15) and (10 17)] are all transverse waves; i e" + }, + { + "Chapter": "9", + "sentence_range": "1449-1452", + "Text": "15) and (10 17)] are all transverse waves; i e , the\ndisplacement of each point of the string is always at right angles to the\ndirection of propagation of the wave" + }, + { + "Chapter": "9", + "sentence_range": "1450-1453", + "Text": "17)] are all transverse waves; i e , the\ndisplacement of each point of the string is always at right angles to the\ndirection of propagation of the wave Finally, if the plane of vibration of\nthe string is changed randomly in very short intervals of time, then we\nhave what is known as an unpolarised wave" + }, + { + "Chapter": "9", + "sentence_range": "1451-1454", + "Text": "e , the\ndisplacement of each point of the string is always at right angles to the\ndirection of propagation of the wave Finally, if the plane of vibration of\nthe string is changed randomly in very short intervals of time, then we\nhave what is known as an unpolarised wave Thus, for an unpolarised\nwave the displacement will be randomly changing with time though it\nwill always be perpendicular to the direction of propagation" + }, + { + "Chapter": "9", + "sentence_range": "1452-1455", + "Text": ", the\ndisplacement of each point of the string is always at right angles to the\ndirection of propagation of the wave Finally, if the plane of vibration of\nthe string is changed randomly in very short intervals of time, then we\nhave what is known as an unpolarised wave Thus, for an unpolarised\nwave the displacement will be randomly changing with time though it\nwill always be perpendicular to the direction of propagation Light waves are transverse in nature; i" + }, + { + "Chapter": "9", + "sentence_range": "1453-1456", + "Text": "Finally, if the plane of vibration of\nthe string is changed randomly in very short intervals of time, then we\nhave what is known as an unpolarised wave Thus, for an unpolarised\nwave the displacement will be randomly changing with time though it\nwill always be perpendicular to the direction of propagation Light waves are transverse in nature; i e" + }, + { + "Chapter": "9", + "sentence_range": "1454-1457", + "Text": "Thus, for an unpolarised\nwave the displacement will be randomly changing with time though it\nwill always be perpendicular to the direction of propagation Light waves are transverse in nature; i e , the electric field associated\nwith a propagating light wave is always at right angles to the direction of\npropagation of the wave" + }, + { + "Chapter": "9", + "sentence_range": "1455-1458", + "Text": "Light waves are transverse in nature; i e , the electric field associated\nwith a propagating light wave is always at right angles to the direction of\npropagation of the wave This can be easily demonstrated using a simple\npolaroid" + }, + { + "Chapter": "9", + "sentence_range": "1456-1459", + "Text": "e , the electric field associated\nwith a propagating light wave is always at right angles to the direction of\npropagation of the wave This can be easily demonstrated using a simple\npolaroid You must have seen thin plastic like sheets, which are called\npolaroids" + }, + { + "Chapter": "9", + "sentence_range": "1457-1460", + "Text": ", the electric field associated\nwith a propagating light wave is always at right angles to the direction of\npropagation of the wave This can be easily demonstrated using a simple\npolaroid You must have seen thin plastic like sheets, which are called\npolaroids A polaroid consists of long chain molecules aligned in a\nparticular direction" + }, + { + "Chapter": "9", + "sentence_range": "1458-1461", + "Text": "This can be easily demonstrated using a simple\npolaroid You must have seen thin plastic like sheets, which are called\npolaroids A polaroid consists of long chain molecules aligned in a\nparticular direction The electric vectors (associated with the propagating\nlight wave) along the direction of the aligned molecules get absorbed" + }, + { + "Chapter": "9", + "sentence_range": "1459-1462", + "Text": "You must have seen thin plastic like sheets, which are called\npolaroids A polaroid consists of long chain molecules aligned in a\nparticular direction The electric vectors (associated with the propagating\nlight wave) along the direction of the aligned molecules get absorbed Thus, if an unpolarised light wave is incident on such a polaroid then\nthe light wave will get linearly polarised with the electric vector oscillating\nalong a direction perpendicular to the aligned molecules; this direction\nis known as the pass-axis of the polaroid" + }, + { + "Chapter": "9", + "sentence_range": "1460-1463", + "Text": "A polaroid consists of long chain molecules aligned in a\nparticular direction The electric vectors (associated with the propagating\nlight wave) along the direction of the aligned molecules get absorbed Thus, if an unpolarised light wave is incident on such a polaroid then\nthe light wave will get linearly polarised with the electric vector oscillating\nalong a direction perpendicular to the aligned molecules; this direction\nis known as the pass-axis of the polaroid Thus, if the light from an ordinary source (like a sodium lamp) passes\nthrough a polaroid sheet P1, it is observed that its intensity is reduced by\nhalf" + }, + { + "Chapter": "9", + "sentence_range": "1461-1464", + "Text": "The electric vectors (associated with the propagating\nlight wave) along the direction of the aligned molecules get absorbed Thus, if an unpolarised light wave is incident on such a polaroid then\nthe light wave will get linearly polarised with the electric vector oscillating\nalong a direction perpendicular to the aligned molecules; this direction\nis known as the pass-axis of the polaroid Thus, if the light from an ordinary source (like a sodium lamp) passes\nthrough a polaroid sheet P1, it is observed that its intensity is reduced by\nhalf Rotating P1 has no effect on the transmitted beam and transmitted\nintensity remains constant" + }, + { + "Chapter": "9", + "sentence_range": "1462-1465", + "Text": "Thus, if an unpolarised light wave is incident on such a polaroid then\nthe light wave will get linearly polarised with the electric vector oscillating\nalong a direction perpendicular to the aligned molecules; this direction\nis known as the pass-axis of the polaroid Thus, if the light from an ordinary source (like a sodium lamp) passes\nthrough a polaroid sheet P1, it is observed that its intensity is reduced by\nhalf Rotating P1 has no effect on the transmitted beam and transmitted\nintensity remains constant Now, let an identical piece of polaroid P2 be\nplaced before P1" + }, + { + "Chapter": "9", + "sentence_range": "1463-1466", + "Text": "Thus, if the light from an ordinary source (like a sodium lamp) passes\nthrough a polaroid sheet P1, it is observed that its intensity is reduced by\nhalf Rotating P1 has no effect on the transmitted beam and transmitted\nintensity remains constant Now, let an identical piece of polaroid P2 be\nplaced before P1 As expected, the light from the lamp is reduced in\nintensity on passing through P2 alone" + }, + { + "Chapter": "9", + "sentence_range": "1464-1467", + "Text": "Rotating P1 has no effect on the transmitted beam and transmitted\nintensity remains constant Now, let an identical piece of polaroid P2 be\nplaced before P1 As expected, the light from the lamp is reduced in\nintensity on passing through P2 alone But now rotating P1 has a dramatic\neffect on the light coming from P2" + }, + { + "Chapter": "9", + "sentence_range": "1465-1468", + "Text": "Now, let an identical piece of polaroid P2 be\nplaced before P1 As expected, the light from the lamp is reduced in\nintensity on passing through P2 alone But now rotating P1 has a dramatic\neffect on the light coming from P2 In one position, the intensity transmitted\nby P2 followed by P1 is nearly zero" + }, + { + "Chapter": "9", + "sentence_range": "1466-1469", + "Text": "As expected, the light from the lamp is reduced in\nintensity on passing through P2 alone But now rotating P1 has a dramatic\neffect on the light coming from P2 In one position, the intensity transmitted\nby P2 followed by P1 is nearly zero When turned by 90\u00b0 from this position,\nP1 transmits nearly the full intensity emerging from P2 (Fig" + }, + { + "Chapter": "9", + "sentence_range": "1467-1470", + "Text": "But now rotating P1 has a dramatic\neffect on the light coming from P2 In one position, the intensity transmitted\nby P2 followed by P1 is nearly zero When turned by 90\u00b0 from this position,\nP1 transmits nearly the full intensity emerging from P2 (Fig 10" + }, + { + "Chapter": "9", + "sentence_range": "1468-1471", + "Text": "In one position, the intensity transmitted\nby P2 followed by P1 is nearly zero When turned by 90\u00b0 from this position,\nP1 transmits nearly the full intensity emerging from P2 (Fig 10 18)" + }, + { + "Chapter": "9", + "sentence_range": "1469-1472", + "Text": "When turned by 90\u00b0 from this position,\nP1 transmits nearly the full intensity emerging from P2 (Fig 10 18) The experiment at figure 10" + }, + { + "Chapter": "9", + "sentence_range": "1470-1473", + "Text": "10 18) The experiment at figure 10 18 can be easily understood by assuming\nthat light passing through the polaroid P2 gets polarised along the pass-\naxis of P2" + }, + { + "Chapter": "9", + "sentence_range": "1471-1474", + "Text": "18) The experiment at figure 10 18 can be easily understood by assuming\nthat light passing through the polaroid P2 gets polarised along the pass-\naxis of P2 If the pass-axis of P2 makes an angle q with the pass-axis of\nP1, then when the polarised beam passes through the polaroid P2, the\ncomponent E cos q (along the pass-axis of P2) will pass through P2" + }, + { + "Chapter": "9", + "sentence_range": "1472-1475", + "Text": "The experiment at figure 10 18 can be easily understood by assuming\nthat light passing through the polaroid P2 gets polarised along the pass-\naxis of P2 If the pass-axis of P2 makes an angle q with the pass-axis of\nP1, then when the polarised beam passes through the polaroid P2, the\ncomponent E cos q (along the pass-axis of P2) will pass through P2 Thus, as we rotate the polaroid P1 (or P2), the intensity will vary as:\nI = I0 cos2q\n(10" + }, + { + "Chapter": "9", + "sentence_range": "1473-1476", + "Text": "18 can be easily understood by assuming\nthat light passing through the polaroid P2 gets polarised along the pass-\naxis of P2 If the pass-axis of P2 makes an angle q with the pass-axis of\nP1, then when the polarised beam passes through the polaroid P2, the\ncomponent E cos q (along the pass-axis of P2) will pass through P2 Thus, as we rotate the polaroid P1 (or P2), the intensity will vary as:\nI = I0 cos2q\n(10 18)\nwhere I0 is the intensity of the polarized light after passing through\nP1" + }, + { + "Chapter": "9", + "sentence_range": "1474-1477", + "Text": "If the pass-axis of P2 makes an angle q with the pass-axis of\nP1, then when the polarised beam passes through the polaroid P2, the\ncomponent E cos q (along the pass-axis of P2) will pass through P2 Thus, as we rotate the polaroid P1 (or P2), the intensity will vary as:\nI = I0 cos2q\n(10 18)\nwhere I0 is the intensity of the polarized light after passing through\nP1 This is known as Malus\u2019 law" + }, + { + "Chapter": "9", + "sentence_range": "1475-1478", + "Text": "Thus, as we rotate the polaroid P1 (or P2), the intensity will vary as:\nI = I0 cos2q\n(10 18)\nwhere I0 is the intensity of the polarized light after passing through\nP1 This is known as Malus\u2019 law The above discussion shows that the\nRationalised 2023-24\n271\nWave Optics\nFIGURE 10" + }, + { + "Chapter": "9", + "sentence_range": "1476-1479", + "Text": "18)\nwhere I0 is the intensity of the polarized light after passing through\nP1 This is known as Malus\u2019 law The above discussion shows that the\nRationalised 2023-24\n271\nWave Optics\nFIGURE 10 18 (a) Passage of light through two polaroids P2 and P1" + }, + { + "Chapter": "9", + "sentence_range": "1477-1480", + "Text": "This is known as Malus\u2019 law The above discussion shows that the\nRationalised 2023-24\n271\nWave Optics\nFIGURE 10 18 (a) Passage of light through two polaroids P2 and P1 The\ntransmitted fraction falls from 1 to 0 as the angle between them varies\nfrom 0\u00b0 to 90\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "1478-1481", + "Text": "The above discussion shows that the\nRationalised 2023-24\n271\nWave Optics\nFIGURE 10 18 (a) Passage of light through two polaroids P2 and P1 The\ntransmitted fraction falls from 1 to 0 as the angle between them varies\nfrom 0\u00b0 to 90\u00b0 Notice that the light seen through a single polaroid\nP1 does not vary with angle" + }, + { + "Chapter": "9", + "sentence_range": "1479-1482", + "Text": "18 (a) Passage of light through two polaroids P2 and P1 The\ntransmitted fraction falls from 1 to 0 as the angle between them varies\nfrom 0\u00b0 to 90\u00b0 Notice that the light seen through a single polaroid\nP1 does not vary with angle (b) Behaviour of the electric vector\nwhen light passes through two polaroids" + }, + { + "Chapter": "9", + "sentence_range": "1480-1483", + "Text": "The\ntransmitted fraction falls from 1 to 0 as the angle between them varies\nfrom 0\u00b0 to 90\u00b0 Notice that the light seen through a single polaroid\nP1 does not vary with angle (b) Behaviour of the electric vector\nwhen light passes through two polaroids The transmitted\npolarisation is the component parallel to the polaroid axis" + }, + { + "Chapter": "9", + "sentence_range": "1481-1484", + "Text": "Notice that the light seen through a single polaroid\nP1 does not vary with angle (b) Behaviour of the electric vector\nwhen light passes through two polaroids The transmitted\npolarisation is the component parallel to the polaroid axis The double arrows show the oscillations of the electric vector" + }, + { + "Chapter": "9", + "sentence_range": "1482-1485", + "Text": "(b) Behaviour of the electric vector\nwhen light passes through two polaroids The transmitted\npolarisation is the component parallel to the polaroid axis The double arrows show the oscillations of the electric vector intensity coming out of a single polaroid is half of the incident intensity" + }, + { + "Chapter": "9", + "sentence_range": "1483-1486", + "Text": "The transmitted\npolarisation is the component parallel to the polaroid axis The double arrows show the oscillations of the electric vector intensity coming out of a single polaroid is half of the incident intensity By putting a second polaroid, the intensity can be further controlled\nfrom 50% to zero of the incident intensity by adjusting the angle between\nthe pass-axes of two polaroids" + }, + { + "Chapter": "9", + "sentence_range": "1484-1487", + "Text": "The double arrows show the oscillations of the electric vector intensity coming out of a single polaroid is half of the incident intensity By putting a second polaroid, the intensity can be further controlled\nfrom 50% to zero of the incident intensity by adjusting the angle between\nthe pass-axes of two polaroids Polaroids can be used to control the intensity, in sunglasses,\nwindowpanes, etc" + }, + { + "Chapter": "9", + "sentence_range": "1485-1488", + "Text": "intensity coming out of a single polaroid is half of the incident intensity By putting a second polaroid, the intensity can be further controlled\nfrom 50% to zero of the incident intensity by adjusting the angle between\nthe pass-axes of two polaroids Polaroids can be used to control the intensity, in sunglasses,\nwindowpanes, etc Polaroids are also used in photographic cameras and\n3D movie cameras" + }, + { + "Chapter": "9", + "sentence_range": "1486-1489", + "Text": "By putting a second polaroid, the intensity can be further controlled\nfrom 50% to zero of the incident intensity by adjusting the angle between\nthe pass-axes of two polaroids Polaroids can be used to control the intensity, in sunglasses,\nwindowpanes, etc Polaroids are also used in photographic cameras and\n3D movie cameras EXAMPLE 10" + }, + { + "Chapter": "9", + "sentence_range": "1487-1490", + "Text": "Polaroids can be used to control the intensity, in sunglasses,\nwindowpanes, etc Polaroids are also used in photographic cameras and\n3D movie cameras EXAMPLE 10 2\nExample 10" + }, + { + "Chapter": "9", + "sentence_range": "1488-1491", + "Text": "Polaroids are also used in photographic cameras and\n3D movie cameras EXAMPLE 10 2\nExample 10 2 Discuss the intensity of transmitted light when a\npolaroid sheet is rotated between two crossed polaroids" + }, + { + "Chapter": "9", + "sentence_range": "1489-1492", + "Text": "EXAMPLE 10 2\nExample 10 2 Discuss the intensity of transmitted light when a\npolaroid sheet is rotated between two crossed polaroids Solution Let I0 be the intensity of polarised light after passing through\nthe first polariser P1" + }, + { + "Chapter": "9", + "sentence_range": "1490-1493", + "Text": "2\nExample 10 2 Discuss the intensity of transmitted light when a\npolaroid sheet is rotated between two crossed polaroids Solution Let I0 be the intensity of polarised light after passing through\nthe first polariser P1 Then the intensity of light after passing through\nsecond polariser P2 will be\n2\n0cos\nI\nI\n\u03b8\n=\n,\nwhere q is the angle between pass axes of P1 and P2" + }, + { + "Chapter": "9", + "sentence_range": "1491-1494", + "Text": "2 Discuss the intensity of transmitted light when a\npolaroid sheet is rotated between two crossed polaroids Solution Let I0 be the intensity of polarised light after passing through\nthe first polariser P1 Then the intensity of light after passing through\nsecond polariser P2 will be\n2\n0cos\nI\nI\n\u03b8\n=\n,\nwhere q is the angle between pass axes of P1 and P2 Since P1 and P3\nare crossed the angle between the pass axes of P2 and P3 will be\n(p/2\u2013q)" + }, + { + "Chapter": "9", + "sentence_range": "1492-1495", + "Text": "Solution Let I0 be the intensity of polarised light after passing through\nthe first polariser P1 Then the intensity of light after passing through\nsecond polariser P2 will be\n2\n0cos\nI\nI\n\u03b8\n=\n,\nwhere q is the angle between pass axes of P1 and P2 Since P1 and P3\nare crossed the angle between the pass axes of P2 and P3 will be\n(p/2\u2013q) Hence the intensity of light emerging from P3 will be\nI\n=I\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\n0\n2\n2\n2\ncos\n\u03b8cos\n\u03b8\n\u03c0 \u2013\n = I0 cos2q sin2q =(I0/4) sin22q\nTherefore, the transmitted intensity will be maximum when q = p/4" + }, + { + "Chapter": "9", + "sentence_range": "1493-1496", + "Text": "Then the intensity of light after passing through\nsecond polariser P2 will be\n2\n0cos\nI\nI\n\u03b8\n=\n,\nwhere q is the angle between pass axes of P1 and P2 Since P1 and P3\nare crossed the angle between the pass axes of P2 and P3 will be\n(p/2\u2013q) Hence the intensity of light emerging from P3 will be\nI\n=I\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\n0\n2\n2\n2\ncos\n\u03b8cos\n\u03b8\n\u03c0 \u2013\n = I0 cos2q sin2q =(I0/4) sin22q\nTherefore, the transmitted intensity will be maximum when q = p/4 Rationalised 2023-24\nPhysics\n272\nPOINTS TO PONDER\n1" + }, + { + "Chapter": "9", + "sentence_range": "1494-1497", + "Text": "Since P1 and P3\nare crossed the angle between the pass axes of P2 and P3 will be\n(p/2\u2013q) Hence the intensity of light emerging from P3 will be\nI\n=I\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\n0\n2\n2\n2\ncos\n\u03b8cos\n\u03b8\n\u03c0 \u2013\n = I0 cos2q sin2q =(I0/4) sin22q\nTherefore, the transmitted intensity will be maximum when q = p/4 Rationalised 2023-24\nPhysics\n272\nPOINTS TO PONDER\n1 Waves from a point source spread out in all directions, while light was\nseen to travel along narrow rays" + }, + { + "Chapter": "9", + "sentence_range": "1495-1498", + "Text": "Hence the intensity of light emerging from P3 will be\nI\n=I\n\uf8ed\uf8ec\uf8eb\n\uf8f8\uf8f7\uf8f6\n0\n2\n2\n2\ncos\n\u03b8cos\n\u03b8\n\u03c0 \u2013\n = I0 cos2q sin2q =(I0/4) sin22q\nTherefore, the transmitted intensity will be maximum when q = p/4 Rationalised 2023-24\nPhysics\n272\nPOINTS TO PONDER\n1 Waves from a point source spread out in all directions, while light was\nseen to travel along narrow rays It required the insight and experiment\nof Huygens, Young and Fresnel to understand how a wave theory could\nexplain all aspects of the behaviour of light" + }, + { + "Chapter": "9", + "sentence_range": "1496-1499", + "Text": "Rationalised 2023-24\nPhysics\n272\nPOINTS TO PONDER\n1 Waves from a point source spread out in all directions, while light was\nseen to travel along narrow rays It required the insight and experiment\nof Huygens, Young and Fresnel to understand how a wave theory could\nexplain all aspects of the behaviour of light 2" + }, + { + "Chapter": "9", + "sentence_range": "1497-1500", + "Text": "Waves from a point source spread out in all directions, while light was\nseen to travel along narrow rays It required the insight and experiment\nof Huygens, Young and Fresnel to understand how a wave theory could\nexplain all aspects of the behaviour of light 2 The crucial new feature of waves is interference of amplitudes from different\nsources which can be both constructive and destructive, as shown in\nYoung\u2019s experiment" + }, + { + "Chapter": "9", + "sentence_range": "1498-1501", + "Text": "It required the insight and experiment\nof Huygens, Young and Fresnel to understand how a wave theory could\nexplain all aspects of the behaviour of light 2 The crucial new feature of waves is interference of amplitudes from different\nsources which can be both constructive and destructive, as shown in\nYoung\u2019s experiment 3" + }, + { + "Chapter": "9", + "sentence_range": "1499-1502", + "Text": "2 The crucial new feature of waves is interference of amplitudes from different\nsources which can be both constructive and destructive, as shown in\nYoung\u2019s experiment 3 Diffraction phenomena define the limits of ray optics" + }, + { + "Chapter": "9", + "sentence_range": "1500-1503", + "Text": "The crucial new feature of waves is interference of amplitudes from different\nsources which can be both constructive and destructive, as shown in\nYoung\u2019s experiment 3 Diffraction phenomena define the limits of ray optics The limit of the\nability of microscopes and telescopes to distinguish very close objects is\nset by the wavelength of light" + }, + { + "Chapter": "9", + "sentence_range": "1501-1504", + "Text": "3 Diffraction phenomena define the limits of ray optics The limit of the\nability of microscopes and telescopes to distinguish very close objects is\nset by the wavelength of light 4" + }, + { + "Chapter": "9", + "sentence_range": "1502-1505", + "Text": "Diffraction phenomena define the limits of ray optics The limit of the\nability of microscopes and telescopes to distinguish very close objects is\nset by the wavelength of light 4 Most interference and diffraction effects exist even for longitudinal waves\nlike sound in air" + }, + { + "Chapter": "9", + "sentence_range": "1503-1506", + "Text": "The limit of the\nability of microscopes and telescopes to distinguish very close objects is\nset by the wavelength of light 4 Most interference and diffraction effects exist even for longitudinal waves\nlike sound in air But polarisation phenomena are special to transverse\nwaves like light waves" + }, + { + "Chapter": "9", + "sentence_range": "1504-1507", + "Text": "4 Most interference and diffraction effects exist even for longitudinal waves\nlike sound in air But polarisation phenomena are special to transverse\nwaves like light waves SUMMARY\n1" + }, + { + "Chapter": "9", + "sentence_range": "1505-1508", + "Text": "Most interference and diffraction effects exist even for longitudinal waves\nlike sound in air But polarisation phenomena are special to transverse\nwaves like light waves SUMMARY\n1 Huygens\u2019 principle tells us that each point on a wavefront is a source\nof secondary waves, which add up to give the wavefront at a later time" + }, + { + "Chapter": "9", + "sentence_range": "1506-1509", + "Text": "But polarisation phenomena are special to transverse\nwaves like light waves SUMMARY\n1 Huygens\u2019 principle tells us that each point on a wavefront is a source\nof secondary waves, which add up to give the wavefront at a later time 2" + }, + { + "Chapter": "9", + "sentence_range": "1507-1510", + "Text": "SUMMARY\n1 Huygens\u2019 principle tells us that each point on a wavefront is a source\nof secondary waves, which add up to give the wavefront at a later time 2 Huygens\u2019 construction tells us that the new wavefront is the forward\nenvelope of the secondary waves" + }, + { + "Chapter": "9", + "sentence_range": "1508-1511", + "Text": "Huygens\u2019 principle tells us that each point on a wavefront is a source\nof secondary waves, which add up to give the wavefront at a later time 2 Huygens\u2019 construction tells us that the new wavefront is the forward\nenvelope of the secondary waves When the speed of light is\nindependent of direction, the secondary waves are spherical" + }, + { + "Chapter": "9", + "sentence_range": "1509-1512", + "Text": "2 Huygens\u2019 construction tells us that the new wavefront is the forward\nenvelope of the secondary waves When the speed of light is\nindependent of direction, the secondary waves are spherical The rays\nare then perpendicular to both the wavefronts and the time of travel\nis the same measured along any ray" + }, + { + "Chapter": "9", + "sentence_range": "1510-1513", + "Text": "Huygens\u2019 construction tells us that the new wavefront is the forward\nenvelope of the secondary waves When the speed of light is\nindependent of direction, the secondary waves are spherical The rays\nare then perpendicular to both the wavefronts and the time of travel\nis the same measured along any ray This principle leads to the well\nknown laws of reflection and refraction" + }, + { + "Chapter": "9", + "sentence_range": "1511-1514", + "Text": "When the speed of light is\nindependent of direction, the secondary waves are spherical The rays\nare then perpendicular to both the wavefronts and the time of travel\nis the same measured along any ray This principle leads to the well\nknown laws of reflection and refraction 3" + }, + { + "Chapter": "9", + "sentence_range": "1512-1515", + "Text": "The rays\nare then perpendicular to both the wavefronts and the time of travel\nis the same measured along any ray This principle leads to the well\nknown laws of reflection and refraction 3 The principle of superposition of waves applies whenever two or more\nsources of light illuminate the same point" + }, + { + "Chapter": "9", + "sentence_range": "1513-1516", + "Text": "This principle leads to the well\nknown laws of reflection and refraction 3 The principle of superposition of waves applies whenever two or more\nsources of light illuminate the same point When we consider the\nintensity of light due to these sources at the given point, there is an\ninterference term in addition to the sum of the individual intensities" + }, + { + "Chapter": "9", + "sentence_range": "1514-1517", + "Text": "3 The principle of superposition of waves applies whenever two or more\nsources of light illuminate the same point When we consider the\nintensity of light due to these sources at the given point, there is an\ninterference term in addition to the sum of the individual intensities But this term is important only if it has a non-zero average, which\noccurs only if the sources have the same frequency and a stable phase\ndifference" + }, + { + "Chapter": "9", + "sentence_range": "1515-1518", + "Text": "The principle of superposition of waves applies whenever two or more\nsources of light illuminate the same point When we consider the\nintensity of light due to these sources at the given point, there is an\ninterference term in addition to the sum of the individual intensities But this term is important only if it has a non-zero average, which\noccurs only if the sources have the same frequency and a stable phase\ndifference 4" + }, + { + "Chapter": "9", + "sentence_range": "1516-1519", + "Text": "When we consider the\nintensity of light due to these sources at the given point, there is an\ninterference term in addition to the sum of the individual intensities But this term is important only if it has a non-zero average, which\noccurs only if the sources have the same frequency and a stable phase\ndifference 4 Young\u2019s double slit of separation d gives equally spaced interference\nfringes" + }, + { + "Chapter": "9", + "sentence_range": "1517-1520", + "Text": "But this term is important only if it has a non-zero average, which\noccurs only if the sources have the same frequency and a stable phase\ndifference 4 Young\u2019s double slit of separation d gives equally spaced interference\nfringes 5" + }, + { + "Chapter": "9", + "sentence_range": "1518-1521", + "Text": "4 Young\u2019s double slit of separation d gives equally spaced interference\nfringes 5 A single slit of width a gives a diffraction pattern with a central\nmaximum" + }, + { + "Chapter": "9", + "sentence_range": "1519-1522", + "Text": "Young\u2019s double slit of separation d gives equally spaced interference\nfringes 5 A single slit of width a gives a diffraction pattern with a central\nmaximum The intensity falls to zero at angles of \n2\n,\n,\na\na\n\u03bb\n\u03bb\n\u00b1\n\u00b1\n etc" + }, + { + "Chapter": "9", + "sentence_range": "1520-1523", + "Text": "5 A single slit of width a gives a diffraction pattern with a central\nmaximum The intensity falls to zero at angles of \n2\n,\n,\na\na\n\u03bb\n\u03bb\n\u00b1\n\u00b1\n etc ,\nwith successively weaker secondary maxima in between" + }, + { + "Chapter": "9", + "sentence_range": "1521-1524", + "Text": "A single slit of width a gives a diffraction pattern with a central\nmaximum The intensity falls to zero at angles of \n2\n,\n,\na\na\n\u03bb\n\u03bb\n\u00b1\n\u00b1\n etc ,\nwith successively weaker secondary maxima in between 6" + }, + { + "Chapter": "9", + "sentence_range": "1522-1525", + "Text": "The intensity falls to zero at angles of \n2\n,\n,\na\na\n\u03bb\n\u03bb\n\u00b1\n\u00b1\n etc ,\nwith successively weaker secondary maxima in between 6 Natural light, e" + }, + { + "Chapter": "9", + "sentence_range": "1523-1526", + "Text": ",\nwith successively weaker secondary maxima in between 6 Natural light, e g" + }, + { + "Chapter": "9", + "sentence_range": "1524-1527", + "Text": "6 Natural light, e g , from the sun is unpolarised" + }, + { + "Chapter": "9", + "sentence_range": "1525-1528", + "Text": "Natural light, e g , from the sun is unpolarised This means the electric\nvector takes all possible directions in the transverse plane, rapidly\nand randomly, during a measurement" + }, + { + "Chapter": "9", + "sentence_range": "1526-1529", + "Text": "g , from the sun is unpolarised This means the electric\nvector takes all possible directions in the transverse plane, rapidly\nand randomly, during a measurement A polaroid transmits only one\ncomponent (parallel to a special axis)" + }, + { + "Chapter": "9", + "sentence_range": "1527-1530", + "Text": ", from the sun is unpolarised This means the electric\nvector takes all possible directions in the transverse plane, rapidly\nand randomly, during a measurement A polaroid transmits only one\ncomponent (parallel to a special axis) The resulting light is called\nlinearly polarised or plane polarised" + }, + { + "Chapter": "9", + "sentence_range": "1528-1531", + "Text": "This means the electric\nvector takes all possible directions in the transverse plane, rapidly\nand randomly, during a measurement A polaroid transmits only one\ncomponent (parallel to a special axis) The resulting light is called\nlinearly polarised or plane polarised When this kind of light is viewed\nthrough a second polaroid whose axis turns through 2p, two maxima\nand minima of intensity are seen" + }, + { + "Chapter": "9", + "sentence_range": "1529-1532", + "Text": "A polaroid transmits only one\ncomponent (parallel to a special axis) The resulting light is called\nlinearly polarised or plane polarised When this kind of light is viewed\nthrough a second polaroid whose axis turns through 2p, two maxima\nand minima of intensity are seen Rationalised 2023-24\n273\nWave Optics\nEXERCISES\n10" + }, + { + "Chapter": "9", + "sentence_range": "1530-1533", + "Text": "The resulting light is called\nlinearly polarised or plane polarised When this kind of light is viewed\nthrough a second polaroid whose axis turns through 2p, two maxima\nand minima of intensity are seen Rationalised 2023-24\n273\nWave Optics\nEXERCISES\n10 1\nMonochromatic light of wavelength 589 nm is incident from air on a\nwater surface" + }, + { + "Chapter": "9", + "sentence_range": "1531-1534", + "Text": "When this kind of light is viewed\nthrough a second polaroid whose axis turns through 2p, two maxima\nand minima of intensity are seen Rationalised 2023-24\n273\nWave Optics\nEXERCISES\n10 1\nMonochromatic light of wavelength 589 nm is incident from air on a\nwater surface What are the wavelength, frequency and speed of\n(a) reflected, and (b) refracted light" + }, + { + "Chapter": "9", + "sentence_range": "1532-1535", + "Text": "Rationalised 2023-24\n273\nWave Optics\nEXERCISES\n10 1\nMonochromatic light of wavelength 589 nm is incident from air on a\nwater surface What are the wavelength, frequency and speed of\n(a) reflected, and (b) refracted light Refractive index of water is\n1" + }, + { + "Chapter": "9", + "sentence_range": "1533-1536", + "Text": "1\nMonochromatic light of wavelength 589 nm is incident from air on a\nwater surface What are the wavelength, frequency and speed of\n(a) reflected, and (b) refracted light Refractive index of water is\n1 33" + }, + { + "Chapter": "9", + "sentence_range": "1534-1537", + "Text": "What are the wavelength, frequency and speed of\n(a) reflected, and (b) refracted light Refractive index of water is\n1 33 10" + }, + { + "Chapter": "9", + "sentence_range": "1535-1538", + "Text": "Refractive index of water is\n1 33 10 2\nWhat is the shape of the wavefront in each of the following cases:\n(a) Light diverging from a point source" + }, + { + "Chapter": "9", + "sentence_range": "1536-1539", + "Text": "33 10 2\nWhat is the shape of the wavefront in each of the following cases:\n(a) Light diverging from a point source (b) Light emerging out of a convex lens when a point source is placed\nat its focus" + }, + { + "Chapter": "9", + "sentence_range": "1537-1540", + "Text": "10 2\nWhat is the shape of the wavefront in each of the following cases:\n(a) Light diverging from a point source (b) Light emerging out of a convex lens when a point source is placed\nat its focus (c) The portion of the wavefront of light from a distant star intercepted\nby the Earth" + }, + { + "Chapter": "9", + "sentence_range": "1538-1541", + "Text": "2\nWhat is the shape of the wavefront in each of the following cases:\n(a) Light diverging from a point source (b) Light emerging out of a convex lens when a point source is placed\nat its focus (c) The portion of the wavefront of light from a distant star intercepted\nby the Earth 10" + }, + { + "Chapter": "9", + "sentence_range": "1539-1542", + "Text": "(b) Light emerging out of a convex lens when a point source is placed\nat its focus (c) The portion of the wavefront of light from a distant star intercepted\nby the Earth 10 3\n(a) The refractive index of glass is 1" + }, + { + "Chapter": "9", + "sentence_range": "1540-1543", + "Text": "(c) The portion of the wavefront of light from a distant star intercepted\nby the Earth 10 3\n(a) The refractive index of glass is 1 5" + }, + { + "Chapter": "9", + "sentence_range": "1541-1544", + "Text": "10 3\n(a) The refractive index of glass is 1 5 What is the speed of light in\nglass" + }, + { + "Chapter": "9", + "sentence_range": "1542-1545", + "Text": "3\n(a) The refractive index of glass is 1 5 What is the speed of light in\nglass (Speed of light in vacuum is 3" + }, + { + "Chapter": "9", + "sentence_range": "1543-1546", + "Text": "5 What is the speed of light in\nglass (Speed of light in vacuum is 3 0 \u00d7 108 m s\u20131)\n(b) Is the speed of light in glass independent of the colour of light" + }, + { + "Chapter": "9", + "sentence_range": "1544-1547", + "Text": "What is the speed of light in\nglass (Speed of light in vacuum is 3 0 \u00d7 108 m s\u20131)\n(b) Is the speed of light in glass independent of the colour of light If\nnot, which of the two colours red and violet travels slower in a\nglass prism" + }, + { + "Chapter": "9", + "sentence_range": "1545-1548", + "Text": "(Speed of light in vacuum is 3 0 \u00d7 108 m s\u20131)\n(b) Is the speed of light in glass independent of the colour of light If\nnot, which of the two colours red and violet travels slower in a\nglass prism 10" + }, + { + "Chapter": "9", + "sentence_range": "1546-1549", + "Text": "0 \u00d7 108 m s\u20131)\n(b) Is the speed of light in glass independent of the colour of light If\nnot, which of the two colours red and violet travels slower in a\nglass prism 10 4\nIn a Young\u2019s double-slit experiment, the slits are separated by\n0" + }, + { + "Chapter": "9", + "sentence_range": "1547-1550", + "Text": "If\nnot, which of the two colours red and violet travels slower in a\nglass prism 10 4\nIn a Young\u2019s double-slit experiment, the slits are separated by\n0 28 mm and the screen is placed 1" + }, + { + "Chapter": "9", + "sentence_range": "1548-1551", + "Text": "10 4\nIn a Young\u2019s double-slit experiment, the slits are separated by\n0 28 mm and the screen is placed 1 4 m away" + }, + { + "Chapter": "9", + "sentence_range": "1549-1552", + "Text": "4\nIn a Young\u2019s double-slit experiment, the slits are separated by\n0 28 mm and the screen is placed 1 4 m away The distance between\nthe central bright fringe and the fourth bright fringe is measured\nto be 1" + }, + { + "Chapter": "9", + "sentence_range": "1550-1553", + "Text": "28 mm and the screen is placed 1 4 m away The distance between\nthe central bright fringe and the fourth bright fringe is measured\nto be 1 2 cm" + }, + { + "Chapter": "9", + "sentence_range": "1551-1554", + "Text": "4 m away The distance between\nthe central bright fringe and the fourth bright fringe is measured\nto be 1 2 cm Determine the wavelength of light used in the\nexperiment" + }, + { + "Chapter": "9", + "sentence_range": "1552-1555", + "Text": "The distance between\nthe central bright fringe and the fourth bright fringe is measured\nto be 1 2 cm Determine the wavelength of light used in the\nexperiment 10" + }, + { + "Chapter": "9", + "sentence_range": "1553-1556", + "Text": "2 cm Determine the wavelength of light used in the\nexperiment 10 5\nIn Young\u2019s double-slit experiment using monochromatic light of\nwavelength l, the intensity of light at a point on the screen where\npath difference is l, is K units" + }, + { + "Chapter": "9", + "sentence_range": "1554-1557", + "Text": "Determine the wavelength of light used in the\nexperiment 10 5\nIn Young\u2019s double-slit experiment using monochromatic light of\nwavelength l, the intensity of light at a point on the screen where\npath difference is l, is K units What is the intensity of light at a\npoint where path difference is l/3" + }, + { + "Chapter": "9", + "sentence_range": "1555-1558", + "Text": "10 5\nIn Young\u2019s double-slit experiment using monochromatic light of\nwavelength l, the intensity of light at a point on the screen where\npath difference is l, is K units What is the intensity of light at a\npoint where path difference is l/3 10" + }, + { + "Chapter": "9", + "sentence_range": "1556-1559", + "Text": "5\nIn Young\u2019s double-slit experiment using monochromatic light of\nwavelength l, the intensity of light at a point on the screen where\npath difference is l, is K units What is the intensity of light at a\npoint where path difference is l/3 10 6\nA beam of light consisting of two wavelengths, 650 nm and 520 nm,\nis used to obtain interference fringes in a Young\u2019s double-slit\nexperiment" + }, + { + "Chapter": "9", + "sentence_range": "1557-1560", + "Text": "What is the intensity of light at a\npoint where path difference is l/3 10 6\nA beam of light consisting of two wavelengths, 650 nm and 520 nm,\nis used to obtain interference fringes in a Young\u2019s double-slit\nexperiment (a) Find the distance of the third bright fringe on the screen from\nthe central maximum for wavelength 650 nm" + }, + { + "Chapter": "9", + "sentence_range": "1558-1561", + "Text": "10 6\nA beam of light consisting of two wavelengths, 650 nm and 520 nm,\nis used to obtain interference fringes in a Young\u2019s double-slit\nexperiment (a) Find the distance of the third bright fringe on the screen from\nthe central maximum for wavelength 650 nm (b) What is the least distance from the central maximum where the\nbright fringes due to both the wavelengths coincide" + }, + { + "Chapter": "9", + "sentence_range": "1559-1562", + "Text": "6\nA beam of light consisting of two wavelengths, 650 nm and 520 nm,\nis used to obtain interference fringes in a Young\u2019s double-slit\nexperiment (a) Find the distance of the third bright fringe on the screen from\nthe central maximum for wavelength 650 nm (b) What is the least distance from the central maximum where the\nbright fringes due to both the wavelengths coincide Rationalised 2023-24\nPhysics\n274\n11" + }, + { + "Chapter": "9", + "sentence_range": "1560-1563", + "Text": "(a) Find the distance of the third bright fringe on the screen from\nthe central maximum for wavelength 650 nm (b) What is the least distance from the central maximum where the\nbright fringes due to both the wavelengths coincide Rationalised 2023-24\nPhysics\n274\n11 1 INTRODUCTION\nThe Maxwell\u2019s equations of electromagnetism and Hertz experiments on\nthe generation and detection of electromagnetic waves in 1887 strongly\nestablished the wave nature of light" + }, + { + "Chapter": "9", + "sentence_range": "1561-1564", + "Text": "(b) What is the least distance from the central maximum where the\nbright fringes due to both the wavelengths coincide Rationalised 2023-24\nPhysics\n274\n11 1 INTRODUCTION\nThe Maxwell\u2019s equations of electromagnetism and Hertz experiments on\nthe generation and detection of electromagnetic waves in 1887 strongly\nestablished the wave nature of light Towards the same period at the end\nof 19th century, experimental investigations on conduction of electricity\n(electric discharge) through gases at low pressure in a discharge tube led\nto many historic discoveries" + }, + { + "Chapter": "9", + "sentence_range": "1562-1565", + "Text": "Rationalised 2023-24\nPhysics\n274\n11 1 INTRODUCTION\nThe Maxwell\u2019s equations of electromagnetism and Hertz experiments on\nthe generation and detection of electromagnetic waves in 1887 strongly\nestablished the wave nature of light Towards the same period at the end\nof 19th century, experimental investigations on conduction of electricity\n(electric discharge) through gases at low pressure in a discharge tube led\nto many historic discoveries The discovery of X-rays by Roentgen in 1895,\nand of electron by J" + }, + { + "Chapter": "9", + "sentence_range": "1563-1566", + "Text": "1 INTRODUCTION\nThe Maxwell\u2019s equations of electromagnetism and Hertz experiments on\nthe generation and detection of electromagnetic waves in 1887 strongly\nestablished the wave nature of light Towards the same period at the end\nof 19th century, experimental investigations on conduction of electricity\n(electric discharge) through gases at low pressure in a discharge tube led\nto many historic discoveries The discovery of X-rays by Roentgen in 1895,\nand of electron by J J" + }, + { + "Chapter": "9", + "sentence_range": "1564-1567", + "Text": "Towards the same period at the end\nof 19th century, experimental investigations on conduction of electricity\n(electric discharge) through gases at low pressure in a discharge tube led\nto many historic discoveries The discovery of X-rays by Roentgen in 1895,\nand of electron by J J Thomson in 1897, were important milestones in\nthe understanding of atomic structure" + }, + { + "Chapter": "9", + "sentence_range": "1565-1568", + "Text": "The discovery of X-rays by Roentgen in 1895,\nand of electron by J J Thomson in 1897, were important milestones in\nthe understanding of atomic structure It was found that at sufficiently\nlow pressure of about 0" + }, + { + "Chapter": "9", + "sentence_range": "1566-1569", + "Text": "J Thomson in 1897, were important milestones in\nthe understanding of atomic structure It was found that at sufficiently\nlow pressure of about 0 001 mm of mercury column, a discharge took\nplace between the two electrodes on applying the electric field to the gas\nin the discharge tube" + }, + { + "Chapter": "9", + "sentence_range": "1567-1570", + "Text": "Thomson in 1897, were important milestones in\nthe understanding of atomic structure It was found that at sufficiently\nlow pressure of about 0 001 mm of mercury column, a discharge took\nplace between the two electrodes on applying the electric field to the gas\nin the discharge tube A fluorescent glow appeared on the glass opposite\nto cathode" + }, + { + "Chapter": "9", + "sentence_range": "1568-1571", + "Text": "It was found that at sufficiently\nlow pressure of about 0 001 mm of mercury column, a discharge took\nplace between the two electrodes on applying the electric field to the gas\nin the discharge tube A fluorescent glow appeared on the glass opposite\nto cathode The colour of glow of the glass depended on the type of glass,\nit being yellowish-green for soda glass" + }, + { + "Chapter": "9", + "sentence_range": "1569-1572", + "Text": "001 mm of mercury column, a discharge took\nplace between the two electrodes on applying the electric field to the gas\nin the discharge tube A fluorescent glow appeared on the glass opposite\nto cathode The colour of glow of the glass depended on the type of glass,\nit being yellowish-green for soda glass The cause of this fluorescence\nwas attributed to the radiation which appeared to be coming from the\ncathode" + }, + { + "Chapter": "9", + "sentence_range": "1570-1573", + "Text": "A fluorescent glow appeared on the glass opposite\nto cathode The colour of glow of the glass depended on the type of glass,\nit being yellowish-green for soda glass The cause of this fluorescence\nwas attributed to the radiation which appeared to be coming from the\ncathode These cathode rays were discovered, in 1870, by William\nCrookes who later, in 1879, suggested that these rays consisted of streams\nof fast moving negatively charged particles" + }, + { + "Chapter": "9", + "sentence_range": "1571-1574", + "Text": "The colour of glow of the glass depended on the type of glass,\nit being yellowish-green for soda glass The cause of this fluorescence\nwas attributed to the radiation which appeared to be coming from the\ncathode These cathode rays were discovered, in 1870, by William\nCrookes who later, in 1879, suggested that these rays consisted of streams\nof fast moving negatively charged particles The British physicist\nJ" + }, + { + "Chapter": "9", + "sentence_range": "1572-1575", + "Text": "The cause of this fluorescence\nwas attributed to the radiation which appeared to be coming from the\ncathode These cathode rays were discovered, in 1870, by William\nCrookes who later, in 1879, suggested that these rays consisted of streams\nof fast moving negatively charged particles The British physicist\nJ J" + }, + { + "Chapter": "9", + "sentence_range": "1573-1576", + "Text": "These cathode rays were discovered, in 1870, by William\nCrookes who later, in 1879, suggested that these rays consisted of streams\nof fast moving negatively charged particles The British physicist\nJ J Thomson (1856-1940) confirmed this hypothesis" + }, + { + "Chapter": "9", + "sentence_range": "1574-1577", + "Text": "The British physicist\nJ J Thomson (1856-1940) confirmed this hypothesis By applying\nmutually perpendicular electric and magnetic fields across the discharge\ntube, J" + }, + { + "Chapter": "9", + "sentence_range": "1575-1578", + "Text": "J Thomson (1856-1940) confirmed this hypothesis By applying\nmutually perpendicular electric and magnetic fields across the discharge\ntube, J J" + }, + { + "Chapter": "9", + "sentence_range": "1576-1579", + "Text": "Thomson (1856-1940) confirmed this hypothesis By applying\nmutually perpendicular electric and magnetic fields across the discharge\ntube, J J Thomson was the first to determine experimentally the speed\nChapter Eleven\nDUAL NATURE OF\nRADIATION AND\nMATTER\nRationalised 2023-24\n275\nDual Nature of Radiation\nand Matter\nand the specific charge [charge to mass ratio (e/m)] of the cathode ray\nparticles" + }, + { + "Chapter": "9", + "sentence_range": "1577-1580", + "Text": "By applying\nmutually perpendicular electric and magnetic fields across the discharge\ntube, J J Thomson was the first to determine experimentally the speed\nChapter Eleven\nDUAL NATURE OF\nRADIATION AND\nMATTER\nRationalised 2023-24\n275\nDual Nature of Radiation\nand Matter\nand the specific charge [charge to mass ratio (e/m)] of the cathode ray\nparticles They were found to travel with speeds ranging from about 0" + }, + { + "Chapter": "9", + "sentence_range": "1578-1581", + "Text": "J Thomson was the first to determine experimentally the speed\nChapter Eleven\nDUAL NATURE OF\nRADIATION AND\nMATTER\nRationalised 2023-24\n275\nDual Nature of Radiation\nand Matter\nand the specific charge [charge to mass ratio (e/m)] of the cathode ray\nparticles They were found to travel with speeds ranging from about 0 1\nto 0" + }, + { + "Chapter": "9", + "sentence_range": "1579-1582", + "Text": "Thomson was the first to determine experimentally the speed\nChapter Eleven\nDUAL NATURE OF\nRADIATION AND\nMATTER\nRationalised 2023-24\n275\nDual Nature of Radiation\nand Matter\nand the specific charge [charge to mass ratio (e/m)] of the cathode ray\nparticles They were found to travel with speeds ranging from about 0 1\nto 0 2 times the speed of light (3 \u00d7108 m/s)" + }, + { + "Chapter": "9", + "sentence_range": "1580-1583", + "Text": "They were found to travel with speeds ranging from about 0 1\nto 0 2 times the speed of light (3 \u00d7108 m/s) The presently accepted value\nof e/m is 1" + }, + { + "Chapter": "9", + "sentence_range": "1581-1584", + "Text": "1\nto 0 2 times the speed of light (3 \u00d7108 m/s) The presently accepted value\nof e/m is 1 76 \u00d7 1011 C/kg" + }, + { + "Chapter": "9", + "sentence_range": "1582-1585", + "Text": "2 times the speed of light (3 \u00d7108 m/s) The presently accepted value\nof e/m is 1 76 \u00d7 1011 C/kg Further, the value of e/m was found to be\nindependent of the nature of the material/metal used as the cathode\n(emitter), or the gas introduced in the discharge tube" + }, + { + "Chapter": "9", + "sentence_range": "1583-1586", + "Text": "The presently accepted value\nof e/m is 1 76 \u00d7 1011 C/kg Further, the value of e/m was found to be\nindependent of the nature of the material/metal used as the cathode\n(emitter), or the gas introduced in the discharge tube This observation\nsuggested the universality of the cathode ray particles" + }, + { + "Chapter": "9", + "sentence_range": "1584-1587", + "Text": "76 \u00d7 1011 C/kg Further, the value of e/m was found to be\nindependent of the nature of the material/metal used as the cathode\n(emitter), or the gas introduced in the discharge tube This observation\nsuggested the universality of the cathode ray particles Around the same time, in 1887, it was found that certain metals, when\nirradiated by ultraviolet light, emitted negatively charged particles having\nsmall speeds" + }, + { + "Chapter": "9", + "sentence_range": "1585-1588", + "Text": "Further, the value of e/m was found to be\nindependent of the nature of the material/metal used as the cathode\n(emitter), or the gas introduced in the discharge tube This observation\nsuggested the universality of the cathode ray particles Around the same time, in 1887, it was found that certain metals, when\nirradiated by ultraviolet light, emitted negatively charged particles having\nsmall speeds Also, certain metals when heated to a high temperature were\nfound to emit negatively charged particles" + }, + { + "Chapter": "9", + "sentence_range": "1586-1589", + "Text": "This observation\nsuggested the universality of the cathode ray particles Around the same time, in 1887, it was found that certain metals, when\nirradiated by ultraviolet light, emitted negatively charged particles having\nsmall speeds Also, certain metals when heated to a high temperature were\nfound to emit negatively charged particles The value of e/m of these particles\nwas found to be the same as that for cathode ray particles" + }, + { + "Chapter": "9", + "sentence_range": "1587-1590", + "Text": "Around the same time, in 1887, it was found that certain metals, when\nirradiated by ultraviolet light, emitted negatively charged particles having\nsmall speeds Also, certain metals when heated to a high temperature were\nfound to emit negatively charged particles The value of e/m of these particles\nwas found to be the same as that for cathode ray particles These\nobservations thus established that all these particles, although produced\nunder different conditions, were identical in nature" + }, + { + "Chapter": "9", + "sentence_range": "1588-1591", + "Text": "Also, certain metals when heated to a high temperature were\nfound to emit negatively charged particles The value of e/m of these particles\nwas found to be the same as that for cathode ray particles These\nobservations thus established that all these particles, although produced\nunder different conditions, were identical in nature J" + }, + { + "Chapter": "9", + "sentence_range": "1589-1592", + "Text": "The value of e/m of these particles\nwas found to be the same as that for cathode ray particles These\nobservations thus established that all these particles, although produced\nunder different conditions, were identical in nature J J" + }, + { + "Chapter": "9", + "sentence_range": "1590-1593", + "Text": "These\nobservations thus established that all these particles, although produced\nunder different conditions, were identical in nature J J Thomson, in 1897,\nnamed these particles as electrons, and suggested that they were\nfundamental, universal constituents of matter" + }, + { + "Chapter": "9", + "sentence_range": "1591-1594", + "Text": "J J Thomson, in 1897,\nnamed these particles as electrons, and suggested that they were\nfundamental, universal constituents of matter For his epoch-making\ndiscovery of electron, through his theoretical and experimental\ninvestigations on conduction of electricity by gasses, he was awarded the\nNobel Prize in Physics in 1906" + }, + { + "Chapter": "9", + "sentence_range": "1592-1595", + "Text": "J Thomson, in 1897,\nnamed these particles as electrons, and suggested that they were\nfundamental, universal constituents of matter For his epoch-making\ndiscovery of electron, through his theoretical and experimental\ninvestigations on conduction of electricity by gasses, he was awarded the\nNobel Prize in Physics in 1906 In 1913, the American physicist R" + }, + { + "Chapter": "9", + "sentence_range": "1593-1596", + "Text": "Thomson, in 1897,\nnamed these particles as electrons, and suggested that they were\nfundamental, universal constituents of matter For his epoch-making\ndiscovery of electron, through his theoretical and experimental\ninvestigations on conduction of electricity by gasses, he was awarded the\nNobel Prize in Physics in 1906 In 1913, the American physicist R A" + }, + { + "Chapter": "9", + "sentence_range": "1594-1597", + "Text": "For his epoch-making\ndiscovery of electron, through his theoretical and experimental\ninvestigations on conduction of electricity by gasses, he was awarded the\nNobel Prize in Physics in 1906 In 1913, the American physicist R A Millikan (1868-1953) performed the pioneering oil-drop experiment for\nthe precise measurement of the charge on an electron" + }, + { + "Chapter": "9", + "sentence_range": "1595-1598", + "Text": "In 1913, the American physicist R A Millikan (1868-1953) performed the pioneering oil-drop experiment for\nthe precise measurement of the charge on an electron He found that the\ncharge on an oil-droplet was always an integral multiple of an elementary\ncharge, 1" + }, + { + "Chapter": "9", + "sentence_range": "1596-1599", + "Text": "A Millikan (1868-1953) performed the pioneering oil-drop experiment for\nthe precise measurement of the charge on an electron He found that the\ncharge on an oil-droplet was always an integral multiple of an elementary\ncharge, 1 602 \u00d7 10\u201319 C" + }, + { + "Chapter": "9", + "sentence_range": "1597-1600", + "Text": "Millikan (1868-1953) performed the pioneering oil-drop experiment for\nthe precise measurement of the charge on an electron He found that the\ncharge on an oil-droplet was always an integral multiple of an elementary\ncharge, 1 602 \u00d7 10\u201319 C Millikan\u2019s experiment established that electric\ncharge is quantised" + }, + { + "Chapter": "9", + "sentence_range": "1598-1601", + "Text": "He found that the\ncharge on an oil-droplet was always an integral multiple of an elementary\ncharge, 1 602 \u00d7 10\u201319 C Millikan\u2019s experiment established that electric\ncharge is quantised From the values of charge (e) and specific charge\n(e/m), the mass (m) of the electron could be determined" + }, + { + "Chapter": "9", + "sentence_range": "1599-1602", + "Text": "602 \u00d7 10\u201319 C Millikan\u2019s experiment established that electric\ncharge is quantised From the values of charge (e) and specific charge\n(e/m), the mass (m) of the electron could be determined 11" + }, + { + "Chapter": "9", + "sentence_range": "1600-1603", + "Text": "Millikan\u2019s experiment established that electric\ncharge is quantised From the values of charge (e) and specific charge\n(e/m), the mass (m) of the electron could be determined 11 2 ELECTRON EMISSION\nWe know that metals have free electrons (negatively charged particles) that\nare responsible for their conductivity" + }, + { + "Chapter": "9", + "sentence_range": "1601-1604", + "Text": "From the values of charge (e) and specific charge\n(e/m), the mass (m) of the electron could be determined 11 2 ELECTRON EMISSION\nWe know that metals have free electrons (negatively charged particles) that\nare responsible for their conductivity However, the free electrons cannot\nnormally escape out of the metal surface" + }, + { + "Chapter": "9", + "sentence_range": "1602-1605", + "Text": "11 2 ELECTRON EMISSION\nWe know that metals have free electrons (negatively charged particles) that\nare responsible for their conductivity However, the free electrons cannot\nnormally escape out of the metal surface If an electron attempts to come\nout of the metal, the metal surface acquires a positive charge and pulls the\nelectron back to the metal" + }, + { + "Chapter": "9", + "sentence_range": "1603-1606", + "Text": "2 ELECTRON EMISSION\nWe know that metals have free electrons (negatively charged particles) that\nare responsible for their conductivity However, the free electrons cannot\nnormally escape out of the metal surface If an electron attempts to come\nout of the metal, the metal surface acquires a positive charge and pulls the\nelectron back to the metal The free electron is thus held inside the metal\nsurface by the attractive forces of the ions" + }, + { + "Chapter": "9", + "sentence_range": "1604-1607", + "Text": "However, the free electrons cannot\nnormally escape out of the metal surface If an electron attempts to come\nout of the metal, the metal surface acquires a positive charge and pulls the\nelectron back to the metal The free electron is thus held inside the metal\nsurface by the attractive forces of the ions Consequently, the electron can\ncome out of the metal surface only if it has got sufficient energy to overcome\nthe attractive pull" + }, + { + "Chapter": "9", + "sentence_range": "1605-1608", + "Text": "If an electron attempts to come\nout of the metal, the metal surface acquires a positive charge and pulls the\nelectron back to the metal The free electron is thus held inside the metal\nsurface by the attractive forces of the ions Consequently, the electron can\ncome out of the metal surface only if it has got sufficient energy to overcome\nthe attractive pull A certain minimum amount of energy is required to be\ngiven to an electron to pull it out from the surface of the metal" + }, + { + "Chapter": "9", + "sentence_range": "1606-1609", + "Text": "The free electron is thus held inside the metal\nsurface by the attractive forces of the ions Consequently, the electron can\ncome out of the metal surface only if it has got sufficient energy to overcome\nthe attractive pull A certain minimum amount of energy is required to be\ngiven to an electron to pull it out from the surface of the metal This\nminimum energy required by an electron to escape from the metal surface\nis called the work function of the metal" + }, + { + "Chapter": "9", + "sentence_range": "1607-1610", + "Text": "Consequently, the electron can\ncome out of the metal surface only if it has got sufficient energy to overcome\nthe attractive pull A certain minimum amount of energy is required to be\ngiven to an electron to pull it out from the surface of the metal This\nminimum energy required by an electron to escape from the metal surface\nis called the work function of the metal It is generally denoted by f0 and\nmeasured in eV (electron volt)" + }, + { + "Chapter": "9", + "sentence_range": "1608-1611", + "Text": "A certain minimum amount of energy is required to be\ngiven to an electron to pull it out from the surface of the metal This\nminimum energy required by an electron to escape from the metal surface\nis called the work function of the metal It is generally denoted by f0 and\nmeasured in eV (electron volt) One electron volt is the energy gained by an\nelectron when it has been accelerated by a potential difference of 1 volt, so\nthat 1 eV = 1" + }, + { + "Chapter": "9", + "sentence_range": "1609-1612", + "Text": "This\nminimum energy required by an electron to escape from the metal surface\nis called the work function of the metal It is generally denoted by f0 and\nmeasured in eV (electron volt) One electron volt is the energy gained by an\nelectron when it has been accelerated by a potential difference of 1 volt, so\nthat 1 eV = 1 602 \u00d710\u201319 J" + }, + { + "Chapter": "9", + "sentence_range": "1610-1613", + "Text": "It is generally denoted by f0 and\nmeasured in eV (electron volt) One electron volt is the energy gained by an\nelectron when it has been accelerated by a potential difference of 1 volt, so\nthat 1 eV = 1 602 \u00d710\u201319 J This unit of energy is commonly used in atomic and nuclear physics" + }, + { + "Chapter": "9", + "sentence_range": "1611-1614", + "Text": "One electron volt is the energy gained by an\nelectron when it has been accelerated by a potential difference of 1 volt, so\nthat 1 eV = 1 602 \u00d710\u201319 J This unit of energy is commonly used in atomic and nuclear physics The work function (f0) depends on the properties of the metal and the\nnature of its surface" + }, + { + "Chapter": "9", + "sentence_range": "1612-1615", + "Text": "602 \u00d710\u201319 J This unit of energy is commonly used in atomic and nuclear physics The work function (f0) depends on the properties of the metal and the\nnature of its surface The minimum energy required for the electron emission from the metal\nsurface can be supplied to the free electrons by any one of the following\nphysical processes:\n(i)\nThermionic emission: By suitably heating, sufficient thermal energy\ncan be imparted to the free electrons to enable them to come out of the\nmetal" + }, + { + "Chapter": "9", + "sentence_range": "1613-1616", + "Text": "This unit of energy is commonly used in atomic and nuclear physics The work function (f0) depends on the properties of the metal and the\nnature of its surface The minimum energy required for the electron emission from the metal\nsurface can be supplied to the free electrons by any one of the following\nphysical processes:\n(i)\nThermionic emission: By suitably heating, sufficient thermal energy\ncan be imparted to the free electrons to enable them to come out of the\nmetal Rationalised 2023-24\nPhysics\n276\n(ii) Field emission: By applying a very strong electric field (of the order of\n108 V m\u20131) to a metal, electrons can be pulled out of the metal, as in a\nspark plug" + }, + { + "Chapter": "9", + "sentence_range": "1614-1617", + "Text": "The work function (f0) depends on the properties of the metal and the\nnature of its surface The minimum energy required for the electron emission from the metal\nsurface can be supplied to the free electrons by any one of the following\nphysical processes:\n(i)\nThermionic emission: By suitably heating, sufficient thermal energy\ncan be imparted to the free electrons to enable them to come out of the\nmetal Rationalised 2023-24\nPhysics\n276\n(ii) Field emission: By applying a very strong electric field (of the order of\n108 V m\u20131) to a metal, electrons can be pulled out of the metal, as in a\nspark plug (iii) Photoelectric emission: When light of suitable frequency illuminates\na metal surface, electrons are emitted from the metal surface" + }, + { + "Chapter": "9", + "sentence_range": "1615-1618", + "Text": "The minimum energy required for the electron emission from the metal\nsurface can be supplied to the free electrons by any one of the following\nphysical processes:\n(i)\nThermionic emission: By suitably heating, sufficient thermal energy\ncan be imparted to the free electrons to enable them to come out of the\nmetal Rationalised 2023-24\nPhysics\n276\n(ii) Field emission: By applying a very strong electric field (of the order of\n108 V m\u20131) to a metal, electrons can be pulled out of the metal, as in a\nspark plug (iii) Photoelectric emission: When light of suitable frequency illuminates\na metal surface, electrons are emitted from the metal surface These\nphoto(light)-generated electrons are called photoelectrons" + }, + { + "Chapter": "9", + "sentence_range": "1616-1619", + "Text": "Rationalised 2023-24\nPhysics\n276\n(ii) Field emission: By applying a very strong electric field (of the order of\n108 V m\u20131) to a metal, electrons can be pulled out of the metal, as in a\nspark plug (iii) Photoelectric emission: When light of suitable frequency illuminates\na metal surface, electrons are emitted from the metal surface These\nphoto(light)-generated electrons are called photoelectrons 11" + }, + { + "Chapter": "9", + "sentence_range": "1617-1620", + "Text": "(iii) Photoelectric emission: When light of suitable frequency illuminates\na metal surface, electrons are emitted from the metal surface These\nphoto(light)-generated electrons are called photoelectrons 11 3 PHOTOELECTRIC EFFECT\n11" + }, + { + "Chapter": "9", + "sentence_range": "1618-1621", + "Text": "These\nphoto(light)-generated electrons are called photoelectrons 11 3 PHOTOELECTRIC EFFECT\n11 3" + }, + { + "Chapter": "9", + "sentence_range": "1619-1622", + "Text": "11 3 PHOTOELECTRIC EFFECT\n11 3 1 Hertz\u2019s observations\nThe phenomenon of photoelectric emission was discovered in 1887 by\nHeinrich Hertz (1857-1894), during his electromagnetic wave experiments" + }, + { + "Chapter": "9", + "sentence_range": "1620-1623", + "Text": "3 PHOTOELECTRIC EFFECT\n11 3 1 Hertz\u2019s observations\nThe phenomenon of photoelectric emission was discovered in 1887 by\nHeinrich Hertz (1857-1894), during his electromagnetic wave experiments In his experimental investigation on the production of electromagnetic\nwaves by means of a spark discharge, Hertz observed that high voltage\nsparks across the detector loop were enhanced when the emitter plate\nwas illuminated by ultraviolet light from an arc lamp" + }, + { + "Chapter": "9", + "sentence_range": "1621-1624", + "Text": "3 1 Hertz\u2019s observations\nThe phenomenon of photoelectric emission was discovered in 1887 by\nHeinrich Hertz (1857-1894), during his electromagnetic wave experiments In his experimental investigation on the production of electromagnetic\nwaves by means of a spark discharge, Hertz observed that high voltage\nsparks across the detector loop were enhanced when the emitter plate\nwas illuminated by ultraviolet light from an arc lamp Light shining on the metal surface somehow facilitated the escape of\nfree, charged particles which we now know as electrons" + }, + { + "Chapter": "9", + "sentence_range": "1622-1625", + "Text": "1 Hertz\u2019s observations\nThe phenomenon of photoelectric emission was discovered in 1887 by\nHeinrich Hertz (1857-1894), during his electromagnetic wave experiments In his experimental investigation on the production of electromagnetic\nwaves by means of a spark discharge, Hertz observed that high voltage\nsparks across the detector loop were enhanced when the emitter plate\nwas illuminated by ultraviolet light from an arc lamp Light shining on the metal surface somehow facilitated the escape of\nfree, charged particles which we now know as electrons When light falls\non a metal surface, some electrons near the surface absorb enough energy\nfrom the incident radiation to overcome the attraction of the positive ions\nin the material of the surface" + }, + { + "Chapter": "9", + "sentence_range": "1623-1626", + "Text": "In his experimental investigation on the production of electromagnetic\nwaves by means of a spark discharge, Hertz observed that high voltage\nsparks across the detector loop were enhanced when the emitter plate\nwas illuminated by ultraviolet light from an arc lamp Light shining on the metal surface somehow facilitated the escape of\nfree, charged particles which we now know as electrons When light falls\non a metal surface, some electrons near the surface absorb enough energy\nfrom the incident radiation to overcome the attraction of the positive ions\nin the material of the surface After gaining sufficient energy from the\nincident light, the electrons escape from the surface of the metal into the\nsurrounding space" + }, + { + "Chapter": "9", + "sentence_range": "1624-1627", + "Text": "Light shining on the metal surface somehow facilitated the escape of\nfree, charged particles which we now know as electrons When light falls\non a metal surface, some electrons near the surface absorb enough energy\nfrom the incident radiation to overcome the attraction of the positive ions\nin the material of the surface After gaining sufficient energy from the\nincident light, the electrons escape from the surface of the metal into the\nsurrounding space 11" + }, + { + "Chapter": "9", + "sentence_range": "1625-1628", + "Text": "When light falls\non a metal surface, some electrons near the surface absorb enough energy\nfrom the incident radiation to overcome the attraction of the positive ions\nin the material of the surface After gaining sufficient energy from the\nincident light, the electrons escape from the surface of the metal into the\nsurrounding space 11 3" + }, + { + "Chapter": "9", + "sentence_range": "1626-1629", + "Text": "After gaining sufficient energy from the\nincident light, the electrons escape from the surface of the metal into the\nsurrounding space 11 3 2 Hallwachs\u2019 and Lenard\u2019s observations\nWilhelm Hallwachs and Philipp Lenard investigated the phenomenon of\nphotoelectric emission in detail during 1886-1902" + }, + { + "Chapter": "9", + "sentence_range": "1627-1630", + "Text": "11 3 2 Hallwachs\u2019 and Lenard\u2019s observations\nWilhelm Hallwachs and Philipp Lenard investigated the phenomenon of\nphotoelectric emission in detail during 1886-1902 Lenard (1862-1947) observed that when ultraviolet radiations were\nallowed to fall on the emitter plate of an evacuated glass tube enclosing\ntwo electrodes (metal plates), current flows in the circuit (Fig" + }, + { + "Chapter": "9", + "sentence_range": "1628-1631", + "Text": "3 2 Hallwachs\u2019 and Lenard\u2019s observations\nWilhelm Hallwachs and Philipp Lenard investigated the phenomenon of\nphotoelectric emission in detail during 1886-1902 Lenard (1862-1947) observed that when ultraviolet radiations were\nallowed to fall on the emitter plate of an evacuated glass tube enclosing\ntwo electrodes (metal plates), current flows in the circuit (Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1629-1632", + "Text": "2 Hallwachs\u2019 and Lenard\u2019s observations\nWilhelm Hallwachs and Philipp Lenard investigated the phenomenon of\nphotoelectric emission in detail during 1886-1902 Lenard (1862-1947) observed that when ultraviolet radiations were\nallowed to fall on the emitter plate of an evacuated glass tube enclosing\ntwo electrodes (metal plates), current flows in the circuit (Fig 11 1)" + }, + { + "Chapter": "9", + "sentence_range": "1630-1633", + "Text": "Lenard (1862-1947) observed that when ultraviolet radiations were\nallowed to fall on the emitter plate of an evacuated glass tube enclosing\ntwo electrodes (metal plates), current flows in the circuit (Fig 11 1) As\nsoon as the ultraviolet radiations were stopped, the current flow also\nstopped" + }, + { + "Chapter": "9", + "sentence_range": "1631-1634", + "Text": "11 1) As\nsoon as the ultraviolet radiations were stopped, the current flow also\nstopped These observations indicate that when ultraviolet radiations fall\non the emitter plate C, electrons are ejected from it which are attracted\ntowards the positive, collector plate A by the electric field" + }, + { + "Chapter": "9", + "sentence_range": "1632-1635", + "Text": "1) As\nsoon as the ultraviolet radiations were stopped, the current flow also\nstopped These observations indicate that when ultraviolet radiations fall\non the emitter plate C, electrons are ejected from it which are attracted\ntowards the positive, collector plate A by the electric field The electrons\nflow through the evacuated glass tube, resulting in the current flow" + }, + { + "Chapter": "9", + "sentence_range": "1633-1636", + "Text": "As\nsoon as the ultraviolet radiations were stopped, the current flow also\nstopped These observations indicate that when ultraviolet radiations fall\non the emitter plate C, electrons are ejected from it which are attracted\ntowards the positive, collector plate A by the electric field The electrons\nflow through the evacuated glass tube, resulting in the current flow Thus,\nlight falling on the surface of the emitter causes current in the external\ncircuit" + }, + { + "Chapter": "9", + "sentence_range": "1634-1637", + "Text": "These observations indicate that when ultraviolet radiations fall\non the emitter plate C, electrons are ejected from it which are attracted\ntowards the positive, collector plate A by the electric field The electrons\nflow through the evacuated glass tube, resulting in the current flow Thus,\nlight falling on the surface of the emitter causes current in the external\ncircuit Hallwachs and Lenard studied how this photo current varied with\ncollector plate potential, and with frequency and intensity of incident light" + }, + { + "Chapter": "9", + "sentence_range": "1635-1638", + "Text": "The electrons\nflow through the evacuated glass tube, resulting in the current flow Thus,\nlight falling on the surface of the emitter causes current in the external\ncircuit Hallwachs and Lenard studied how this photo current varied with\ncollector plate potential, and with frequency and intensity of incident light Hallwachs, in 1888, undertook the study further and connected a\nnegatively charged zinc plate to an electroscope" + }, + { + "Chapter": "9", + "sentence_range": "1636-1639", + "Text": "Thus,\nlight falling on the surface of the emitter causes current in the external\ncircuit Hallwachs and Lenard studied how this photo current varied with\ncollector plate potential, and with frequency and intensity of incident light Hallwachs, in 1888, undertook the study further and connected a\nnegatively charged zinc plate to an electroscope He observed that the\nzinc plate lost its charge when it was illuminated by ultraviolet light" + }, + { + "Chapter": "9", + "sentence_range": "1637-1640", + "Text": "Hallwachs and Lenard studied how this photo current varied with\ncollector plate potential, and with frequency and intensity of incident light Hallwachs, in 1888, undertook the study further and connected a\nnegatively charged zinc plate to an electroscope He observed that the\nzinc plate lost its charge when it was illuminated by ultraviolet light Further, the uncharged zinc plate became positively charged when it was\nirradiated by ultraviolet light" + }, + { + "Chapter": "9", + "sentence_range": "1638-1641", + "Text": "Hallwachs, in 1888, undertook the study further and connected a\nnegatively charged zinc plate to an electroscope He observed that the\nzinc plate lost its charge when it was illuminated by ultraviolet light Further, the uncharged zinc plate became positively charged when it was\nirradiated by ultraviolet light Positive charge on a positively charged\nzinc plate was found to be further enhanced when it was illuminated by\nultraviolet light" + }, + { + "Chapter": "9", + "sentence_range": "1639-1642", + "Text": "He observed that the\nzinc plate lost its charge when it was illuminated by ultraviolet light Further, the uncharged zinc plate became positively charged when it was\nirradiated by ultraviolet light Positive charge on a positively charged\nzinc plate was found to be further enhanced when it was illuminated by\nultraviolet light From these observations he concluded that negatively\ncharged particles were emitted from the zinc plate under the action of\nultraviolet light" + }, + { + "Chapter": "9", + "sentence_range": "1640-1643", + "Text": "Further, the uncharged zinc plate became positively charged when it was\nirradiated by ultraviolet light Positive charge on a positively charged\nzinc plate was found to be further enhanced when it was illuminated by\nultraviolet light From these observations he concluded that negatively\ncharged particles were emitted from the zinc plate under the action of\nultraviolet light After the discovery of the electron in 1897, it became evident that the\nincident light causes electrons to be emitted from the emitter plate" + }, + { + "Chapter": "9", + "sentence_range": "1641-1644", + "Text": "Positive charge on a positively charged\nzinc plate was found to be further enhanced when it was illuminated by\nultraviolet light From these observations he concluded that negatively\ncharged particles were emitted from the zinc plate under the action of\nultraviolet light After the discovery of the electron in 1897, it became evident that the\nincident light causes electrons to be emitted from the emitter plate Due\nRationalised 2023-24\n277\nDual Nature of Radiation\nand Matter\nto negative charge, the emitted electrons are pushed towards the collector\nplate by the electric field" + }, + { + "Chapter": "9", + "sentence_range": "1642-1645", + "Text": "From these observations he concluded that negatively\ncharged particles were emitted from the zinc plate under the action of\nultraviolet light After the discovery of the electron in 1897, it became evident that the\nincident light causes electrons to be emitted from the emitter plate Due\nRationalised 2023-24\n277\nDual Nature of Radiation\nand Matter\nto negative charge, the emitted electrons are pushed towards the collector\nplate by the electric field Hallwachs and Lenard also observed that when\nultraviolet light fell on the emitter plate, no electrons were emitted at all\nwhen the frequency of the incident light was smaller than a certain\nminimum value, called the threshold frequency" + }, + { + "Chapter": "9", + "sentence_range": "1643-1646", + "Text": "After the discovery of the electron in 1897, it became evident that the\nincident light causes electrons to be emitted from the emitter plate Due\nRationalised 2023-24\n277\nDual Nature of Radiation\nand Matter\nto negative charge, the emitted electrons are pushed towards the collector\nplate by the electric field Hallwachs and Lenard also observed that when\nultraviolet light fell on the emitter plate, no electrons were emitted at all\nwhen the frequency of the incident light was smaller than a certain\nminimum value, called the threshold frequency This minimum frequency\ndepends on the nature of the material of the emitter plate" + }, + { + "Chapter": "9", + "sentence_range": "1644-1647", + "Text": "Due\nRationalised 2023-24\n277\nDual Nature of Radiation\nand Matter\nto negative charge, the emitted electrons are pushed towards the collector\nplate by the electric field Hallwachs and Lenard also observed that when\nultraviolet light fell on the emitter plate, no electrons were emitted at all\nwhen the frequency of the incident light was smaller than a certain\nminimum value, called the threshold frequency This minimum frequency\ndepends on the nature of the material of the emitter plate It was found that certain metals like zinc, cadmium, magnesium, etc" + }, + { + "Chapter": "9", + "sentence_range": "1645-1648", + "Text": "Hallwachs and Lenard also observed that when\nultraviolet light fell on the emitter plate, no electrons were emitted at all\nwhen the frequency of the incident light was smaller than a certain\nminimum value, called the threshold frequency This minimum frequency\ndepends on the nature of the material of the emitter plate It was found that certain metals like zinc, cadmium, magnesium, etc ,\nresponded only to ultraviolet light, having short wavelength, to cause\nelectron emission from the surface" + }, + { + "Chapter": "9", + "sentence_range": "1646-1649", + "Text": "This minimum frequency\ndepends on the nature of the material of the emitter plate It was found that certain metals like zinc, cadmium, magnesium, etc ,\nresponded only to ultraviolet light, having short wavelength, to cause\nelectron emission from the surface However, some alkali metals such as\nlithium, sodium, potassium, caesium and rubidium were sensitive\neven to visible light" + }, + { + "Chapter": "9", + "sentence_range": "1647-1650", + "Text": "It was found that certain metals like zinc, cadmium, magnesium, etc ,\nresponded only to ultraviolet light, having short wavelength, to cause\nelectron emission from the surface However, some alkali metals such as\nlithium, sodium, potassium, caesium and rubidium were sensitive\neven to visible light All these photosensitive substances emit electrons\nwhen they are illuminated by light" + }, + { + "Chapter": "9", + "sentence_range": "1648-1651", + "Text": ",\nresponded only to ultraviolet light, having short wavelength, to cause\nelectron emission from the surface However, some alkali metals such as\nlithium, sodium, potassium, caesium and rubidium were sensitive\neven to visible light All these photosensitive substances emit electrons\nwhen they are illuminated by light After the discovery of electrons, these\nelectrons were termed as photoelectrons" + }, + { + "Chapter": "9", + "sentence_range": "1649-1652", + "Text": "However, some alkali metals such as\nlithium, sodium, potassium, caesium and rubidium were sensitive\neven to visible light All these photosensitive substances emit electrons\nwhen they are illuminated by light After the discovery of electrons, these\nelectrons were termed as photoelectrons The phenomenon is called\nphotoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1650-1653", + "Text": "All these photosensitive substances emit electrons\nwhen they are illuminated by light After the discovery of electrons, these\nelectrons were termed as photoelectrons The phenomenon is called\nphotoelectric effect 11" + }, + { + "Chapter": "9", + "sentence_range": "1651-1654", + "Text": "After the discovery of electrons, these\nelectrons were termed as photoelectrons The phenomenon is called\nphotoelectric effect 11 4 EXPERIMENTAL STUDY OF PHOTOELECTRIC\nEFFECT\nFigure 11" + }, + { + "Chapter": "9", + "sentence_range": "1652-1655", + "Text": "The phenomenon is called\nphotoelectric effect 11 4 EXPERIMENTAL STUDY OF PHOTOELECTRIC\nEFFECT\nFigure 11 1 depicts a schematic view of the arrangement used for the\nexperimental study of the photoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1653-1656", + "Text": "11 4 EXPERIMENTAL STUDY OF PHOTOELECTRIC\nEFFECT\nFigure 11 1 depicts a schematic view of the arrangement used for the\nexperimental study of the photoelectric effect It consists of an evacuated\nglass/quartz tube having a thin photosensitive plate C and another metal\nplate A" + }, + { + "Chapter": "9", + "sentence_range": "1654-1657", + "Text": "4 EXPERIMENTAL STUDY OF PHOTOELECTRIC\nEFFECT\nFigure 11 1 depicts a schematic view of the arrangement used for the\nexperimental study of the photoelectric effect It consists of an evacuated\nglass/quartz tube having a thin photosensitive plate C and another metal\nplate A Monochromatic light from the source S of sufficiently short\nwavelength passes through the window W and falls on the photosensitive\nplate C (emitter)" + }, + { + "Chapter": "9", + "sentence_range": "1655-1658", + "Text": "1 depicts a schematic view of the arrangement used for the\nexperimental study of the photoelectric effect It consists of an evacuated\nglass/quartz tube having a thin photosensitive plate C and another metal\nplate A Monochromatic light from the source S of sufficiently short\nwavelength passes through the window W and falls on the photosensitive\nplate C (emitter) A transparent quartz window is sealed on to the glass\ntube, which permits ultraviolet radiation to pass through it and irradiate\nthe photosensitive plate C" + }, + { + "Chapter": "9", + "sentence_range": "1656-1659", + "Text": "It consists of an evacuated\nglass/quartz tube having a thin photosensitive plate C and another metal\nplate A Monochromatic light from the source S of sufficiently short\nwavelength passes through the window W and falls on the photosensitive\nplate C (emitter) A transparent quartz window is sealed on to the glass\ntube, which permits ultraviolet radiation to pass through it and irradiate\nthe photosensitive plate C The electrons are emitted by the plate C and\nare collected by the plate A (collector), by the electric field created by the\nbattery" + }, + { + "Chapter": "9", + "sentence_range": "1657-1660", + "Text": "Monochromatic light from the source S of sufficiently short\nwavelength passes through the window W and falls on the photosensitive\nplate C (emitter) A transparent quartz window is sealed on to the glass\ntube, which permits ultraviolet radiation to pass through it and irradiate\nthe photosensitive plate C The electrons are emitted by the plate C and\nare collected by the plate A (collector), by the electric field created by the\nbattery The battery maintains the potential difference between the plates\nC and A, that can be varied" + }, + { + "Chapter": "9", + "sentence_range": "1658-1661", + "Text": "A transparent quartz window is sealed on to the glass\ntube, which permits ultraviolet radiation to pass through it and irradiate\nthe photosensitive plate C The electrons are emitted by the plate C and\nare collected by the plate A (collector), by the electric field created by the\nbattery The battery maintains the potential difference between the plates\nC and A, that can be varied The polarity of the plates C and A can be\nreversed by a commutator" + }, + { + "Chapter": "9", + "sentence_range": "1659-1662", + "Text": "The electrons are emitted by the plate C and\nare collected by the plate A (collector), by the electric field created by the\nbattery The battery maintains the potential difference between the plates\nC and A, that can be varied The polarity of the plates C and A can be\nreversed by a commutator Thus, the plate A can be maintained at a desired\npositive or negative potential with respect to emitter C" + }, + { + "Chapter": "9", + "sentence_range": "1660-1663", + "Text": "The battery maintains the potential difference between the plates\nC and A, that can be varied The polarity of the plates C and A can be\nreversed by a commutator Thus, the plate A can be maintained at a desired\npositive or negative potential with respect to emitter C When the collector plate A is positive with respect to the\nemitter plate C, the electrons are attracted to it" + }, + { + "Chapter": "9", + "sentence_range": "1661-1664", + "Text": "The polarity of the plates C and A can be\nreversed by a commutator Thus, the plate A can be maintained at a desired\npositive or negative potential with respect to emitter C When the collector plate A is positive with respect to the\nemitter plate C, the electrons are attracted to it The\nemission of electrons causes flow of electric current in\nthe circuit" + }, + { + "Chapter": "9", + "sentence_range": "1662-1665", + "Text": "Thus, the plate A can be maintained at a desired\npositive or negative potential with respect to emitter C When the collector plate A is positive with respect to the\nemitter plate C, the electrons are attracted to it The\nemission of electrons causes flow of electric current in\nthe circuit The potential difference between the emitter\nand collector plates is measured by a voltmeter (V)\nwhereas the resulting photo current flowing in the circuit\nis measured by a microammeter (mA)" + }, + { + "Chapter": "9", + "sentence_range": "1663-1666", + "Text": "When the collector plate A is positive with respect to the\nemitter plate C, the electrons are attracted to it The\nemission of electrons causes flow of electric current in\nthe circuit The potential difference between the emitter\nand collector plates is measured by a voltmeter (V)\nwhereas the resulting photo current flowing in the circuit\nis measured by a microammeter (mA) The photoelectric\ncurrent can be increased or decreased by varying the\npotential of collector plate A with respect to the emitter\nplate C" + }, + { + "Chapter": "9", + "sentence_range": "1664-1667", + "Text": "The\nemission of electrons causes flow of electric current in\nthe circuit The potential difference between the emitter\nand collector plates is measured by a voltmeter (V)\nwhereas the resulting photo current flowing in the circuit\nis measured by a microammeter (mA) The photoelectric\ncurrent can be increased or decreased by varying the\npotential of collector plate A with respect to the emitter\nplate C The intensity and frequency of the incident light\ncan be varied, as can the potential difference V between\nthe emitter C and the collector A" + }, + { + "Chapter": "9", + "sentence_range": "1665-1668", + "Text": "The potential difference between the emitter\nand collector plates is measured by a voltmeter (V)\nwhereas the resulting photo current flowing in the circuit\nis measured by a microammeter (mA) The photoelectric\ncurrent can be increased or decreased by varying the\npotential of collector plate A with respect to the emitter\nplate C The intensity and frequency of the incident light\ncan be varied, as can the potential difference V between\nthe emitter C and the collector A We can use the experimental arrangement of Fig" + }, + { + "Chapter": "9", + "sentence_range": "1666-1669", + "Text": "The photoelectric\ncurrent can be increased or decreased by varying the\npotential of collector plate A with respect to the emitter\nplate C The intensity and frequency of the incident light\ncan be varied, as can the potential difference V between\nthe emitter C and the collector A We can use the experimental arrangement of Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1667-1670", + "Text": "The intensity and frequency of the incident light\ncan be varied, as can the potential difference V between\nthe emitter C and the collector A We can use the experimental arrangement of Fig 11 1 to study the variation of photocurrent with (a)\nintensity of radiation, (b) frequency of incident radiation,\n(c) the potential difference between the plates A and C,\nand (d) the nature of the material of plate C" + }, + { + "Chapter": "9", + "sentence_range": "1668-1671", + "Text": "We can use the experimental arrangement of Fig 11 1 to study the variation of photocurrent with (a)\nintensity of radiation, (b) frequency of incident radiation,\n(c) the potential difference between the plates A and C,\nand (d) the nature of the material of plate C Light of\ndifferent frequencies can be used by putting appropriate\ncoloured filter or coloured glass in the path of light falling\nFIGURE 11" + }, + { + "Chapter": "9", + "sentence_range": "1669-1672", + "Text": "11 1 to study the variation of photocurrent with (a)\nintensity of radiation, (b) frequency of incident radiation,\n(c) the potential difference between the plates A and C,\nand (d) the nature of the material of plate C Light of\ndifferent frequencies can be used by putting appropriate\ncoloured filter or coloured glass in the path of light falling\nFIGURE 11 1 Experimental\narrangement for study of\nphotoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1670-1673", + "Text": "1 to study the variation of photocurrent with (a)\nintensity of radiation, (b) frequency of incident radiation,\n(c) the potential difference between the plates A and C,\nand (d) the nature of the material of plate C Light of\ndifferent frequencies can be used by putting appropriate\ncoloured filter or coloured glass in the path of light falling\nFIGURE 11 1 Experimental\narrangement for study of\nphotoelectric effect Rationalised 2023-24\nPhysics\n278\non the emitter C" + }, + { + "Chapter": "9", + "sentence_range": "1671-1674", + "Text": "Light of\ndifferent frequencies can be used by putting appropriate\ncoloured filter or coloured glass in the path of light falling\nFIGURE 11 1 Experimental\narrangement for study of\nphotoelectric effect Rationalised 2023-24\nPhysics\n278\non the emitter C The intensity of light is varied by changing\nthe distance of the light source from the emitter" + }, + { + "Chapter": "9", + "sentence_range": "1672-1675", + "Text": "1 Experimental\narrangement for study of\nphotoelectric effect Rationalised 2023-24\nPhysics\n278\non the emitter C The intensity of light is varied by changing\nthe distance of the light source from the emitter 11" + }, + { + "Chapter": "9", + "sentence_range": "1673-1676", + "Text": "Rationalised 2023-24\nPhysics\n278\non the emitter C The intensity of light is varied by changing\nthe distance of the light source from the emitter 11 4" + }, + { + "Chapter": "9", + "sentence_range": "1674-1677", + "Text": "The intensity of light is varied by changing\nthe distance of the light source from the emitter 11 4 1 Effect of intensity of light on photocurrent\nThe collector A is maintained at a positive potential with\nrespect to emitter C so that electrons ejected from C are\nattracted towards collector A" + }, + { + "Chapter": "9", + "sentence_range": "1675-1678", + "Text": "11 4 1 Effect of intensity of light on photocurrent\nThe collector A is maintained at a positive potential with\nrespect to emitter C so that electrons ejected from C are\nattracted towards collector A Keeping the frequency of the\nincident radiation and the potential fixed, the intensity of\nlight is varied and the resulting photoelectric current is\nmeasured each time" + }, + { + "Chapter": "9", + "sentence_range": "1676-1679", + "Text": "4 1 Effect of intensity of light on photocurrent\nThe collector A is maintained at a positive potential with\nrespect to emitter C so that electrons ejected from C are\nattracted towards collector A Keeping the frequency of the\nincident radiation and the potential fixed, the intensity of\nlight is varied and the resulting photoelectric current is\nmeasured each time It is found that the photocurrent\nincreases linearly with intensity of incident light as shown\ngraphically in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1677-1680", + "Text": "1 Effect of intensity of light on photocurrent\nThe collector A is maintained at a positive potential with\nrespect to emitter C so that electrons ejected from C are\nattracted towards collector A Keeping the frequency of the\nincident radiation and the potential fixed, the intensity of\nlight is varied and the resulting photoelectric current is\nmeasured each time It is found that the photocurrent\nincreases linearly with intensity of incident light as shown\ngraphically in Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1678-1681", + "Text": "Keeping the frequency of the\nincident radiation and the potential fixed, the intensity of\nlight is varied and the resulting photoelectric current is\nmeasured each time It is found that the photocurrent\nincreases linearly with intensity of incident light as shown\ngraphically in Fig 11 2" + }, + { + "Chapter": "9", + "sentence_range": "1679-1682", + "Text": "It is found that the photocurrent\nincreases linearly with intensity of incident light as shown\ngraphically in Fig 11 2 The photocurrent is directly\nproportional to the number of photoelectrons emitted per\nsecond" + }, + { + "Chapter": "9", + "sentence_range": "1680-1683", + "Text": "11 2 The photocurrent is directly\nproportional to the number of photoelectrons emitted per\nsecond This implies that the number of photoelectrons\nemitted per second is directly proportional to the intensity\nof incident radiation" + }, + { + "Chapter": "9", + "sentence_range": "1681-1684", + "Text": "2 The photocurrent is directly\nproportional to the number of photoelectrons emitted per\nsecond This implies that the number of photoelectrons\nemitted per second is directly proportional to the intensity\nof incident radiation 11" + }, + { + "Chapter": "9", + "sentence_range": "1682-1685", + "Text": "The photocurrent is directly\nproportional to the number of photoelectrons emitted per\nsecond This implies that the number of photoelectrons\nemitted per second is directly proportional to the intensity\nof incident radiation 11 4" + }, + { + "Chapter": "9", + "sentence_range": "1683-1686", + "Text": "This implies that the number of photoelectrons\nemitted per second is directly proportional to the intensity\nof incident radiation 11 4 2 Effect of potential on photoelectric current\nWe first keep the plate A at some positive potential with respect to the\nplate C and illuminate the plate C with light of fixed frequency n and fixed\nintensity I1" + }, + { + "Chapter": "9", + "sentence_range": "1684-1687", + "Text": "11 4 2 Effect of potential on photoelectric current\nWe first keep the plate A at some positive potential with respect to the\nplate C and illuminate the plate C with light of fixed frequency n and fixed\nintensity I1 We next vary the positive potential of plate A gradually and\nmeasure the resulting photocurrent each time" + }, + { + "Chapter": "9", + "sentence_range": "1685-1688", + "Text": "4 2 Effect of potential on photoelectric current\nWe first keep the plate A at some positive potential with respect to the\nplate C and illuminate the plate C with light of fixed frequency n and fixed\nintensity I1 We next vary the positive potential of plate A gradually and\nmeasure the resulting photocurrent each time It is found that the\nphotoelectric current increases with increase in positive (accelerating)\npotential" + }, + { + "Chapter": "9", + "sentence_range": "1686-1689", + "Text": "2 Effect of potential on photoelectric current\nWe first keep the plate A at some positive potential with respect to the\nplate C and illuminate the plate C with light of fixed frequency n and fixed\nintensity I1 We next vary the positive potential of plate A gradually and\nmeasure the resulting photocurrent each time It is found that the\nphotoelectric current increases with increase in positive (accelerating)\npotential At some stage, for a certain positive potential of plate A, all the\nemitted electrons are collected by the plate A and the photoelectric current\nbecomes maximum or saturates" + }, + { + "Chapter": "9", + "sentence_range": "1687-1690", + "Text": "We next vary the positive potential of plate A gradually and\nmeasure the resulting photocurrent each time It is found that the\nphotoelectric current increases with increase in positive (accelerating)\npotential At some stage, for a certain positive potential of plate A, all the\nemitted electrons are collected by the plate A and the photoelectric current\nbecomes maximum or saturates If we increase the accelerating potential\nof plate A further, the photocurrent does not increase" + }, + { + "Chapter": "9", + "sentence_range": "1688-1691", + "Text": "It is found that the\nphotoelectric current increases with increase in positive (accelerating)\npotential At some stage, for a certain positive potential of plate A, all the\nemitted electrons are collected by the plate A and the photoelectric current\nbecomes maximum or saturates If we increase the accelerating potential\nof plate A further, the photocurrent does not increase This maximum\nvalue of the photoelectric current is called saturation current" + }, + { + "Chapter": "9", + "sentence_range": "1689-1692", + "Text": "At some stage, for a certain positive potential of plate A, all the\nemitted electrons are collected by the plate A and the photoelectric current\nbecomes maximum or saturates If we increase the accelerating potential\nof plate A further, the photocurrent does not increase This maximum\nvalue of the photoelectric current is called saturation current Saturation\ncurrent corresponds to the case when all the photoelectrons emitted by\nthe emitter plate C reach the collector plate A" + }, + { + "Chapter": "9", + "sentence_range": "1690-1693", + "Text": "If we increase the accelerating potential\nof plate A further, the photocurrent does not increase This maximum\nvalue of the photoelectric current is called saturation current Saturation\ncurrent corresponds to the case when all the photoelectrons emitted by\nthe emitter plate C reach the collector plate A We now apply a negative (retarding)\npotential to the plate A with respect to the\nplate C and make it increasingly negative\ngradually" + }, + { + "Chapter": "9", + "sentence_range": "1691-1694", + "Text": "This maximum\nvalue of the photoelectric current is called saturation current Saturation\ncurrent corresponds to the case when all the photoelectrons emitted by\nthe emitter plate C reach the collector plate A We now apply a negative (retarding)\npotential to the plate A with respect to the\nplate C and make it increasingly negative\ngradually When the polarity is reversed,\nthe electrons are repelled and only the\nsufficiently energetic electrons are able to\nreach the collector A" + }, + { + "Chapter": "9", + "sentence_range": "1692-1695", + "Text": "Saturation\ncurrent corresponds to the case when all the photoelectrons emitted by\nthe emitter plate C reach the collector plate A We now apply a negative (retarding)\npotential to the plate A with respect to the\nplate C and make it increasingly negative\ngradually When the polarity is reversed,\nthe electrons are repelled and only the\nsufficiently energetic electrons are able to\nreach the collector A The photocurrent\nis found to decrease rapidly until it drops\nto zero at a certain sharply defined,\ncritical value of the negative potential V0\non the plate A" + }, + { + "Chapter": "9", + "sentence_range": "1693-1696", + "Text": "We now apply a negative (retarding)\npotential to the plate A with respect to the\nplate C and make it increasingly negative\ngradually When the polarity is reversed,\nthe electrons are repelled and only the\nsufficiently energetic electrons are able to\nreach the collector A The photocurrent\nis found to decrease rapidly until it drops\nto zero at a certain sharply defined,\ncritical value of the negative potential V0\non the plate A For a particular frequency\nof incident radiation, the minimum\nnegative (retarding) potential V0 given to\nthe plate A for which the photocurrent\nstops or becomes zero is called the cut-\noff or stopping potential" + }, + { + "Chapter": "9", + "sentence_range": "1694-1697", + "Text": "When the polarity is reversed,\nthe electrons are repelled and only the\nsufficiently energetic electrons are able to\nreach the collector A The photocurrent\nis found to decrease rapidly until it drops\nto zero at a certain sharply defined,\ncritical value of the negative potential V0\non the plate A For a particular frequency\nof incident radiation, the minimum\nnegative (retarding) potential V0 given to\nthe plate A for which the photocurrent\nstops or becomes zero is called the cut-\noff or stopping potential in The interpretation of the observation\nterms \nof \nphotoelectrons \nis\nstraightforward" + }, + { + "Chapter": "9", + "sentence_range": "1695-1698", + "Text": "The photocurrent\nis found to decrease rapidly until it drops\nto zero at a certain sharply defined,\ncritical value of the negative potential V0\non the plate A For a particular frequency\nof incident radiation, the minimum\nnegative (retarding) potential V0 given to\nthe plate A for which the photocurrent\nstops or becomes zero is called the cut-\noff or stopping potential in The interpretation of the observation\nterms \nof \nphotoelectrons \nis\nstraightforward All the photoelectrons\nemitted from the metal do not have the\nFIGURE 11" + }, + { + "Chapter": "9", + "sentence_range": "1696-1699", + "Text": "For a particular frequency\nof incident radiation, the minimum\nnegative (retarding) potential V0 given to\nthe plate A for which the photocurrent\nstops or becomes zero is called the cut-\noff or stopping potential in The interpretation of the observation\nterms \nof \nphotoelectrons \nis\nstraightforward All the photoelectrons\nemitted from the metal do not have the\nFIGURE 11 2 Variation of\nPhotoelectric current with\nintensity of light" + }, + { + "Chapter": "9", + "sentence_range": "1697-1700", + "Text": "in The interpretation of the observation\nterms \nof \nphotoelectrons \nis\nstraightforward All the photoelectrons\nemitted from the metal do not have the\nFIGURE 11 2 Variation of\nPhotoelectric current with\nintensity of light FIGURE 11" + }, + { + "Chapter": "9", + "sentence_range": "1698-1701", + "Text": "All the photoelectrons\nemitted from the metal do not have the\nFIGURE 11 2 Variation of\nPhotoelectric current with\nintensity of light FIGURE 11 3 Variation of photocurrent with\ncollector plate potential for different\nintensity of incident radiation" + }, + { + "Chapter": "9", + "sentence_range": "1699-1702", + "Text": "2 Variation of\nPhotoelectric current with\nintensity of light FIGURE 11 3 Variation of photocurrent with\ncollector plate potential for different\nintensity of incident radiation Rationalised 2023-24\n279\nDual Nature of Radiation\nand Matter\nsame energy" + }, + { + "Chapter": "9", + "sentence_range": "1700-1703", + "Text": "FIGURE 11 3 Variation of photocurrent with\ncollector plate potential for different\nintensity of incident radiation Rationalised 2023-24\n279\nDual Nature of Radiation\nand Matter\nsame energy Photoelectric current is zero when the stopping potential is\nsufficient to repel even the most energetic photoelectrons, with the\nmaximum kinetic energy (Kmax), so that\nKmax = e V0\n(11" + }, + { + "Chapter": "9", + "sentence_range": "1701-1704", + "Text": "3 Variation of photocurrent with\ncollector plate potential for different\nintensity of incident radiation Rationalised 2023-24\n279\nDual Nature of Radiation\nand Matter\nsame energy Photoelectric current is zero when the stopping potential is\nsufficient to repel even the most energetic photoelectrons, with the\nmaximum kinetic energy (Kmax), so that\nKmax = e V0\n(11 1)\nWe can now repeat this experiment with incident radiation of the same\nfrequency but of higher intensity I2 and I3 (I3 > I2 > I1)" + }, + { + "Chapter": "9", + "sentence_range": "1702-1705", + "Text": "Rationalised 2023-24\n279\nDual Nature of Radiation\nand Matter\nsame energy Photoelectric current is zero when the stopping potential is\nsufficient to repel even the most energetic photoelectrons, with the\nmaximum kinetic energy (Kmax), so that\nKmax = e V0\n(11 1)\nWe can now repeat this experiment with incident radiation of the same\nfrequency but of higher intensity I2 and I3 (I3 > I2 > I1) We note that the\nsaturation currents are now found to be at higher values" + }, + { + "Chapter": "9", + "sentence_range": "1703-1706", + "Text": "Photoelectric current is zero when the stopping potential is\nsufficient to repel even the most energetic photoelectrons, with the\nmaximum kinetic energy (Kmax), so that\nKmax = e V0\n(11 1)\nWe can now repeat this experiment with incident radiation of the same\nfrequency but of higher intensity I2 and I3 (I3 > I2 > I1) We note that the\nsaturation currents are now found to be at higher values This shows\nthat more electrons are being emitted per second, proportional to the\nintensity of incident radiation" + }, + { + "Chapter": "9", + "sentence_range": "1704-1707", + "Text": "1)\nWe can now repeat this experiment with incident radiation of the same\nfrequency but of higher intensity I2 and I3 (I3 > I2 > I1) We note that the\nsaturation currents are now found to be at higher values This shows\nthat more electrons are being emitted per second, proportional to the\nintensity of incident radiation But the stopping potential remains the\nsame as that for the incident radiation of intensity I1, as shown graphically\nin Fig" + }, + { + "Chapter": "9", + "sentence_range": "1705-1708", + "Text": "We note that the\nsaturation currents are now found to be at higher values This shows\nthat more electrons are being emitted per second, proportional to the\nintensity of incident radiation But the stopping potential remains the\nsame as that for the incident radiation of intensity I1, as shown graphically\nin Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1706-1709", + "Text": "This shows\nthat more electrons are being emitted per second, proportional to the\nintensity of incident radiation But the stopping potential remains the\nsame as that for the incident radiation of intensity I1, as shown graphically\nin Fig 11 3" + }, + { + "Chapter": "9", + "sentence_range": "1707-1710", + "Text": "But the stopping potential remains the\nsame as that for the incident radiation of intensity I1, as shown graphically\nin Fig 11 3 Thus, for a given frequency of the incident radiation, the\nstopping potential is independent of its intensity" + }, + { + "Chapter": "9", + "sentence_range": "1708-1711", + "Text": "11 3 Thus, for a given frequency of the incident radiation, the\nstopping potential is independent of its intensity In other words, the\nmaximum kinetic energy of photoelectrons depends on the light source\nand the emitter plate material, but is independent of intensity of incident\nradiation" + }, + { + "Chapter": "9", + "sentence_range": "1709-1712", + "Text": "3 Thus, for a given frequency of the incident radiation, the\nstopping potential is independent of its intensity In other words, the\nmaximum kinetic energy of photoelectrons depends on the light source\nand the emitter plate material, but is independent of intensity of incident\nradiation 11" + }, + { + "Chapter": "9", + "sentence_range": "1710-1713", + "Text": "Thus, for a given frequency of the incident radiation, the\nstopping potential is independent of its intensity In other words, the\nmaximum kinetic energy of photoelectrons depends on the light source\nand the emitter plate material, but is independent of intensity of incident\nradiation 11 4" + }, + { + "Chapter": "9", + "sentence_range": "1711-1714", + "Text": "In other words, the\nmaximum kinetic energy of photoelectrons depends on the light source\nand the emitter plate material, but is independent of intensity of incident\nradiation 11 4 3 Effect of frequency of incident radiation on\nstopping potential\nFIGURE 11" + }, + { + "Chapter": "9", + "sentence_range": "1712-1715", + "Text": "11 4 3 Effect of frequency of incident radiation on\nstopping potential\nFIGURE 11 4 Variation of photoelectric current\nwith collector plate potential for different\nfrequencies of incident radiation" + }, + { + "Chapter": "9", + "sentence_range": "1713-1716", + "Text": "4 3 Effect of frequency of incident radiation on\nstopping potential\nFIGURE 11 4 Variation of photoelectric current\nwith collector plate potential for different\nfrequencies of incident radiation FIGURE 11" + }, + { + "Chapter": "9", + "sentence_range": "1714-1717", + "Text": "3 Effect of frequency of incident radiation on\nstopping potential\nFIGURE 11 4 Variation of photoelectric current\nwith collector plate potential for different\nfrequencies of incident radiation FIGURE 11 5 Variation of stopping potential V0\nwith frequency n of incident radiation for a\ngiven photosensitive material" + }, + { + "Chapter": "9", + "sentence_range": "1715-1718", + "Text": "4 Variation of photoelectric current\nwith collector plate potential for different\nfrequencies of incident radiation FIGURE 11 5 Variation of stopping potential V0\nwith frequency n of incident radiation for a\ngiven photosensitive material We now study the relation between the frequency\nn of the incident radiation and the stopping\npotential V0" + }, + { + "Chapter": "9", + "sentence_range": "1716-1719", + "Text": "FIGURE 11 5 Variation of stopping potential V0\nwith frequency n of incident radiation for a\ngiven photosensitive material We now study the relation between the frequency\nn of the incident radiation and the stopping\npotential V0 We suitably adjust the same\nintensity of light radiation at various frequencies\nand study the variation of photocurrent with\ncollector plate potential" + }, + { + "Chapter": "9", + "sentence_range": "1717-1720", + "Text": "5 Variation of stopping potential V0\nwith frequency n of incident radiation for a\ngiven photosensitive material We now study the relation between the frequency\nn of the incident radiation and the stopping\npotential V0 We suitably adjust the same\nintensity of light radiation at various frequencies\nand study the variation of photocurrent with\ncollector plate potential The resulting variation\nis shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1718-1721", + "Text": "We now study the relation between the frequency\nn of the incident radiation and the stopping\npotential V0 We suitably adjust the same\nintensity of light radiation at various frequencies\nand study the variation of photocurrent with\ncollector plate potential The resulting variation\nis shown in Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1719-1722", + "Text": "We suitably adjust the same\nintensity of light radiation at various frequencies\nand study the variation of photocurrent with\ncollector plate potential The resulting variation\nis shown in Fig 11 4" + }, + { + "Chapter": "9", + "sentence_range": "1720-1723", + "Text": "The resulting variation\nis shown in Fig 11 4 We obtain different values\nof stopping potential but the same value of the\nsaturation current for incident radiation of\ndifferent frequencies" + }, + { + "Chapter": "9", + "sentence_range": "1721-1724", + "Text": "11 4 We obtain different values\nof stopping potential but the same value of the\nsaturation current for incident radiation of\ndifferent frequencies The energy of the emitted\nelectrons depends on the frequency of the\nincident radiations" + }, + { + "Chapter": "9", + "sentence_range": "1722-1725", + "Text": "4 We obtain different values\nof stopping potential but the same value of the\nsaturation current for incident radiation of\ndifferent frequencies The energy of the emitted\nelectrons depends on the frequency of the\nincident radiations The stopping potential is\nmore negative for higher frequencies of incident\nradiation" + }, + { + "Chapter": "9", + "sentence_range": "1723-1726", + "Text": "We obtain different values\nof stopping potential but the same value of the\nsaturation current for incident radiation of\ndifferent frequencies The energy of the emitted\nelectrons depends on the frequency of the\nincident radiations The stopping potential is\nmore negative for higher frequencies of incident\nradiation Note from Fig" + }, + { + "Chapter": "9", + "sentence_range": "1724-1727", + "Text": "The energy of the emitted\nelectrons depends on the frequency of the\nincident radiations The stopping potential is\nmore negative for higher frequencies of incident\nradiation Note from Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1725-1728", + "Text": "The stopping potential is\nmore negative for higher frequencies of incident\nradiation Note from Fig 11 4 that the stopping\npotentials are in the order V03 > V02 > V01 if the\nfrequencies are in the order n3 > n2 > n1" + }, + { + "Chapter": "9", + "sentence_range": "1726-1729", + "Text": "Note from Fig 11 4 that the stopping\npotentials are in the order V03 > V02 > V01 if the\nfrequencies are in the order n3 > n2 > n1 This\nimplies that greater the frequency of incident\nlight, greater is the maximum kinetic energy of\nthe photoelectrons" + }, + { + "Chapter": "9", + "sentence_range": "1727-1730", + "Text": "11 4 that the stopping\npotentials are in the order V03 > V02 > V01 if the\nfrequencies are in the order n3 > n2 > n1 This\nimplies that greater the frequency of incident\nlight, greater is the maximum kinetic energy of\nthe photoelectrons Consequently, we need\ngreater retarding potential to stop them\ncompletely" + }, + { + "Chapter": "9", + "sentence_range": "1728-1731", + "Text": "4 that the stopping\npotentials are in the order V03 > V02 > V01 if the\nfrequencies are in the order n3 > n2 > n1 This\nimplies that greater the frequency of incident\nlight, greater is the maximum kinetic energy of\nthe photoelectrons Consequently, we need\ngreater retarding potential to stop them\ncompletely If we plot a graph between the\nfrequency of incident radiation and the\ncorresponding stopping potential for different\nmetals we get a straight line, as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1729-1732", + "Text": "This\nimplies that greater the frequency of incident\nlight, greater is the maximum kinetic energy of\nthe photoelectrons Consequently, we need\ngreater retarding potential to stop them\ncompletely If we plot a graph between the\nfrequency of incident radiation and the\ncorresponding stopping potential for different\nmetals we get a straight line, as shown in Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1730-1733", + "Text": "Consequently, we need\ngreater retarding potential to stop them\ncompletely If we plot a graph between the\nfrequency of incident radiation and the\ncorresponding stopping potential for different\nmetals we get a straight line, as shown in Fig 11 5" + }, + { + "Chapter": "9", + "sentence_range": "1731-1734", + "Text": "If we plot a graph between the\nfrequency of incident radiation and the\ncorresponding stopping potential for different\nmetals we get a straight line, as shown in Fig 11 5 The graph shows that\n(i)\nthe stopping potential V0 varies linearly with\nthe frequency of incident radiation for a given\nphotosensitive material" + }, + { + "Chapter": "9", + "sentence_range": "1732-1735", + "Text": "11 5 The graph shows that\n(i)\nthe stopping potential V0 varies linearly with\nthe frequency of incident radiation for a given\nphotosensitive material (ii) there exists a certain minimum cut-off\nfrequency n0 for which the stopping potential\nis zero" + }, + { + "Chapter": "9", + "sentence_range": "1733-1736", + "Text": "5 The graph shows that\n(i)\nthe stopping potential V0 varies linearly with\nthe frequency of incident radiation for a given\nphotosensitive material (ii) there exists a certain minimum cut-off\nfrequency n0 for which the stopping potential\nis zero Rationalised 2023-24\nPhysics\n280\nThese observations have two implications:\n(i)\nThe maximum kinetic energy of the photoelectrons varies linearly\nwith the frequency of incident radiation, but is independent of its\nintensity" + }, + { + "Chapter": "9", + "sentence_range": "1734-1737", + "Text": "The graph shows that\n(i)\nthe stopping potential V0 varies linearly with\nthe frequency of incident radiation for a given\nphotosensitive material (ii) there exists a certain minimum cut-off\nfrequency n0 for which the stopping potential\nis zero Rationalised 2023-24\nPhysics\n280\nThese observations have two implications:\n(i)\nThe maximum kinetic energy of the photoelectrons varies linearly\nwith the frequency of incident radiation, but is independent of its\nintensity (ii) For a frequency n of incident radiation, lower than the cut-off\nfrequency n0, no photoelectric emission is possible even if the\nintensity is large" + }, + { + "Chapter": "9", + "sentence_range": "1735-1738", + "Text": "(ii) there exists a certain minimum cut-off\nfrequency n0 for which the stopping potential\nis zero Rationalised 2023-24\nPhysics\n280\nThese observations have two implications:\n(i)\nThe maximum kinetic energy of the photoelectrons varies linearly\nwith the frequency of incident radiation, but is independent of its\nintensity (ii) For a frequency n of incident radiation, lower than the cut-off\nfrequency n0, no photoelectric emission is possible even if the\nintensity is large This minimum, cut-off frequency n0, is called the threshold frequency" + }, + { + "Chapter": "9", + "sentence_range": "1736-1739", + "Text": "Rationalised 2023-24\nPhysics\n280\nThese observations have two implications:\n(i)\nThe maximum kinetic energy of the photoelectrons varies linearly\nwith the frequency of incident radiation, but is independent of its\nintensity (ii) For a frequency n of incident radiation, lower than the cut-off\nfrequency n0, no photoelectric emission is possible even if the\nintensity is large This minimum, cut-off frequency n0, is called the threshold frequency It is different for different metals" + }, + { + "Chapter": "9", + "sentence_range": "1737-1740", + "Text": "(ii) For a frequency n of incident radiation, lower than the cut-off\nfrequency n0, no photoelectric emission is possible even if the\nintensity is large This minimum, cut-off frequency n0, is called the threshold frequency It is different for different metals Different photosensitive materials respond differently to light" + }, + { + "Chapter": "9", + "sentence_range": "1738-1741", + "Text": "This minimum, cut-off frequency n0, is called the threshold frequency It is different for different metals Different photosensitive materials respond differently to light Selenium\nis more sensitive than zinc or copper" + }, + { + "Chapter": "9", + "sentence_range": "1739-1742", + "Text": "It is different for different metals Different photosensitive materials respond differently to light Selenium\nis more sensitive than zinc or copper The same photosensitive substance\ngives different response to light of different wavelengths" + }, + { + "Chapter": "9", + "sentence_range": "1740-1743", + "Text": "Different photosensitive materials respond differently to light Selenium\nis more sensitive than zinc or copper The same photosensitive substance\ngives different response to light of different wavelengths For example,\nultraviolet light gives rise to photoelectric effect in copper while green or\nred light does not" + }, + { + "Chapter": "9", + "sentence_range": "1741-1744", + "Text": "Selenium\nis more sensitive than zinc or copper The same photosensitive substance\ngives different response to light of different wavelengths For example,\nultraviolet light gives rise to photoelectric effect in copper while green or\nred light does not Note that in all the above experiments, it is found that, if frequency of\nthe incident radiation exceeds the threshold frequency, the photoelectric\nemission starts instantaneously without any apparent time lag, even if\nthe incident radiation is very dim" + }, + { + "Chapter": "9", + "sentence_range": "1742-1745", + "Text": "The same photosensitive substance\ngives different response to light of different wavelengths For example,\nultraviolet light gives rise to photoelectric effect in copper while green or\nred light does not Note that in all the above experiments, it is found that, if frequency of\nthe incident radiation exceeds the threshold frequency, the photoelectric\nemission starts instantaneously without any apparent time lag, even if\nthe incident radiation is very dim It is now known that emission starts in\na time of the order of 10\u2013 9 s or less" + }, + { + "Chapter": "9", + "sentence_range": "1743-1746", + "Text": "For example,\nultraviolet light gives rise to photoelectric effect in copper while green or\nred light does not Note that in all the above experiments, it is found that, if frequency of\nthe incident radiation exceeds the threshold frequency, the photoelectric\nemission starts instantaneously without any apparent time lag, even if\nthe incident radiation is very dim It is now known that emission starts in\na time of the order of 10\u2013 9 s or less We now summarise the experimental features and observations\ndescribed in this section" + }, + { + "Chapter": "9", + "sentence_range": "1744-1747", + "Text": "Note that in all the above experiments, it is found that, if frequency of\nthe incident radiation exceeds the threshold frequency, the photoelectric\nemission starts instantaneously without any apparent time lag, even if\nthe incident radiation is very dim It is now known that emission starts in\na time of the order of 10\u2013 9 s or less We now summarise the experimental features and observations\ndescribed in this section (i)\nFor a given photosensitive material and frequency of incident radiation\n(above the threshold frequency), the photoelectric current is directly\nproportional to the intensity of incident light (Fig" + }, + { + "Chapter": "9", + "sentence_range": "1745-1748", + "Text": "It is now known that emission starts in\na time of the order of 10\u2013 9 s or less We now summarise the experimental features and observations\ndescribed in this section (i)\nFor a given photosensitive material and frequency of incident radiation\n(above the threshold frequency), the photoelectric current is directly\nproportional to the intensity of incident light (Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1746-1749", + "Text": "We now summarise the experimental features and observations\ndescribed in this section (i)\nFor a given photosensitive material and frequency of incident radiation\n(above the threshold frequency), the photoelectric current is directly\nproportional to the intensity of incident light (Fig 11 2)" + }, + { + "Chapter": "9", + "sentence_range": "1747-1750", + "Text": "(i)\nFor a given photosensitive material and frequency of incident radiation\n(above the threshold frequency), the photoelectric current is directly\nproportional to the intensity of incident light (Fig 11 2) (ii) For a given photosensitive material and frequency of incident radiation,\nsaturation current is found to be proportional to the intensity of\nincident radiation whereas the stopping potential is independent of\nits intensity (Fig" + }, + { + "Chapter": "9", + "sentence_range": "1748-1751", + "Text": "11 2) (ii) For a given photosensitive material and frequency of incident radiation,\nsaturation current is found to be proportional to the intensity of\nincident radiation whereas the stopping potential is independent of\nits intensity (Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1749-1752", + "Text": "2) (ii) For a given photosensitive material and frequency of incident radiation,\nsaturation current is found to be proportional to the intensity of\nincident radiation whereas the stopping potential is independent of\nits intensity (Fig 11 3)" + }, + { + "Chapter": "9", + "sentence_range": "1750-1753", + "Text": "(ii) For a given photosensitive material and frequency of incident radiation,\nsaturation current is found to be proportional to the intensity of\nincident radiation whereas the stopping potential is independent of\nits intensity (Fig 11 3) (iii) For a given photosensitive material, there exists a certain minimum\ncut-off frequency of the incident radiation, called the threshold\nfrequency, below which no emission of photoelectrons takes place,\nno matter how intense the incident light is" + }, + { + "Chapter": "9", + "sentence_range": "1751-1754", + "Text": "11 3) (iii) For a given photosensitive material, there exists a certain minimum\ncut-off frequency of the incident radiation, called the threshold\nfrequency, below which no emission of photoelectrons takes place,\nno matter how intense the incident light is Above the threshold\nfrequency, the stopping potential or equivalently the maximum kinetic\nenergy of the emitted photoelectrons increases linearly with the\nfrequency of the incident radiation, but is independent of its intensity\n(Fig" + }, + { + "Chapter": "9", + "sentence_range": "1752-1755", + "Text": "3) (iii) For a given photosensitive material, there exists a certain minimum\ncut-off frequency of the incident radiation, called the threshold\nfrequency, below which no emission of photoelectrons takes place,\nno matter how intense the incident light is Above the threshold\nfrequency, the stopping potential or equivalently the maximum kinetic\nenergy of the emitted photoelectrons increases linearly with the\nfrequency of the incident radiation, but is independent of its intensity\n(Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1753-1756", + "Text": "(iii) For a given photosensitive material, there exists a certain minimum\ncut-off frequency of the incident radiation, called the threshold\nfrequency, below which no emission of photoelectrons takes place,\nno matter how intense the incident light is Above the threshold\nfrequency, the stopping potential or equivalently the maximum kinetic\nenergy of the emitted photoelectrons increases linearly with the\nfrequency of the incident radiation, but is independent of its intensity\n(Fig 11 5)" + }, + { + "Chapter": "9", + "sentence_range": "1754-1757", + "Text": "Above the threshold\nfrequency, the stopping potential or equivalently the maximum kinetic\nenergy of the emitted photoelectrons increases linearly with the\nfrequency of the incident radiation, but is independent of its intensity\n(Fig 11 5) (iv) The photoelectric emission is an instantaneous process without any\napparent time lag (~10\u2013 9s or less), even when the incident radiation is\nmade exceedingly dim" + }, + { + "Chapter": "9", + "sentence_range": "1755-1758", + "Text": "11 5) (iv) The photoelectric emission is an instantaneous process without any\napparent time lag (~10\u2013 9s or less), even when the incident radiation is\nmade exceedingly dim 11" + }, + { + "Chapter": "9", + "sentence_range": "1756-1759", + "Text": "5) (iv) The photoelectric emission is an instantaneous process without any\napparent time lag (~10\u2013 9s or less), even when the incident radiation is\nmade exceedingly dim 11 5 PHOTOELECTRIC EFFECT AND WAVE THEORY\nOF LIGHT\nThe wave nature of light was well established by the end of the nineteenth\ncentury" + }, + { + "Chapter": "9", + "sentence_range": "1757-1760", + "Text": "(iv) The photoelectric emission is an instantaneous process without any\napparent time lag (~10\u2013 9s or less), even when the incident radiation is\nmade exceedingly dim 11 5 PHOTOELECTRIC EFFECT AND WAVE THEORY\nOF LIGHT\nThe wave nature of light was well established by the end of the nineteenth\ncentury The phenomena of interference, diffraction and polarisation were\nexplained in a natural and satisfactory way by the wave picture of light" + }, + { + "Chapter": "9", + "sentence_range": "1758-1761", + "Text": "11 5 PHOTOELECTRIC EFFECT AND WAVE THEORY\nOF LIGHT\nThe wave nature of light was well established by the end of the nineteenth\ncentury The phenomena of interference, diffraction and polarisation were\nexplained in a natural and satisfactory way by the wave picture of light According to this picture, light is an electromagnetic wave consisting of\nelectric and magnetic fields with continuous distribution of energy over\nthe region of space over which the wave is extended" + }, + { + "Chapter": "9", + "sentence_range": "1759-1762", + "Text": "5 PHOTOELECTRIC EFFECT AND WAVE THEORY\nOF LIGHT\nThe wave nature of light was well established by the end of the nineteenth\ncentury The phenomena of interference, diffraction and polarisation were\nexplained in a natural and satisfactory way by the wave picture of light According to this picture, light is an electromagnetic wave consisting of\nelectric and magnetic fields with continuous distribution of energy over\nthe region of space over which the wave is extended Let us now see if this\nRationalised 2023-24\n281\nDual Nature of Radiation\nand Matter\nwave picture of light can explain the observations on photoelectric\nemission given in the previous section" + }, + { + "Chapter": "9", + "sentence_range": "1760-1763", + "Text": "The phenomena of interference, diffraction and polarisation were\nexplained in a natural and satisfactory way by the wave picture of light According to this picture, light is an electromagnetic wave consisting of\nelectric and magnetic fields with continuous distribution of energy over\nthe region of space over which the wave is extended Let us now see if this\nRationalised 2023-24\n281\nDual Nature of Radiation\nand Matter\nwave picture of light can explain the observations on photoelectric\nemission given in the previous section According to the wave picture of light, the free electrons at the surface\nof the metal (over which the beam of radiation falls) absorb the radiant\nenergy continuously" + }, + { + "Chapter": "9", + "sentence_range": "1761-1764", + "Text": "According to this picture, light is an electromagnetic wave consisting of\nelectric and magnetic fields with continuous distribution of energy over\nthe region of space over which the wave is extended Let us now see if this\nRationalised 2023-24\n281\nDual Nature of Radiation\nand Matter\nwave picture of light can explain the observations on photoelectric\nemission given in the previous section According to the wave picture of light, the free electrons at the surface\nof the metal (over which the beam of radiation falls) absorb the radiant\nenergy continuously The greater the intensity of radiation, the greater are\nthe amplitude of electric and magnetic fields" + }, + { + "Chapter": "9", + "sentence_range": "1762-1765", + "Text": "Let us now see if this\nRationalised 2023-24\n281\nDual Nature of Radiation\nand Matter\nwave picture of light can explain the observations on photoelectric\nemission given in the previous section According to the wave picture of light, the free electrons at the surface\nof the metal (over which the beam of radiation falls) absorb the radiant\nenergy continuously The greater the intensity of radiation, the greater are\nthe amplitude of electric and magnetic fields Consequently, the greater\nthe intensity, the greater should be the energy absorbed by each electron" + }, + { + "Chapter": "9", + "sentence_range": "1763-1766", + "Text": "According to the wave picture of light, the free electrons at the surface\nof the metal (over which the beam of radiation falls) absorb the radiant\nenergy continuously The greater the intensity of radiation, the greater are\nthe amplitude of electric and magnetic fields Consequently, the greater\nthe intensity, the greater should be the energy absorbed by each electron In this picture, the maximum kinetic energy of the photoelectrons on the\nsurface is then expected to increase with increase in intensity" + }, + { + "Chapter": "9", + "sentence_range": "1764-1767", + "Text": "The greater the intensity of radiation, the greater are\nthe amplitude of electric and magnetic fields Consequently, the greater\nthe intensity, the greater should be the energy absorbed by each electron In this picture, the maximum kinetic energy of the photoelectrons on the\nsurface is then expected to increase with increase in intensity Also, no\nmatter what the frequency of radiation is, a sufficiently intense beam of\nradiation (over sufficient time) should be able to impart enough energy to\nthe electrons, so that they exceed the minimum energy needed to escape\nfrom the metal surface" + }, + { + "Chapter": "9", + "sentence_range": "1765-1768", + "Text": "Consequently, the greater\nthe intensity, the greater should be the energy absorbed by each electron In this picture, the maximum kinetic energy of the photoelectrons on the\nsurface is then expected to increase with increase in intensity Also, no\nmatter what the frequency of radiation is, a sufficiently intense beam of\nradiation (over sufficient time) should be able to impart enough energy to\nthe electrons, so that they exceed the minimum energy needed to escape\nfrom the metal surface A threshold frequency, therefore, should not exist" + }, + { + "Chapter": "9", + "sentence_range": "1766-1769", + "Text": "In this picture, the maximum kinetic energy of the photoelectrons on the\nsurface is then expected to increase with increase in intensity Also, no\nmatter what the frequency of radiation is, a sufficiently intense beam of\nradiation (over sufficient time) should be able to impart enough energy to\nthe electrons, so that they exceed the minimum energy needed to escape\nfrom the metal surface A threshold frequency, therefore, should not exist These expectations of the wave theory directly contradict observations (i),\n(ii) and (iii) given at the end of sub-section 11" + }, + { + "Chapter": "9", + "sentence_range": "1767-1770", + "Text": "Also, no\nmatter what the frequency of radiation is, a sufficiently intense beam of\nradiation (over sufficient time) should be able to impart enough energy to\nthe electrons, so that they exceed the minimum energy needed to escape\nfrom the metal surface A threshold frequency, therefore, should not exist These expectations of the wave theory directly contradict observations (i),\n(ii) and (iii) given at the end of sub-section 11 4" + }, + { + "Chapter": "9", + "sentence_range": "1768-1771", + "Text": "A threshold frequency, therefore, should not exist These expectations of the wave theory directly contradict observations (i),\n(ii) and (iii) given at the end of sub-section 11 4 3" + }, + { + "Chapter": "9", + "sentence_range": "1769-1772", + "Text": "These expectations of the wave theory directly contradict observations (i),\n(ii) and (iii) given at the end of sub-section 11 4 3 Further, we should note that in the wave picture, the absorption of\nenergy by electron takes place continuously over the entire\nwavefront of the radiation" + }, + { + "Chapter": "9", + "sentence_range": "1770-1773", + "Text": "4 3 Further, we should note that in the wave picture, the absorption of\nenergy by electron takes place continuously over the entire\nwavefront of the radiation Since a large number of electrons absorb energy,\nthe energy absorbed per electron per unit time turns out to be small" + }, + { + "Chapter": "9", + "sentence_range": "1771-1774", + "Text": "3 Further, we should note that in the wave picture, the absorption of\nenergy by electron takes place continuously over the entire\nwavefront of the radiation Since a large number of electrons absorb energy,\nthe energy absorbed per electron per unit time turns out to be small Explicit calculations estimate that it can take hours or more for a single\nelectron to pick up sufficient energy to overcome the work function and\ncome out of the metal" + }, + { + "Chapter": "9", + "sentence_range": "1772-1775", + "Text": "Further, we should note that in the wave picture, the absorption of\nenergy by electron takes place continuously over the entire\nwavefront of the radiation Since a large number of electrons absorb energy,\nthe energy absorbed per electron per unit time turns out to be small Explicit calculations estimate that it can take hours or more for a single\nelectron to pick up sufficient energy to overcome the work function and\ncome out of the metal This conclusion is again in striking contrast to\nobservation (iv) that the photoelectric emission is instantaneous" + }, + { + "Chapter": "9", + "sentence_range": "1773-1776", + "Text": "Since a large number of electrons absorb energy,\nthe energy absorbed per electron per unit time turns out to be small Explicit calculations estimate that it can take hours or more for a single\nelectron to pick up sufficient energy to overcome the work function and\ncome out of the metal This conclusion is again in striking contrast to\nobservation (iv) that the photoelectric emission is instantaneous In short,\nthe wave picture is unable to explain the most basic features of\nphotoelectric emission" + }, + { + "Chapter": "9", + "sentence_range": "1774-1777", + "Text": "Explicit calculations estimate that it can take hours or more for a single\nelectron to pick up sufficient energy to overcome the work function and\ncome out of the metal This conclusion is again in striking contrast to\nobservation (iv) that the photoelectric emission is instantaneous In short,\nthe wave picture is unable to explain the most basic features of\nphotoelectric emission 11" + }, + { + "Chapter": "9", + "sentence_range": "1775-1778", + "Text": "This conclusion is again in striking contrast to\nobservation (iv) that the photoelectric emission is instantaneous In short,\nthe wave picture is unable to explain the most basic features of\nphotoelectric emission 11 6 EINSTEIN\u2019S PHOTOELECTRIC EQUATION: ENERGY\nQUANTUM OF RADIATION\nIn 1905, Albert Einstein (1879-1955) proposed a radically new picture\nof electromagnetic radiation to explain photoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1776-1779", + "Text": "In short,\nthe wave picture is unable to explain the most basic features of\nphotoelectric emission 11 6 EINSTEIN\u2019S PHOTOELECTRIC EQUATION: ENERGY\nQUANTUM OF RADIATION\nIn 1905, Albert Einstein (1879-1955) proposed a radically new picture\nof electromagnetic radiation to explain photoelectric effect In this picture,\nphotoelectric emission does not take place by continuous absorption of\nenergy from radiation" + }, + { + "Chapter": "9", + "sentence_range": "1777-1780", + "Text": "11 6 EINSTEIN\u2019S PHOTOELECTRIC EQUATION: ENERGY\nQUANTUM OF RADIATION\nIn 1905, Albert Einstein (1879-1955) proposed a radically new picture\nof electromagnetic radiation to explain photoelectric effect In this picture,\nphotoelectric emission does not take place by continuous absorption of\nenergy from radiation Radiation energy is built up of discrete units \u2013 the\nso called quanta of energy of radiation" + }, + { + "Chapter": "9", + "sentence_range": "1778-1781", + "Text": "6 EINSTEIN\u2019S PHOTOELECTRIC EQUATION: ENERGY\nQUANTUM OF RADIATION\nIn 1905, Albert Einstein (1879-1955) proposed a radically new picture\nof electromagnetic radiation to explain photoelectric effect In this picture,\nphotoelectric emission does not take place by continuous absorption of\nenergy from radiation Radiation energy is built up of discrete units \u2013 the\nso called quanta of energy of radiation Each quantum of radiant energy\nhas energy hn, where h is Planck\u2019s constant and n the frequency of light" + }, + { + "Chapter": "9", + "sentence_range": "1779-1782", + "Text": "In this picture,\nphotoelectric emission does not take place by continuous absorption of\nenergy from radiation Radiation energy is built up of discrete units \u2013 the\nso called quanta of energy of radiation Each quantum of radiant energy\nhas energy hn, where h is Planck\u2019s constant and n the frequency of light In photoelectric effect, an electron absorbs a quantum of energy (hn ) of\nradiation" + }, + { + "Chapter": "9", + "sentence_range": "1780-1783", + "Text": "Radiation energy is built up of discrete units \u2013 the\nso called quanta of energy of radiation Each quantum of radiant energy\nhas energy hn, where h is Planck\u2019s constant and n the frequency of light In photoelectric effect, an electron absorbs a quantum of energy (hn ) of\nradiation If this quantum of energy absorbed exceeds the minimum\nenergy needed for the electron to escape from the metal surface (work\nfunction f0), the electron is emitted with maximum kinetic energy\nKmax = hn \u2013 f0\n(11" + }, + { + "Chapter": "9", + "sentence_range": "1781-1784", + "Text": "Each quantum of radiant energy\nhas energy hn, where h is Planck\u2019s constant and n the frequency of light In photoelectric effect, an electron absorbs a quantum of energy (hn ) of\nradiation If this quantum of energy absorbed exceeds the minimum\nenergy needed for the electron to escape from the metal surface (work\nfunction f0), the electron is emitted with maximum kinetic energy\nKmax = hn \u2013 f0\n(11 2)\nMore tightly bound electrons will emerge with kinetic energies less\nthan the maximum value" + }, + { + "Chapter": "9", + "sentence_range": "1782-1785", + "Text": "In photoelectric effect, an electron absorbs a quantum of energy (hn ) of\nradiation If this quantum of energy absorbed exceeds the minimum\nenergy needed for the electron to escape from the metal surface (work\nfunction f0), the electron is emitted with maximum kinetic energy\nKmax = hn \u2013 f0\n(11 2)\nMore tightly bound electrons will emerge with kinetic energies less\nthan the maximum value Note that the intensity of light of a given\nfrequency is determined by the number of photons incident per second" + }, + { + "Chapter": "9", + "sentence_range": "1783-1786", + "Text": "If this quantum of energy absorbed exceeds the minimum\nenergy needed for the electron to escape from the metal surface (work\nfunction f0), the electron is emitted with maximum kinetic energy\nKmax = hn \u2013 f0\n(11 2)\nMore tightly bound electrons will emerge with kinetic energies less\nthan the maximum value Note that the intensity of light of a given\nfrequency is determined by the number of photons incident per second Increasing the intensity will increase the number of emitted electrons per\nsecond" + }, + { + "Chapter": "9", + "sentence_range": "1784-1787", + "Text": "2)\nMore tightly bound electrons will emerge with kinetic energies less\nthan the maximum value Note that the intensity of light of a given\nfrequency is determined by the number of photons incident per second Increasing the intensity will increase the number of emitted electrons per\nsecond However, the maximum kinetic energy of the emitted\nphotoelectrons is determined by the energy of each photon" + }, + { + "Chapter": "9", + "sentence_range": "1785-1788", + "Text": "Note that the intensity of light of a given\nfrequency is determined by the number of photons incident per second Increasing the intensity will increase the number of emitted electrons per\nsecond However, the maximum kinetic energy of the emitted\nphotoelectrons is determined by the energy of each photon Equation (11" + }, + { + "Chapter": "9", + "sentence_range": "1786-1789", + "Text": "Increasing the intensity will increase the number of emitted electrons per\nsecond However, the maximum kinetic energy of the emitted\nphotoelectrons is determined by the energy of each photon Equation (11 2) is known as Einstein\u2019s photoelectric equation" + }, + { + "Chapter": "9", + "sentence_range": "1787-1790", + "Text": "However, the maximum kinetic energy of the emitted\nphotoelectrons is determined by the energy of each photon Equation (11 2) is known as Einstein\u2019s photoelectric equation We\nnow see how this equation accounts in a simple and elegant manner all\nthe observations on photoelectric effect given at the end of sub-section\n11" + }, + { + "Chapter": "9", + "sentence_range": "1788-1791", + "Text": "Equation (11 2) is known as Einstein\u2019s photoelectric equation We\nnow see how this equation accounts in a simple and elegant manner all\nthe observations on photoelectric effect given at the end of sub-section\n11 4" + }, + { + "Chapter": "9", + "sentence_range": "1789-1792", + "Text": "2) is known as Einstein\u2019s photoelectric equation We\nnow see how this equation accounts in a simple and elegant manner all\nthe observations on photoelectric effect given at the end of sub-section\n11 4 3" + }, + { + "Chapter": "9", + "sentence_range": "1790-1793", + "Text": "We\nnow see how this equation accounts in a simple and elegant manner all\nthe observations on photoelectric effect given at the end of sub-section\n11 4 3 Rationalised 2023-24\nPhysics\n282\n\u00b7\nAccording to Eq" + }, + { + "Chapter": "9", + "sentence_range": "1791-1794", + "Text": "4 3 Rationalised 2023-24\nPhysics\n282\n\u00b7\nAccording to Eq (11" + }, + { + "Chapter": "9", + "sentence_range": "1792-1795", + "Text": "3 Rationalised 2023-24\nPhysics\n282\n\u00b7\nAccording to Eq (11 2), Kmax depends linearly on n,\nand is independent of intensity of radiation, in\nagreement with observation" + }, + { + "Chapter": "9", + "sentence_range": "1793-1796", + "Text": "Rationalised 2023-24\nPhysics\n282\n\u00b7\nAccording to Eq (11 2), Kmax depends linearly on n,\nand is independent of intensity of radiation, in\nagreement with observation This has happened\nbecause in Einstein\u2019s picture, photoelectric effect arises\nfrom the absorption of a single quantum of radiation\nby a single electron" + }, + { + "Chapter": "9", + "sentence_range": "1794-1797", + "Text": "(11 2), Kmax depends linearly on n,\nand is independent of intensity of radiation, in\nagreement with observation This has happened\nbecause in Einstein\u2019s picture, photoelectric effect arises\nfrom the absorption of a single quantum of radiation\nby a single electron The intensity of radiation (that is\nproportional to the number of energy quanta per unit\narea per unit time) is irrelevant to this basic process" + }, + { + "Chapter": "9", + "sentence_range": "1795-1798", + "Text": "2), Kmax depends linearly on n,\nand is independent of intensity of radiation, in\nagreement with observation This has happened\nbecause in Einstein\u2019s picture, photoelectric effect arises\nfrom the absorption of a single quantum of radiation\nby a single electron The intensity of radiation (that is\nproportional to the number of energy quanta per unit\narea per unit time) is irrelevant to this basic process \u00b7\nSince Kmax must be non-negative, Eq" + }, + { + "Chapter": "9", + "sentence_range": "1796-1799", + "Text": "This has happened\nbecause in Einstein\u2019s picture, photoelectric effect arises\nfrom the absorption of a single quantum of radiation\nby a single electron The intensity of radiation (that is\nproportional to the number of energy quanta per unit\narea per unit time) is irrelevant to this basic process \u00b7\nSince Kmax must be non-negative, Eq (11" + }, + { + "Chapter": "9", + "sentence_range": "1797-1800", + "Text": "The intensity of radiation (that is\nproportional to the number of energy quanta per unit\narea per unit time) is irrelevant to this basic process \u00b7\nSince Kmax must be non-negative, Eq (11 2 ) implies\nthat photoelectric emission is possible only if\nh n > f0\nor n > n0 , where\nn0 = \nh0\n\u03c6\n(11" + }, + { + "Chapter": "9", + "sentence_range": "1798-1801", + "Text": "\u00b7\nSince Kmax must be non-negative, Eq (11 2 ) implies\nthat photoelectric emission is possible only if\nh n > f0\nor n > n0 , where\nn0 = \nh0\n\u03c6\n(11 3)\nEquation (11" + }, + { + "Chapter": "9", + "sentence_range": "1799-1802", + "Text": "(11 2 ) implies\nthat photoelectric emission is possible only if\nh n > f0\nor n > n0 , where\nn0 = \nh0\n\u03c6\n(11 3)\nEquation (11 3) shows that the greater the work\nfunction f0, the higher the minimum or threshold\nfrequency n0 needed to emit photoelectrons" + }, + { + "Chapter": "9", + "sentence_range": "1800-1803", + "Text": "2 ) implies\nthat photoelectric emission is possible only if\nh n > f0\nor n > n0 , where\nn0 = \nh0\n\u03c6\n(11 3)\nEquation (11 3) shows that the greater the work\nfunction f0, the higher the minimum or threshold\nfrequency n0 needed to emit photoelectrons Thus,\nthere exists a threshold frequency n0 (= f0/h) for the\nmetal surface, below which no photoelectric emission\nis possible, no matter how intense the incident\nradiation may be or how long it falls on the surface" + }, + { + "Chapter": "9", + "sentence_range": "1801-1804", + "Text": "3)\nEquation (11 3) shows that the greater the work\nfunction f0, the higher the minimum or threshold\nfrequency n0 needed to emit photoelectrons Thus,\nthere exists a threshold frequency n0 (= f0/h) for the\nmetal surface, below which no photoelectric emission\nis possible, no matter how intense the incident\nradiation may be or how long it falls on the surface \u00b7\nIn this picture, intensity of radiation as noted above,\nis proportional to the number of energy quanta per\nunit area per unit time" + }, + { + "Chapter": "9", + "sentence_range": "1802-1805", + "Text": "3) shows that the greater the work\nfunction f0, the higher the minimum or threshold\nfrequency n0 needed to emit photoelectrons Thus,\nthere exists a threshold frequency n0 (= f0/h) for the\nmetal surface, below which no photoelectric emission\nis possible, no matter how intense the incident\nradiation may be or how long it falls on the surface \u00b7\nIn this picture, intensity of radiation as noted above,\nis proportional to the number of energy quanta per\nunit area per unit time The greater the number of\nenergy quanta available, the greater is the number of\nelectrons absorbing the energy quanta and greater,\ntherefore, is the number of electrons coming out of\nthe metal (for n > n0)" + }, + { + "Chapter": "9", + "sentence_range": "1803-1806", + "Text": "Thus,\nthere exists a threshold frequency n0 (= f0/h) for the\nmetal surface, below which no photoelectric emission\nis possible, no matter how intense the incident\nradiation may be or how long it falls on the surface \u00b7\nIn this picture, intensity of radiation as noted above,\nis proportional to the number of energy quanta per\nunit area per unit time The greater the number of\nenergy quanta available, the greater is the number of\nelectrons absorbing the energy quanta and greater,\ntherefore, is the number of electrons coming out of\nthe metal (for n > n0) This explains why, for n > n0,\nphotoelectric current is proportional to intensity" + }, + { + "Chapter": "9", + "sentence_range": "1804-1807", + "Text": "\u00b7\nIn this picture, intensity of radiation as noted above,\nis proportional to the number of energy quanta per\nunit area per unit time The greater the number of\nenergy quanta available, the greater is the number of\nelectrons absorbing the energy quanta and greater,\ntherefore, is the number of electrons coming out of\nthe metal (for n > n0) This explains why, for n > n0,\nphotoelectric current is proportional to intensity \u00b7\nIn Einstein\u2019s picture, the basic elementary process\ninvolved in photoelectric effect is the absorption of a\nlight quantum by an electron" + }, + { + "Chapter": "9", + "sentence_range": "1805-1808", + "Text": "The greater the number of\nenergy quanta available, the greater is the number of\nelectrons absorbing the energy quanta and greater,\ntherefore, is the number of electrons coming out of\nthe metal (for n > n0) This explains why, for n > n0,\nphotoelectric current is proportional to intensity \u00b7\nIn Einstein\u2019s picture, the basic elementary process\ninvolved in photoelectric effect is the absorption of a\nlight quantum by an electron This process is\ninstantaneous" + }, + { + "Chapter": "9", + "sentence_range": "1806-1809", + "Text": "This explains why, for n > n0,\nphotoelectric current is proportional to intensity \u00b7\nIn Einstein\u2019s picture, the basic elementary process\ninvolved in photoelectric effect is the absorption of a\nlight quantum by an electron This process is\ninstantaneous Thus, whatever may be the intensity\ni" + }, + { + "Chapter": "9", + "sentence_range": "1807-1810", + "Text": "\u00b7\nIn Einstein\u2019s picture, the basic elementary process\ninvolved in photoelectric effect is the absorption of a\nlight quantum by an electron This process is\ninstantaneous Thus, whatever may be the intensity\ni e" + }, + { + "Chapter": "9", + "sentence_range": "1808-1811", + "Text": "This process is\ninstantaneous Thus, whatever may be the intensity\ni e , the number of quanta of radiation per unit area\nper unit time, photoelectric emission is instantaneous" + }, + { + "Chapter": "9", + "sentence_range": "1809-1812", + "Text": "Thus, whatever may be the intensity\ni e , the number of quanta of radiation per unit area\nper unit time, photoelectric emission is instantaneous Low intensity does not mean delay in emission, since\nthe basic elementary process is the same" + }, + { + "Chapter": "9", + "sentence_range": "1810-1813", + "Text": "e , the number of quanta of radiation per unit area\nper unit time, photoelectric emission is instantaneous Low intensity does not mean delay in emission, since\nthe basic elementary process is the same Intensity\nonly determines how many electrons are able to\nparticipate in the elementary process (absorption of a\nlight quantum by a single electron) and, therefore, the\nphotoelectric current" + }, + { + "Chapter": "9", + "sentence_range": "1811-1814", + "Text": ", the number of quanta of radiation per unit area\nper unit time, photoelectric emission is instantaneous Low intensity does not mean delay in emission, since\nthe basic elementary process is the same Intensity\nonly determines how many electrons are able to\nparticipate in the elementary process (absorption of a\nlight quantum by a single electron) and, therefore, the\nphotoelectric current Using Eq" + }, + { + "Chapter": "9", + "sentence_range": "1812-1815", + "Text": "Low intensity does not mean delay in emission, since\nthe basic elementary process is the same Intensity\nonly determines how many electrons are able to\nparticipate in the elementary process (absorption of a\nlight quantum by a single electron) and, therefore, the\nphotoelectric current Using Eq (11" + }, + { + "Chapter": "9", + "sentence_range": "1813-1816", + "Text": "Intensity\nonly determines how many electrons are able to\nparticipate in the elementary process (absorption of a\nlight quantum by a single electron) and, therefore, the\nphotoelectric current Using Eq (11 1), the photoelectric equation, Eq" + }, + { + "Chapter": "9", + "sentence_range": "1814-1817", + "Text": "Using Eq (11 1), the photoelectric equation, Eq (11" + }, + { + "Chapter": "9", + "sentence_range": "1815-1818", + "Text": "(11 1), the photoelectric equation, Eq (11 2),\ncan be written as\ne V0 = h n \u2013 f 0; for \n0\n\u03bd\n\u03bd\n\u2265\nor V0 = \n0\neh\n\u03c6e\n\u03bd\n \n \n\u2212\n \n \n \n \n(11" + }, + { + "Chapter": "9", + "sentence_range": "1816-1819", + "Text": "1), the photoelectric equation, Eq (11 2),\ncan be written as\ne V0 = h n \u2013 f 0; for \n0\n\u03bd\n\u03bd\n\u2265\nor V0 = \n0\neh\n\u03c6e\n\u03bd\n \n \n\u2212\n \n \n \n \n(11 4)\nThis is an important result" + }, + { + "Chapter": "9", + "sentence_range": "1817-1820", + "Text": "(11 2),\ncan be written as\ne V0 = h n \u2013 f 0; for \n0\n\u03bd\n\u03bd\n\u2265\nor V0 = \n0\neh\n\u03c6e\n\u03bd\n \n \n\u2212\n \n \n \n \n(11 4)\nThis is an important result It predicts that the V0\nversus n curve is a straight line with slope = (h/e),\nALBERT EINSTEIN (1879 \u2013 1955)\nAlbert Einstein (1879 \u2013\n1955) Einstein, one of the\ngreatest physicists of all\ntime, was born in Ulm,\nGermany" + }, + { + "Chapter": "9", + "sentence_range": "1818-1821", + "Text": "2),\ncan be written as\ne V0 = h n \u2013 f 0; for \n0\n\u03bd\n\u03bd\n\u2265\nor V0 = \n0\neh\n\u03c6e\n\u03bd\n \n \n\u2212\n \n \n \n \n(11 4)\nThis is an important result It predicts that the V0\nversus n curve is a straight line with slope = (h/e),\nALBERT EINSTEIN (1879 \u2013 1955)\nAlbert Einstein (1879 \u2013\n1955) Einstein, one of the\ngreatest physicists of all\ntime, was born in Ulm,\nGermany In 1905, he\npublished three path-\nbreaking papers" + }, + { + "Chapter": "9", + "sentence_range": "1819-1822", + "Text": "4)\nThis is an important result It predicts that the V0\nversus n curve is a straight line with slope = (h/e),\nALBERT EINSTEIN (1879 \u2013 1955)\nAlbert Einstein (1879 \u2013\n1955) Einstein, one of the\ngreatest physicists of all\ntime, was born in Ulm,\nGermany In 1905, he\npublished three path-\nbreaking papers In the\nfirst paper, he introduced\nthe notion of light quanta\n(now called photons) and\nused it to explain the\nfeatures of photoelectric\neffect" + }, + { + "Chapter": "9", + "sentence_range": "1820-1823", + "Text": "It predicts that the V0\nversus n curve is a straight line with slope = (h/e),\nALBERT EINSTEIN (1879 \u2013 1955)\nAlbert Einstein (1879 \u2013\n1955) Einstein, one of the\ngreatest physicists of all\ntime, was born in Ulm,\nGermany In 1905, he\npublished three path-\nbreaking papers In the\nfirst paper, he introduced\nthe notion of light quanta\n(now called photons) and\nused it to explain the\nfeatures of photoelectric\neffect In the second paper,\nhe developed a theory of\nBrownian \nmotion,\nconfirmed experimentally a\nfew years later and provided\na convincing evidence of\nthe atomic picture of matter" + }, + { + "Chapter": "9", + "sentence_range": "1821-1824", + "Text": "In 1905, he\npublished three path-\nbreaking papers In the\nfirst paper, he introduced\nthe notion of light quanta\n(now called photons) and\nused it to explain the\nfeatures of photoelectric\neffect In the second paper,\nhe developed a theory of\nBrownian \nmotion,\nconfirmed experimentally a\nfew years later and provided\na convincing evidence of\nthe atomic picture of matter The third paper gave birth\nto the special theory of\nrelativity" + }, + { + "Chapter": "9", + "sentence_range": "1822-1825", + "Text": "In the\nfirst paper, he introduced\nthe notion of light quanta\n(now called photons) and\nused it to explain the\nfeatures of photoelectric\neffect In the second paper,\nhe developed a theory of\nBrownian \nmotion,\nconfirmed experimentally a\nfew years later and provided\na convincing evidence of\nthe atomic picture of matter The third paper gave birth\nto the special theory of\nrelativity In 1916, he\npublished the general\ntheory of relativity" + }, + { + "Chapter": "9", + "sentence_range": "1823-1826", + "Text": "In the second paper,\nhe developed a theory of\nBrownian \nmotion,\nconfirmed experimentally a\nfew years later and provided\na convincing evidence of\nthe atomic picture of matter The third paper gave birth\nto the special theory of\nrelativity In 1916, he\npublished the general\ntheory of relativity Some of\nEinstein\u2019s most significant\nlater contributions are: the\nnotion \nof \nstimulated\nemission introduced in an\nalternative derivation of\nPlanck\u2019s \nblackbody\nradiation law, static model\nof the universe which\nstarted modern cosmology,\nquantum statistics of a gas\nof massive bosons, and a\ncritical analysis of the\nfoundations of quantum\nmechanics" + }, + { + "Chapter": "9", + "sentence_range": "1824-1827", + "Text": "The third paper gave birth\nto the special theory of\nrelativity In 1916, he\npublished the general\ntheory of relativity Some of\nEinstein\u2019s most significant\nlater contributions are: the\nnotion \nof \nstimulated\nemission introduced in an\nalternative derivation of\nPlanck\u2019s \nblackbody\nradiation law, static model\nof the universe which\nstarted modern cosmology,\nquantum statistics of a gas\nof massive bosons, and a\ncritical analysis of the\nfoundations of quantum\nmechanics In 1921, he was\nawarded the Nobel Prize in\nphysics for his contribution\nto theoretical physics and\nthe photoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1825-1828", + "Text": "In 1916, he\npublished the general\ntheory of relativity Some of\nEinstein\u2019s most significant\nlater contributions are: the\nnotion \nof \nstimulated\nemission introduced in an\nalternative derivation of\nPlanck\u2019s \nblackbody\nradiation law, static model\nof the universe which\nstarted modern cosmology,\nquantum statistics of a gas\nof massive bosons, and a\ncritical analysis of the\nfoundations of quantum\nmechanics In 1921, he was\nawarded the Nobel Prize in\nphysics for his contribution\nto theoretical physics and\nthe photoelectric effect Rationalised 2023-24\n283\nDual Nature of Radiation\nand Matter\nindependent of the nature of the material" + }, + { + "Chapter": "9", + "sentence_range": "1826-1829", + "Text": "Some of\nEinstein\u2019s most significant\nlater contributions are: the\nnotion \nof \nstimulated\nemission introduced in an\nalternative derivation of\nPlanck\u2019s \nblackbody\nradiation law, static model\nof the universe which\nstarted modern cosmology,\nquantum statistics of a gas\nof massive bosons, and a\ncritical analysis of the\nfoundations of quantum\nmechanics In 1921, he was\nawarded the Nobel Prize in\nphysics for his contribution\nto theoretical physics and\nthe photoelectric effect Rationalised 2023-24\n283\nDual Nature of Radiation\nand Matter\nindependent of the nature of the material During 1906-1916, Millikan\nperformed a series of experiments on photoelectric effect, aimed at\ndisproving Einstein\u2019s photoelectric equation" + }, + { + "Chapter": "9", + "sentence_range": "1827-1830", + "Text": "In 1921, he was\nawarded the Nobel Prize in\nphysics for his contribution\nto theoretical physics and\nthe photoelectric effect Rationalised 2023-24\n283\nDual Nature of Radiation\nand Matter\nindependent of the nature of the material During 1906-1916, Millikan\nperformed a series of experiments on photoelectric effect, aimed at\ndisproving Einstein\u2019s photoelectric equation He measured the slope of\nthe straight line obtained for sodium, similar to that shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "1828-1831", + "Text": "Rationalised 2023-24\n283\nDual Nature of Radiation\nand Matter\nindependent of the nature of the material During 1906-1916, Millikan\nperformed a series of experiments on photoelectric effect, aimed at\ndisproving Einstein\u2019s photoelectric equation He measured the slope of\nthe straight line obtained for sodium, similar to that shown in Fig 11" + }, + { + "Chapter": "9", + "sentence_range": "1829-1832", + "Text": "During 1906-1916, Millikan\nperformed a series of experiments on photoelectric effect, aimed at\ndisproving Einstein\u2019s photoelectric equation He measured the slope of\nthe straight line obtained for sodium, similar to that shown in Fig 11 5" + }, + { + "Chapter": "9", + "sentence_range": "1830-1833", + "Text": "He measured the slope of\nthe straight line obtained for sodium, similar to that shown in Fig 11 5 Using the known value of e, he determined the value of Planck\u2019s constant\nh" + }, + { + "Chapter": "9", + "sentence_range": "1831-1834", + "Text": "11 5 Using the known value of e, he determined the value of Planck\u2019s constant\nh This value was close to the value of Planck\u2019s contant (= 6" + }, + { + "Chapter": "9", + "sentence_range": "1832-1835", + "Text": "5 Using the known value of e, he determined the value of Planck\u2019s constant\nh This value was close to the value of Planck\u2019s contant (= 6 626 \u00d7 10\u2013\n34J s) determined in an entirely different context" + }, + { + "Chapter": "9", + "sentence_range": "1833-1836", + "Text": "Using the known value of e, he determined the value of Planck\u2019s constant\nh This value was close to the value of Planck\u2019s contant (= 6 626 \u00d7 10\u2013\n34J s) determined in an entirely different context In this way, in 1916,\nMillikan proved the validity of Einstein\u2019s photoelectric equation, instead\nof disproving it" + }, + { + "Chapter": "9", + "sentence_range": "1834-1837", + "Text": "This value was close to the value of Planck\u2019s contant (= 6 626 \u00d7 10\u2013\n34J s) determined in an entirely different context In this way, in 1916,\nMillikan proved the validity of Einstein\u2019s photoelectric equation, instead\nof disproving it The successful explanation of photoelectric effect using the hypothesis\nof light quanta and the experimental determination of values of h and f0,\nin agreement with values obtained from other experiments, led to the\nacceptance of Einstein\u2019s picture of photoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1835-1838", + "Text": "626 \u00d7 10\u2013\n34J s) determined in an entirely different context In this way, in 1916,\nMillikan proved the validity of Einstein\u2019s photoelectric equation, instead\nof disproving it The successful explanation of photoelectric effect using the hypothesis\nof light quanta and the experimental determination of values of h and f0,\nin agreement with values obtained from other experiments, led to the\nacceptance of Einstein\u2019s picture of photoelectric effect Millikan verified\nphotoelectric equation with great precision, for a number of alkali metals\nover a wide range of radiation frequencies" + }, + { + "Chapter": "9", + "sentence_range": "1836-1839", + "Text": "In this way, in 1916,\nMillikan proved the validity of Einstein\u2019s photoelectric equation, instead\nof disproving it The successful explanation of photoelectric effect using the hypothesis\nof light quanta and the experimental determination of values of h and f0,\nin agreement with values obtained from other experiments, led to the\nacceptance of Einstein\u2019s picture of photoelectric effect Millikan verified\nphotoelectric equation with great precision, for a number of alkali metals\nover a wide range of radiation frequencies 11" + }, + { + "Chapter": "9", + "sentence_range": "1837-1840", + "Text": "The successful explanation of photoelectric effect using the hypothesis\nof light quanta and the experimental determination of values of h and f0,\nin agreement with values obtained from other experiments, led to the\nacceptance of Einstein\u2019s picture of photoelectric effect Millikan verified\nphotoelectric equation with great precision, for a number of alkali metals\nover a wide range of radiation frequencies 11 7 PARTICLE NATURE OF LIGHT: THE PHOTON\nPhotoelectric effect thus gave evidence to the strange fact that light in\ninteraction with matter behaved as if it was made of quanta or packets of\nenergy, each of energy h n" + }, + { + "Chapter": "9", + "sentence_range": "1838-1841", + "Text": "Millikan verified\nphotoelectric equation with great precision, for a number of alkali metals\nover a wide range of radiation frequencies 11 7 PARTICLE NATURE OF LIGHT: THE PHOTON\nPhotoelectric effect thus gave evidence to the strange fact that light in\ninteraction with matter behaved as if it was made of quanta or packets of\nenergy, each of energy h n Is the light quantum of energy to be associated with a particle" + }, + { + "Chapter": "9", + "sentence_range": "1839-1842", + "Text": "11 7 PARTICLE NATURE OF LIGHT: THE PHOTON\nPhotoelectric effect thus gave evidence to the strange fact that light in\ninteraction with matter behaved as if it was made of quanta or packets of\nenergy, each of energy h n Is the light quantum of energy to be associated with a particle Einstein\narrived at the important result, that the light quantum can also be\nassociated with momentum (h n/c)" + }, + { + "Chapter": "9", + "sentence_range": "1840-1843", + "Text": "7 PARTICLE NATURE OF LIGHT: THE PHOTON\nPhotoelectric effect thus gave evidence to the strange fact that light in\ninteraction with matter behaved as if it was made of quanta or packets of\nenergy, each of energy h n Is the light quantum of energy to be associated with a particle Einstein\narrived at the important result, that the light quantum can also be\nassociated with momentum (h n/c) A definite value of energy as well as\nmomentum is a strong sign that the light quantum can be associated\nwith a particle" + }, + { + "Chapter": "9", + "sentence_range": "1841-1844", + "Text": "Is the light quantum of energy to be associated with a particle Einstein\narrived at the important result, that the light quantum can also be\nassociated with momentum (h n/c) A definite value of energy as well as\nmomentum is a strong sign that the light quantum can be associated\nwith a particle This particle was later named photon" + }, + { + "Chapter": "9", + "sentence_range": "1842-1845", + "Text": "Einstein\narrived at the important result, that the light quantum can also be\nassociated with momentum (h n/c) A definite value of energy as well as\nmomentum is a strong sign that the light quantum can be associated\nwith a particle This particle was later named photon The particle-like\nbehaviour of light was further confirmed, in 1924, by the experiment of\nA" + }, + { + "Chapter": "9", + "sentence_range": "1843-1846", + "Text": "A definite value of energy as well as\nmomentum is a strong sign that the light quantum can be associated\nwith a particle This particle was later named photon The particle-like\nbehaviour of light was further confirmed, in 1924, by the experiment of\nA H" + }, + { + "Chapter": "9", + "sentence_range": "1844-1847", + "Text": "This particle was later named photon The particle-like\nbehaviour of light was further confirmed, in 1924, by the experiment of\nA H Compton (1892-1962) on scattering of X-rays from electrons" + }, + { + "Chapter": "9", + "sentence_range": "1845-1848", + "Text": "The particle-like\nbehaviour of light was further confirmed, in 1924, by the experiment of\nA H Compton (1892-1962) on scattering of X-rays from electrons In\n1921, Einstein was awarded the Nobel Prize in Physics for his contribution\nto theoretical physics and the photoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1846-1849", + "Text": "H Compton (1892-1962) on scattering of X-rays from electrons In\n1921, Einstein was awarded the Nobel Prize in Physics for his contribution\nto theoretical physics and the photoelectric effect In 1923, Millikan was\nawarded the Nobel Prize in physics for his work on the elementary\ncharge of electricity and on the photoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1847-1850", + "Text": "Compton (1892-1962) on scattering of X-rays from electrons In\n1921, Einstein was awarded the Nobel Prize in Physics for his contribution\nto theoretical physics and the photoelectric effect In 1923, Millikan was\nawarded the Nobel Prize in physics for his work on the elementary\ncharge of electricity and on the photoelectric effect We can summarise the photon picture of electromagnetic radiation\nas follows:\n(i)\nIn interaction of radiation with matter, radiation behaves as if it is\nmade up of particles called photons" + }, + { + "Chapter": "9", + "sentence_range": "1848-1851", + "Text": "In\n1921, Einstein was awarded the Nobel Prize in Physics for his contribution\nto theoretical physics and the photoelectric effect In 1923, Millikan was\nawarded the Nobel Prize in physics for his work on the elementary\ncharge of electricity and on the photoelectric effect We can summarise the photon picture of electromagnetic radiation\nas follows:\n(i)\nIn interaction of radiation with matter, radiation behaves as if it is\nmade up of particles called photons (ii) Each photon has energy E (=hn) and momentum p (= h n/c), and\nspeed c, the speed of light" + }, + { + "Chapter": "9", + "sentence_range": "1849-1852", + "Text": "In 1923, Millikan was\nawarded the Nobel Prize in physics for his work on the elementary\ncharge of electricity and on the photoelectric effect We can summarise the photon picture of electromagnetic radiation\nas follows:\n(i)\nIn interaction of radiation with matter, radiation behaves as if it is\nmade up of particles called photons (ii) Each photon has energy E (=hn) and momentum p (= h n/c), and\nspeed c, the speed of light (iii) All photons of light of a particular frequency n, or wavelength l, have\nthe same energy E (=hn = hc/l) and momentum p (= hn/c= h/l),\nwhatever the intensity of radiation may be" + }, + { + "Chapter": "9", + "sentence_range": "1850-1853", + "Text": "We can summarise the photon picture of electromagnetic radiation\nas follows:\n(i)\nIn interaction of radiation with matter, radiation behaves as if it is\nmade up of particles called photons (ii) Each photon has energy E (=hn) and momentum p (= h n/c), and\nspeed c, the speed of light (iii) All photons of light of a particular frequency n, or wavelength l, have\nthe same energy E (=hn = hc/l) and momentum p (= hn/c= h/l),\nwhatever the intensity of radiation may be By increasing the intensity\nof light of given wavelength, there is only an increase in the number of\nphotons per second crossing a given area, with each photon having\nthe same energy" + }, + { + "Chapter": "9", + "sentence_range": "1851-1854", + "Text": "(ii) Each photon has energy E (=hn) and momentum p (= h n/c), and\nspeed c, the speed of light (iii) All photons of light of a particular frequency n, or wavelength l, have\nthe same energy E (=hn = hc/l) and momentum p (= hn/c= h/l),\nwhatever the intensity of radiation may be By increasing the intensity\nof light of given wavelength, there is only an increase in the number of\nphotons per second crossing a given area, with each photon having\nthe same energy Thus, photon energy is independent of intensity of\nradiation" + }, + { + "Chapter": "9", + "sentence_range": "1852-1855", + "Text": "(iii) All photons of light of a particular frequency n, or wavelength l, have\nthe same energy E (=hn = hc/l) and momentum p (= hn/c= h/l),\nwhatever the intensity of radiation may be By increasing the intensity\nof light of given wavelength, there is only an increase in the number of\nphotons per second crossing a given area, with each photon having\nthe same energy Thus, photon energy is independent of intensity of\nradiation (iv) Photons are electrically neutral and are not deflected by electric and\nmagnetic fields" + }, + { + "Chapter": "9", + "sentence_range": "1853-1856", + "Text": "By increasing the intensity\nof light of given wavelength, there is only an increase in the number of\nphotons per second crossing a given area, with each photon having\nthe same energy Thus, photon energy is independent of intensity of\nradiation (iv) Photons are electrically neutral and are not deflected by electric and\nmagnetic fields (v) In a photon-particle collision (such as photon-electron collision), the\ntotal energy and total momentum are conserved" + }, + { + "Chapter": "9", + "sentence_range": "1854-1857", + "Text": "Thus, photon energy is independent of intensity of\nradiation (iv) Photons are electrically neutral and are not deflected by electric and\nmagnetic fields (v) In a photon-particle collision (such as photon-electron collision), the\ntotal energy and total momentum are conserved However, the number\nof photons may not be conserved in a collision" + }, + { + "Chapter": "9", + "sentence_range": "1855-1858", + "Text": "(iv) Photons are electrically neutral and are not deflected by electric and\nmagnetic fields (v) In a photon-particle collision (such as photon-electron collision), the\ntotal energy and total momentum are conserved However, the number\nof photons may not be conserved in a collision The photon may be\nabsorbed or a new photon may be created" + }, + { + "Chapter": "9", + "sentence_range": "1856-1859", + "Text": "(v) In a photon-particle collision (such as photon-electron collision), the\ntotal energy and total momentum are conserved However, the number\nof photons may not be conserved in a collision The photon may be\nabsorbed or a new photon may be created Rationalised 2023-24\nPhysics\n284\n EXAMPLE 11" + }, + { + "Chapter": "9", + "sentence_range": "1857-1860", + "Text": "However, the number\nof photons may not be conserved in a collision The photon may be\nabsorbed or a new photon may be created Rationalised 2023-24\nPhysics\n284\n EXAMPLE 11 1\n EXAMPLE 11" + }, + { + "Chapter": "9", + "sentence_range": "1858-1861", + "Text": "The photon may be\nabsorbed or a new photon may be created Rationalised 2023-24\nPhysics\n284\n EXAMPLE 11 1\n EXAMPLE 11 2\nExample 11" + }, + { + "Chapter": "9", + "sentence_range": "1859-1862", + "Text": "Rationalised 2023-24\nPhysics\n284\n EXAMPLE 11 1\n EXAMPLE 11 2\nExample 11 1 Monochromatic light of frequency 6" + }, + { + "Chapter": "9", + "sentence_range": "1860-1863", + "Text": "1\n EXAMPLE 11 2\nExample 11 1 Monochromatic light of frequency 6 0 \u00b41014 Hz is\nproduced by a laser" + }, + { + "Chapter": "9", + "sentence_range": "1861-1864", + "Text": "2\nExample 11 1 Monochromatic light of frequency 6 0 \u00b41014 Hz is\nproduced by a laser The power emitted is 2" + }, + { + "Chapter": "9", + "sentence_range": "1862-1865", + "Text": "1 Monochromatic light of frequency 6 0 \u00b41014 Hz is\nproduced by a laser The power emitted is 2 0 \u00b410\u20133 W" + }, + { + "Chapter": "9", + "sentence_range": "1863-1866", + "Text": "0 \u00b41014 Hz is\nproduced by a laser The power emitted is 2 0 \u00b410\u20133 W (a) What is the\nenergy of a photon in the light beam" + }, + { + "Chapter": "9", + "sentence_range": "1864-1867", + "Text": "The power emitted is 2 0 \u00b410\u20133 W (a) What is the\nenergy of a photon in the light beam (b) How many photons per second,\non an average, are emitted by the source" + }, + { + "Chapter": "9", + "sentence_range": "1865-1868", + "Text": "0 \u00b410\u20133 W (a) What is the\nenergy of a photon in the light beam (b) How many photons per second,\non an average, are emitted by the source Solution\n(a) Each photon has an energy\nE = h n = ( 6" + }, + { + "Chapter": "9", + "sentence_range": "1866-1869", + "Text": "(a) What is the\nenergy of a photon in the light beam (b) How many photons per second,\non an average, are emitted by the source Solution\n(a) Each photon has an energy\nE = h n = ( 6 63 \u00b410\u201334 J s) (6" + }, + { + "Chapter": "9", + "sentence_range": "1867-1870", + "Text": "(b) How many photons per second,\non an average, are emitted by the source Solution\n(a) Each photon has an energy\nE = h n = ( 6 63 \u00b410\u201334 J s) (6 0 \u00b41014 Hz)\n = 3" + }, + { + "Chapter": "9", + "sentence_range": "1868-1871", + "Text": "Solution\n(a) Each photon has an energy\nE = h n = ( 6 63 \u00b410\u201334 J s) (6 0 \u00b41014 Hz)\n = 3 98 \u00b4 10\u201319 J\n(b) If N is the number of photons emitted by the source per second,\nthe power P transmitted in the beam equals N times the energy\nper photon E, so that P = N E" + }, + { + "Chapter": "9", + "sentence_range": "1869-1872", + "Text": "63 \u00b410\u201334 J s) (6 0 \u00b41014 Hz)\n = 3 98 \u00b4 10\u201319 J\n(b) If N is the number of photons emitted by the source per second,\nthe power P transmitted in the beam equals N times the energy\nper photon E, so that P = N E Then\nN = \n3\n19\n2" + }, + { + "Chapter": "9", + "sentence_range": "1870-1873", + "Text": "0 \u00b41014 Hz)\n = 3 98 \u00b4 10\u201319 J\n(b) If N is the number of photons emitted by the source per second,\nthe power P transmitted in the beam equals N times the energy\nper photon E, so that P = N E Then\nN = \n3\n19\n2 0 10\nW\n3" + }, + { + "Chapter": "9", + "sentence_range": "1871-1874", + "Text": "98 \u00b4 10\u201319 J\n(b) If N is the number of photons emitted by the source per second,\nthe power P transmitted in the beam equals N times the energy\nper photon E, so that P = N E Then\nN = \n3\n19\n2 0 10\nW\n3 98 10\nJ\nP\nE\n\u2212\n\u2212\n\u00d7\n=\n\u00d7\n = 5" + }, + { + "Chapter": "9", + "sentence_range": "1872-1875", + "Text": "Then\nN = \n3\n19\n2 0 10\nW\n3 98 10\nJ\nP\nE\n\u2212\n\u2212\n\u00d7\n=\n\u00d7\n = 5 0 \u00b41015 photons per second" + }, + { + "Chapter": "9", + "sentence_range": "1873-1876", + "Text": "0 10\nW\n3 98 10\nJ\nP\nE\n\u2212\n\u2212\n\u00d7\n=\n\u00d7\n = 5 0 \u00b41015 photons per second Example 11" + }, + { + "Chapter": "9", + "sentence_range": "1874-1877", + "Text": "98 10\nJ\nP\nE\n\u2212\n\u2212\n\u00d7\n=\n\u00d7\n = 5 0 \u00b41015 photons per second Example 11 2 The work function of caesium is 2" + }, + { + "Chapter": "9", + "sentence_range": "1875-1878", + "Text": "0 \u00b41015 photons per second Example 11 2 The work function of caesium is 2 14 eV" + }, + { + "Chapter": "9", + "sentence_range": "1876-1879", + "Text": "Example 11 2 The work function of caesium is 2 14 eV Find (a) the\nthreshold frequency for caesium, and (b) the wavelength of the incident\nlight if the photocurrent is brought to zero by a stopping potential of\n0" + }, + { + "Chapter": "9", + "sentence_range": "1877-1880", + "Text": "2 The work function of caesium is 2 14 eV Find (a) the\nthreshold frequency for caesium, and (b) the wavelength of the incident\nlight if the photocurrent is brought to zero by a stopping potential of\n0 60 V" + }, + { + "Chapter": "9", + "sentence_range": "1878-1881", + "Text": "14 eV Find (a) the\nthreshold frequency for caesium, and (b) the wavelength of the incident\nlight if the photocurrent is brought to zero by a stopping potential of\n0 60 V Solution\n(a) For the cut-off or threshold frequency, the energy h n0 of the incident\nradiation must be equal to work function f0, so that\nn0 = \n0\n34\n2" + }, + { + "Chapter": "9", + "sentence_range": "1879-1882", + "Text": "Find (a) the\nthreshold frequency for caesium, and (b) the wavelength of the incident\nlight if the photocurrent is brought to zero by a stopping potential of\n0 60 V Solution\n(a) For the cut-off or threshold frequency, the energy h n0 of the incident\nradiation must be equal to work function f0, so that\nn0 = \n0\n34\n2 14eV\n6" + }, + { + "Chapter": "9", + "sentence_range": "1880-1883", + "Text": "60 V Solution\n(a) For the cut-off or threshold frequency, the energy h n0 of the incident\nradiation must be equal to work function f0, so that\nn0 = \n0\n34\n2 14eV\n6 63 10\nJ s\nh\n\u03c6\n\u2212\n=\n\u00d7\n \n19\n14\n34\n2" + }, + { + "Chapter": "9", + "sentence_range": "1881-1884", + "Text": "Solution\n(a) For the cut-off or threshold frequency, the energy h n0 of the incident\nradiation must be equal to work function f0, so that\nn0 = \n0\n34\n2 14eV\n6 63 10\nJ s\nh\n\u03c6\n\u2212\n=\n\u00d7\n \n19\n14\n34\n2 14\n1" + }, + { + "Chapter": "9", + "sentence_range": "1882-1885", + "Text": "14eV\n6 63 10\nJ s\nh\n\u03c6\n\u2212\n=\n\u00d7\n \n19\n14\n34\n2 14\n1 6\n10\nJ\n5" + }, + { + "Chapter": "9", + "sentence_range": "1883-1886", + "Text": "63 10\nJ s\nh\n\u03c6\n\u2212\n=\n\u00d7\n \n19\n14\n34\n2 14\n1 6\n10\nJ\n5 16\n10\nHz\n6" + }, + { + "Chapter": "9", + "sentence_range": "1884-1887", + "Text": "14\n1 6\n10\nJ\n5 16\n10\nHz\n6 63\n10\nJ s\n\u2212\n\u2212\n\u00d7\n\u00d7\n=\n=\n\u00d7\n\u00d7\nThus, for frequencies less than this threshold frequency, no\nphotoelectrons are ejected" + }, + { + "Chapter": "9", + "sentence_range": "1885-1888", + "Text": "6\n10\nJ\n5 16\n10\nHz\n6 63\n10\nJ s\n\u2212\n\u2212\n\u00d7\n\u00d7\n=\n=\n\u00d7\n\u00d7\nThus, for frequencies less than this threshold frequency, no\nphotoelectrons are ejected (b) Photocurrent reduces to zero, when maximum kinetic energy of\nthe emitted photoelectrons equals the potential energy e V0 by the\nretarding potential V0" + }, + { + "Chapter": "9", + "sentence_range": "1886-1889", + "Text": "16\n10\nHz\n6 63\n10\nJ s\n\u2212\n\u2212\n\u00d7\n\u00d7\n=\n=\n\u00d7\n\u00d7\nThus, for frequencies less than this threshold frequency, no\nphotoelectrons are ejected (b) Photocurrent reduces to zero, when maximum kinetic energy of\nthe emitted photoelectrons equals the potential energy e V0 by the\nretarding potential V0 Einstein\u2019s Photoelectric equation is\neV0 = hn \u2013 f 0 = hc\n\u03bb \u2013 f 0\nor,\nl = hc/(eV0 + f0)\n34\n8\n(6" + }, + { + "Chapter": "9", + "sentence_range": "1887-1890", + "Text": "63\n10\nJ s\n\u2212\n\u2212\n\u00d7\n\u00d7\n=\n=\n\u00d7\n\u00d7\nThus, for frequencies less than this threshold frequency, no\nphotoelectrons are ejected (b) Photocurrent reduces to zero, when maximum kinetic energy of\nthe emitted photoelectrons equals the potential energy e V0 by the\nretarding potential V0 Einstein\u2019s Photoelectric equation is\neV0 = hn \u2013 f 0 = hc\n\u03bb \u2013 f 0\nor,\nl = hc/(eV0 + f0)\n34\n8\n(6 63\n10\nJs)\n(3\n10 m/s)\n(0" + }, + { + "Chapter": "9", + "sentence_range": "1888-1891", + "Text": "(b) Photocurrent reduces to zero, when maximum kinetic energy of\nthe emitted photoelectrons equals the potential energy e V0 by the\nretarding potential V0 Einstein\u2019s Photoelectric equation is\neV0 = hn \u2013 f 0 = hc\n\u03bb \u2013 f 0\nor,\nl = hc/(eV0 + f0)\n34\n8\n(6 63\n10\nJs)\n(3\n10 m/s)\n(0 60eV\n2" + }, + { + "Chapter": "9", + "sentence_range": "1889-1892", + "Text": "Einstein\u2019s Photoelectric equation is\neV0 = hn \u2013 f 0 = hc\n\u03bb \u2013 f 0\nor,\nl = hc/(eV0 + f0)\n34\n8\n(6 63\n10\nJs)\n(3\n10 m/s)\n(0 60eV\n2 14eV)\n\u2212\n\u00d7\n\u00d7\n\u00d7\n=\n+\n26\n19" + }, + { + "Chapter": "9", + "sentence_range": "1890-1893", + "Text": "63\n10\nJs)\n(3\n10 m/s)\n(0 60eV\n2 14eV)\n\u2212\n\u00d7\n\u00d7\n\u00d7\n=\n+\n26\n19 89\n10\nJ m\n(2" + }, + { + "Chapter": "9", + "sentence_range": "1891-1894", + "Text": "60eV\n2 14eV)\n\u2212\n\u00d7\n\u00d7\n\u00d7\n=\n+\n26\n19 89\n10\nJ m\n(2 74eV)\n\u2212\n\u00d7\n=\n26\n19\n19" + }, + { + "Chapter": "9", + "sentence_range": "1892-1895", + "Text": "14eV)\n\u2212\n\u00d7\n\u00d7\n\u00d7\n=\n+\n26\n19 89\n10\nJ m\n(2 74eV)\n\u2212\n\u00d7\n=\n26\n19\n19 89\n10\nJ m\n454 nm\n2" + }, + { + "Chapter": "9", + "sentence_range": "1893-1896", + "Text": "89\n10\nJ m\n(2 74eV)\n\u2212\n\u00d7\n=\n26\n19\n19 89\n10\nJ m\n454 nm\n2 74\n1" + }, + { + "Chapter": "9", + "sentence_range": "1894-1897", + "Text": "74eV)\n\u2212\n\u00d7\n=\n26\n19\n19 89\n10\nJ m\n454 nm\n2 74\n1 6\n10\nJ\n\u03bb\n\u2212\n\u2212\n\u00d7\n=\n=\n\u00d7\n\u00d7\n11" + }, + { + "Chapter": "9", + "sentence_range": "1895-1898", + "Text": "89\n10\nJ m\n454 nm\n2 74\n1 6\n10\nJ\n\u03bb\n\u2212\n\u2212\n\u00d7\n=\n=\n\u00d7\n\u00d7\n11 8 WAVE NATURE OF MATTER\nThe dual (wave-particle) nature of light (electromagnetic radiation, in\ngeneral) comes out clearly from what we have learnt in this and the\npreceding chapters" + }, + { + "Chapter": "9", + "sentence_range": "1896-1899", + "Text": "74\n1 6\n10\nJ\n\u03bb\n\u2212\n\u2212\n\u00d7\n=\n=\n\u00d7\n\u00d7\n11 8 WAVE NATURE OF MATTER\nThe dual (wave-particle) nature of light (electromagnetic radiation, in\ngeneral) comes out clearly from what we have learnt in this and the\npreceding chapters The wave nature of light shows up in the phenomena\nof interference, diffraction and polarisation" + }, + { + "Chapter": "9", + "sentence_range": "1897-1900", + "Text": "6\n10\nJ\n\u03bb\n\u2212\n\u2212\n\u00d7\n=\n=\n\u00d7\n\u00d7\n11 8 WAVE NATURE OF MATTER\nThe dual (wave-particle) nature of light (electromagnetic radiation, in\ngeneral) comes out clearly from what we have learnt in this and the\npreceding chapters The wave nature of light shows up in the phenomena\nof interference, diffraction and polarisation On the other hand, in\nRationalised 2023-24\n285\nDual Nature of Radiation\nand Matter\nphotoelectric effect and Compton effect which involve\nenergy and momentum transfer, radiation behaves as if it\nis made up of a bunch of particles \u2013 the photons" + }, + { + "Chapter": "9", + "sentence_range": "1898-1901", + "Text": "8 WAVE NATURE OF MATTER\nThe dual (wave-particle) nature of light (electromagnetic radiation, in\ngeneral) comes out clearly from what we have learnt in this and the\npreceding chapters The wave nature of light shows up in the phenomena\nof interference, diffraction and polarisation On the other hand, in\nRationalised 2023-24\n285\nDual Nature of Radiation\nand Matter\nphotoelectric effect and Compton effect which involve\nenergy and momentum transfer, radiation behaves as if it\nis made up of a bunch of particles \u2013 the photons Whether\na particle or wave description is best suited for\nunderstanding an experiment depends on the nature of\nthe experiment" + }, + { + "Chapter": "9", + "sentence_range": "1899-1902", + "Text": "The wave nature of light shows up in the phenomena\nof interference, diffraction and polarisation On the other hand, in\nRationalised 2023-24\n285\nDual Nature of Radiation\nand Matter\nphotoelectric effect and Compton effect which involve\nenergy and momentum transfer, radiation behaves as if it\nis made up of a bunch of particles \u2013 the photons Whether\na particle or wave description is best suited for\nunderstanding an experiment depends on the nature of\nthe experiment For example, in the familiar phenomenon\nof seeing an object by our eye, both descriptions are\nimportant" + }, + { + "Chapter": "9", + "sentence_range": "1900-1903", + "Text": "On the other hand, in\nRationalised 2023-24\n285\nDual Nature of Radiation\nand Matter\nphotoelectric effect and Compton effect which involve\nenergy and momentum transfer, radiation behaves as if it\nis made up of a bunch of particles \u2013 the photons Whether\na particle or wave description is best suited for\nunderstanding an experiment depends on the nature of\nthe experiment For example, in the familiar phenomenon\nof seeing an object by our eye, both descriptions are\nimportant The gathering and focussing mechanism of\nlight by the eye-lens is well described in the wave picture" + }, + { + "Chapter": "9", + "sentence_range": "1901-1904", + "Text": "Whether\na particle or wave description is best suited for\nunderstanding an experiment depends on the nature of\nthe experiment For example, in the familiar phenomenon\nof seeing an object by our eye, both descriptions are\nimportant The gathering and focussing mechanism of\nlight by the eye-lens is well described in the wave picture But its absorption by the rods and cones (of the retina)\nrequires the photon picture of light" + }, + { + "Chapter": "9", + "sentence_range": "1902-1905", + "Text": "For example, in the familiar phenomenon\nof seeing an object by our eye, both descriptions are\nimportant The gathering and focussing mechanism of\nlight by the eye-lens is well described in the wave picture But its absorption by the rods and cones (of the retina)\nrequires the photon picture of light A natural question arises: If radiation has a dual (wave-\nparticle) nature, might not the particles of nature (the\nelectrons, protons, etc" + }, + { + "Chapter": "9", + "sentence_range": "1903-1906", + "Text": "The gathering and focussing mechanism of\nlight by the eye-lens is well described in the wave picture But its absorption by the rods and cones (of the retina)\nrequires the photon picture of light A natural question arises: If radiation has a dual (wave-\nparticle) nature, might not the particles of nature (the\nelectrons, protons, etc ) also exhibit wave-like character" + }, + { + "Chapter": "9", + "sentence_range": "1904-1907", + "Text": "But its absorption by the rods and cones (of the retina)\nrequires the photon picture of light A natural question arises: If radiation has a dual (wave-\nparticle) nature, might not the particles of nature (the\nelectrons, protons, etc ) also exhibit wave-like character In 1924, the French physicist Louis Victor de Broglie\n(pronounced as de Broy) (1892-1987) put forward the\nbold hypothesis that moving particles of matter should\ndisplay wave-like properties under suitable conditions" + }, + { + "Chapter": "9", + "sentence_range": "1905-1908", + "Text": "A natural question arises: If radiation has a dual (wave-\nparticle) nature, might not the particles of nature (the\nelectrons, protons, etc ) also exhibit wave-like character In 1924, the French physicist Louis Victor de Broglie\n(pronounced as de Broy) (1892-1987) put forward the\nbold hypothesis that moving particles of matter should\ndisplay wave-like properties under suitable conditions He reasoned that nature was symmetrical and that the\ntwo basic physical entities \u2013 matter and energy, must have\nsymmetrical character" + }, + { + "Chapter": "9", + "sentence_range": "1906-1909", + "Text": ") also exhibit wave-like character In 1924, the French physicist Louis Victor de Broglie\n(pronounced as de Broy) (1892-1987) put forward the\nbold hypothesis that moving particles of matter should\ndisplay wave-like properties under suitable conditions He reasoned that nature was symmetrical and that the\ntwo basic physical entities \u2013 matter and energy, must have\nsymmetrical character If radiation shows dual aspects,\nso should matter" + }, + { + "Chapter": "9", + "sentence_range": "1907-1910", + "Text": "In 1924, the French physicist Louis Victor de Broglie\n(pronounced as de Broy) (1892-1987) put forward the\nbold hypothesis that moving particles of matter should\ndisplay wave-like properties under suitable conditions He reasoned that nature was symmetrical and that the\ntwo basic physical entities \u2013 matter and energy, must have\nsymmetrical character If radiation shows dual aspects,\nso should matter De Broglie proposed that the wave\nlength l associated with a particle of momentum p is\ngiven as\nl = h\nh\np\n=m v\n(11" + }, + { + "Chapter": "9", + "sentence_range": "1908-1911", + "Text": "He reasoned that nature was symmetrical and that the\ntwo basic physical entities \u2013 matter and energy, must have\nsymmetrical character If radiation shows dual aspects,\nso should matter De Broglie proposed that the wave\nlength l associated with a particle of momentum p is\ngiven as\nl = h\nh\np\n=m v\n(11 5)\nwhere m is the mass of the particle and v its speed" + }, + { + "Chapter": "9", + "sentence_range": "1909-1912", + "Text": "If radiation shows dual aspects,\nso should matter De Broglie proposed that the wave\nlength l associated with a particle of momentum p is\ngiven as\nl = h\nh\np\n=m v\n(11 5)\nwhere m is the mass of the particle and v its speed Equation (11" + }, + { + "Chapter": "9", + "sentence_range": "1910-1913", + "Text": "De Broglie proposed that the wave\nlength l associated with a particle of momentum p is\ngiven as\nl = h\nh\np\n=m v\n(11 5)\nwhere m is the mass of the particle and v its speed Equation (11 5) is known as the de Broglie relation and\nthe wavelength l of the matter wave is called de Broglie wavelength" + }, + { + "Chapter": "9", + "sentence_range": "1911-1914", + "Text": "5)\nwhere m is the mass of the particle and v its speed Equation (11 5) is known as the de Broglie relation and\nthe wavelength l of the matter wave is called de Broglie wavelength The\ndual aspect of matter is evident in the de Broglie relation" + }, + { + "Chapter": "9", + "sentence_range": "1912-1915", + "Text": "Equation (11 5) is known as the de Broglie relation and\nthe wavelength l of the matter wave is called de Broglie wavelength The\ndual aspect of matter is evident in the de Broglie relation On the left hand\nside of Eq" + }, + { + "Chapter": "9", + "sentence_range": "1913-1916", + "Text": "5) is known as the de Broglie relation and\nthe wavelength l of the matter wave is called de Broglie wavelength The\ndual aspect of matter is evident in the de Broglie relation On the left hand\nside of Eq (11" + }, + { + "Chapter": "9", + "sentence_range": "1914-1917", + "Text": "The\ndual aspect of matter is evident in the de Broglie relation On the left hand\nside of Eq (11 5), l is the attribute of a wave while on the right hand side\nthe momentum p is a typical attribute of a particle" + }, + { + "Chapter": "9", + "sentence_range": "1915-1918", + "Text": "On the left hand\nside of Eq (11 5), l is the attribute of a wave while on the right hand side\nthe momentum p is a typical attribute of a particle Planck\u2019s constant h\nrelates the two attributes" + }, + { + "Chapter": "9", + "sentence_range": "1916-1919", + "Text": "(11 5), l is the attribute of a wave while on the right hand side\nthe momentum p is a typical attribute of a particle Planck\u2019s constant h\nrelates the two attributes Equation (11" + }, + { + "Chapter": "9", + "sentence_range": "1917-1920", + "Text": "5), l is the attribute of a wave while on the right hand side\nthe momentum p is a typical attribute of a particle Planck\u2019s constant h\nrelates the two attributes Equation (11 5) for a material particle is basically a hypothesis whose\nvalidity can be tested only by experiment" + }, + { + "Chapter": "9", + "sentence_range": "1918-1921", + "Text": "Planck\u2019s constant h\nrelates the two attributes Equation (11 5) for a material particle is basically a hypothesis whose\nvalidity can be tested only by experiment However, it is interesting to see\nthat it is satisfied also by a photon" + }, + { + "Chapter": "9", + "sentence_range": "1919-1922", + "Text": "Equation (11 5) for a material particle is basically a hypothesis whose\nvalidity can be tested only by experiment However, it is interesting to see\nthat it is satisfied also by a photon For a photon, as we have seen,\np = hn /c\n(11" + }, + { + "Chapter": "9", + "sentence_range": "1920-1923", + "Text": "5) for a material particle is basically a hypothesis whose\nvalidity can be tested only by experiment However, it is interesting to see\nthat it is satisfied also by a photon For a photon, as we have seen,\np = hn /c\n(11 6)\nTherefore,\nh\nc\np\n\u03bb\n=\u03bd\n=\n(11" + }, + { + "Chapter": "9", + "sentence_range": "1921-1924", + "Text": "However, it is interesting to see\nthat it is satisfied also by a photon For a photon, as we have seen,\np = hn /c\n(11 6)\nTherefore,\nh\nc\np\n\u03bb\n=\u03bd\n=\n(11 7)\nThat is, the de Broglie wavelength of a photon given by Eq" + }, + { + "Chapter": "9", + "sentence_range": "1922-1925", + "Text": "For a photon, as we have seen,\np = hn /c\n(11 6)\nTherefore,\nh\nc\np\n\u03bb\n=\u03bd\n=\n(11 7)\nThat is, the de Broglie wavelength of a photon given by Eq (11" + }, + { + "Chapter": "9", + "sentence_range": "1923-1926", + "Text": "6)\nTherefore,\nh\nc\np\n\u03bb\n=\u03bd\n=\n(11 7)\nThat is, the de Broglie wavelength of a photon given by Eq (11 5) equals\nthe wavelength of electromagnetic radiation of which the photon is a\nquantum of energy and momentum" + }, + { + "Chapter": "9", + "sentence_range": "1924-1927", + "Text": "7)\nThat is, the de Broglie wavelength of a photon given by Eq (11 5) equals\nthe wavelength of electromagnetic radiation of which the photon is a\nquantum of energy and momentum Clearly, from Eq" + }, + { + "Chapter": "9", + "sentence_range": "1925-1928", + "Text": "(11 5) equals\nthe wavelength of electromagnetic radiation of which the photon is a\nquantum of energy and momentum Clearly, from Eq (11" + }, + { + "Chapter": "9", + "sentence_range": "1926-1929", + "Text": "5) equals\nthe wavelength of electromagnetic radiation of which the photon is a\nquantum of energy and momentum Clearly, from Eq (11 5 ), l is smaller for a heavier particle (large m) or\nmore energetic particle (large v)" + }, + { + "Chapter": "9", + "sentence_range": "1927-1930", + "Text": "Clearly, from Eq (11 5 ), l is smaller for a heavier particle (large m) or\nmore energetic particle (large v) For example, the de Broglie wavelength\nof a ball of mass 0" + }, + { + "Chapter": "9", + "sentence_range": "1928-1931", + "Text": "(11 5 ), l is smaller for a heavier particle (large m) or\nmore energetic particle (large v) For example, the de Broglie wavelength\nof a ball of mass 0 12 kg moving with a speed of 20 m s\u20131 is easily\ncalculated:\nLOUIS VICTOR DE BROGLIE (1892 \u2013 1987)\nLouis Victor de Broglie\n(1892 \u2013 1987) French\nphysicist who put forth\nrevolutionary idea of wave\nnature of matter" + }, + { + "Chapter": "9", + "sentence_range": "1929-1932", + "Text": "5 ), l is smaller for a heavier particle (large m) or\nmore energetic particle (large v) For example, the de Broglie wavelength\nof a ball of mass 0 12 kg moving with a speed of 20 m s\u20131 is easily\ncalculated:\nLOUIS VICTOR DE BROGLIE (1892 \u2013 1987)\nLouis Victor de Broglie\n(1892 \u2013 1987) French\nphysicist who put forth\nrevolutionary idea of wave\nnature of matter This idea\nwas developed by Erwin\nSchr\u00f3dinger into a full-\nfledged theory of quantum\nmechanics \ncommonly\nknown as wave mechanics" + }, + { + "Chapter": "9", + "sentence_range": "1930-1933", + "Text": "For example, the de Broglie wavelength\nof a ball of mass 0 12 kg moving with a speed of 20 m s\u20131 is easily\ncalculated:\nLOUIS VICTOR DE BROGLIE (1892 \u2013 1987)\nLouis Victor de Broglie\n(1892 \u2013 1987) French\nphysicist who put forth\nrevolutionary idea of wave\nnature of matter This idea\nwas developed by Erwin\nSchr\u00f3dinger into a full-\nfledged theory of quantum\nmechanics \ncommonly\nknown as wave mechanics In 1929, he was awarded the\nNobel Prize in Physics for his\ndiscovery of the wave nature\nof electrons" + }, + { + "Chapter": "9", + "sentence_range": "1931-1934", + "Text": "12 kg moving with a speed of 20 m s\u20131 is easily\ncalculated:\nLOUIS VICTOR DE BROGLIE (1892 \u2013 1987)\nLouis Victor de Broglie\n(1892 \u2013 1987) French\nphysicist who put forth\nrevolutionary idea of wave\nnature of matter This idea\nwas developed by Erwin\nSchr\u00f3dinger into a full-\nfledged theory of quantum\nmechanics \ncommonly\nknown as wave mechanics In 1929, he was awarded the\nNobel Prize in Physics for his\ndiscovery of the wave nature\nof electrons Rationalised 2023-24\nPhysics\n286\n EXAMPLE 11" + }, + { + "Chapter": "9", + "sentence_range": "1932-1935", + "Text": "This idea\nwas developed by Erwin\nSchr\u00f3dinger into a full-\nfledged theory of quantum\nmechanics \ncommonly\nknown as wave mechanics In 1929, he was awarded the\nNobel Prize in Physics for his\ndiscovery of the wave nature\nof electrons Rationalised 2023-24\nPhysics\n286\n EXAMPLE 11 3\np = m v = 0" + }, + { + "Chapter": "9", + "sentence_range": "1933-1936", + "Text": "In 1929, he was awarded the\nNobel Prize in Physics for his\ndiscovery of the wave nature\nof electrons Rationalised 2023-24\nPhysics\n286\n EXAMPLE 11 3\np = m v = 0 12 kg \u00d7 20 m s\u20131 = 2" + }, + { + "Chapter": "9", + "sentence_range": "1934-1937", + "Text": "Rationalised 2023-24\nPhysics\n286\n EXAMPLE 11 3\np = m v = 0 12 kg \u00d7 20 m s\u20131 = 2 40 kg m s\u20131\nl = h\np = \n34\n1\n6" + }, + { + "Chapter": "9", + "sentence_range": "1935-1938", + "Text": "3\np = m v = 0 12 kg \u00d7 20 m s\u20131 = 2 40 kg m s\u20131\nl = h\np = \n34\n1\n6 63\n10\nJ s\n2" + }, + { + "Chapter": "9", + "sentence_range": "1936-1939", + "Text": "12 kg \u00d7 20 m s\u20131 = 2 40 kg m s\u20131\nl = h\np = \n34\n1\n6 63\n10\nJ s\n2 40 kg m s\n\u2212\n\u2212\n\u00d7\n = 2" + }, + { + "Chapter": "9", + "sentence_range": "1937-1940", + "Text": "40 kg m s\u20131\nl = h\np = \n34\n1\n6 63\n10\nJ s\n2 40 kg m s\n\u2212\n\u2212\n\u00d7\n = 2 76 \u00d7 10\u201334 m\nThis wavelength is so small that it is beyond any measurement" + }, + { + "Chapter": "9", + "sentence_range": "1938-1941", + "Text": "63\n10\nJ s\n2 40 kg m s\n\u2212\n\u2212\n\u00d7\n = 2 76 \u00d7 10\u201334 m\nThis wavelength is so small that it is beyond any measurement This\nis the reason why macroscopic objects in our daily life do not show wave-\nlike properties" + }, + { + "Chapter": "9", + "sentence_range": "1939-1942", + "Text": "40 kg m s\n\u2212\n\u2212\n\u00d7\n = 2 76 \u00d7 10\u201334 m\nThis wavelength is so small that it is beyond any measurement This\nis the reason why macroscopic objects in our daily life do not show wave-\nlike properties On the other hand, in the sub-atomic domain, the wave\ncharacter of particles is significant and measurable" + }, + { + "Chapter": "9", + "sentence_range": "1940-1943", + "Text": "76 \u00d7 10\u201334 m\nThis wavelength is so small that it is beyond any measurement This\nis the reason why macroscopic objects in our daily life do not show wave-\nlike properties On the other hand, in the sub-atomic domain, the wave\ncharacter of particles is significant and measurable Example 11" + }, + { + "Chapter": "9", + "sentence_range": "1941-1944", + "Text": "This\nis the reason why macroscopic objects in our daily life do not show wave-\nlike properties On the other hand, in the sub-atomic domain, the wave\ncharacter of particles is significant and measurable Example 11 3 What is the de Broglie wavelength associated with (a) an\nelectron moving with a speed of 5" + }, + { + "Chapter": "9", + "sentence_range": "1942-1945", + "Text": "On the other hand, in the sub-atomic domain, the wave\ncharacter of particles is significant and measurable Example 11 3 What is the de Broglie wavelength associated with (a) an\nelectron moving with a speed of 5 4\u00b4106 m/s, and (b) a ball of mass 150 g\ntravelling at 30" + }, + { + "Chapter": "9", + "sentence_range": "1943-1946", + "Text": "Example 11 3 What is the de Broglie wavelength associated with (a) an\nelectron moving with a speed of 5 4\u00b4106 m/s, and (b) a ball of mass 150 g\ntravelling at 30 0 m/s" + }, + { + "Chapter": "9", + "sentence_range": "1944-1947", + "Text": "3 What is the de Broglie wavelength associated with (a) an\nelectron moving with a speed of 5 4\u00b4106 m/s, and (b) a ball of mass 150 g\ntravelling at 30 0 m/s Solution\n(a) For the electron:\nMass m = 9" + }, + { + "Chapter": "9", + "sentence_range": "1945-1948", + "Text": "4\u00b4106 m/s, and (b) a ball of mass 150 g\ntravelling at 30 0 m/s Solution\n(a) For the electron:\nMass m = 9 11\u00b410\u201331 kg, speed v = 5" + }, + { + "Chapter": "9", + "sentence_range": "1946-1949", + "Text": "0 m/s Solution\n(a) For the electron:\nMass m = 9 11\u00b410\u201331 kg, speed v = 5 4\u00b4106 m/s" + }, + { + "Chapter": "9", + "sentence_range": "1947-1950", + "Text": "Solution\n(a) For the electron:\nMass m = 9 11\u00b410\u201331 kg, speed v = 5 4\u00b4106 m/s Then, momentum\np = m v = 9" + }, + { + "Chapter": "9", + "sentence_range": "1948-1951", + "Text": "11\u00b410\u201331 kg, speed v = 5 4\u00b4106 m/s Then, momentum\np = m v = 9 11\u00b410\u201331 (kg) \u00b4 5" + }, + { + "Chapter": "9", + "sentence_range": "1949-1952", + "Text": "4\u00b4106 m/s Then, momentum\np = m v = 9 11\u00b410\u201331 (kg) \u00b4 5 4 \u00b4 106 (m/s)\np = 4" + }, + { + "Chapter": "9", + "sentence_range": "1950-1953", + "Text": "Then, momentum\np = m v = 9 11\u00b410\u201331 (kg) \u00b4 5 4 \u00b4 106 (m/s)\np = 4 92 \u00b4 10\u201324 kg m/s\nde Broglie wavelength, l = h/p\n =" + }, + { + "Chapter": "9", + "sentence_range": "1951-1954", + "Text": "11\u00b410\u201331 (kg) \u00b4 5 4 \u00b4 106 (m/s)\np = 4 92 \u00b4 10\u201324 kg m/s\nde Broglie wavelength, l = h/p\n = \u201334\n\u201324\n6 63 10\nJ s\n4 92 10\nkg m/s\n\u00d7\n\u00d7\n l = 0" + }, + { + "Chapter": "9", + "sentence_range": "1952-1955", + "Text": "4 \u00b4 106 (m/s)\np = 4 92 \u00b4 10\u201324 kg m/s\nde Broglie wavelength, l = h/p\n = \u201334\n\u201324\n6 63 10\nJ s\n4 92 10\nkg m/s\n\u00d7\n\u00d7\n l = 0 135 nm\n(b) For the ball:\nMass m \u2019 = 0" + }, + { + "Chapter": "9", + "sentence_range": "1953-1956", + "Text": "92 \u00b4 10\u201324 kg m/s\nde Broglie wavelength, l = h/p\n = \u201334\n\u201324\n6 63 10\nJ s\n4 92 10\nkg m/s\n\u00d7\n\u00d7\n l = 0 135 nm\n(b) For the ball:\nMass m \u2019 = 0 150 kg, speed v \u2019 = 30" + }, + { + "Chapter": "9", + "sentence_range": "1954-1957", + "Text": "\u201334\n\u201324\n6 63 10\nJ s\n4 92 10\nkg m/s\n\u00d7\n\u00d7\n l = 0 135 nm\n(b) For the ball:\nMass m \u2019 = 0 150 kg, speed v \u2019 = 30 0 m/s" + }, + { + "Chapter": "9", + "sentence_range": "1955-1958", + "Text": "135 nm\n(b) For the ball:\nMass m \u2019 = 0 150 kg, speed v \u2019 = 30 0 m/s Then momentum p\u2019 = m\u2019 v\u2019 = 0" + }, + { + "Chapter": "9", + "sentence_range": "1956-1959", + "Text": "150 kg, speed v \u2019 = 30 0 m/s Then momentum p\u2019 = m\u2019 v\u2019 = 0 150 (kg) \u00b4 30" + }, + { + "Chapter": "9", + "sentence_range": "1957-1960", + "Text": "0 m/s Then momentum p\u2019 = m\u2019 v\u2019 = 0 150 (kg) \u00b4 30 0 (m/s)\np \u2019= 4" + }, + { + "Chapter": "9", + "sentence_range": "1958-1961", + "Text": "Then momentum p\u2019 = m\u2019 v\u2019 = 0 150 (kg) \u00b4 30 0 (m/s)\np \u2019= 4 50 kg m/s\nde Broglie wavelength l\u2019 = h/p\u2019" + }, + { + "Chapter": "9", + "sentence_range": "1959-1962", + "Text": "150 (kg) \u00b4 30 0 (m/s)\np \u2019= 4 50 kg m/s\nde Broglie wavelength l\u2019 = h/p\u2019 \u2013" + }, + { + "Chapter": "9", + "sentence_range": "1960-1963", + "Text": "0 (m/s)\np \u2019= 4 50 kg m/s\nde Broglie wavelength l\u2019 = h/p\u2019 \u2013 6 63 1034\nJs\n4 50\nkg m/s\n\u00d7\n=\n\u00d7\nl\u2019= 1" + }, + { + "Chapter": "9", + "sentence_range": "1961-1964", + "Text": "50 kg m/s\nde Broglie wavelength l\u2019 = h/p\u2019 \u2013 6 63 1034\nJs\n4 50\nkg m/s\n\u00d7\n=\n\u00d7\nl\u2019= 1 47 \u00b410\u201334 m\nThe de Broglie wavelength of electron is comparable with X-ray\nwavelengths" + }, + { + "Chapter": "9", + "sentence_range": "1962-1965", + "Text": "\u2013 6 63 1034\nJs\n4 50\nkg m/s\n\u00d7\n=\n\u00d7\nl\u2019= 1 47 \u00b410\u201334 m\nThe de Broglie wavelength of electron is comparable with X-ray\nwavelengths However, for the ball it is about 10\u201319 times the size of\nthe proton, quite beyond experimental measurement" + }, + { + "Chapter": "9", + "sentence_range": "1963-1966", + "Text": "6 63 1034\nJs\n4 50\nkg m/s\n\u00d7\n=\n\u00d7\nl\u2019= 1 47 \u00b410\u201334 m\nThe de Broglie wavelength of electron is comparable with X-ray\nwavelengths However, for the ball it is about 10\u201319 times the size of\nthe proton, quite beyond experimental measurement SUMMARY\n1" + }, + { + "Chapter": "9", + "sentence_range": "1964-1967", + "Text": "47 \u00b410\u201334 m\nThe de Broglie wavelength of electron is comparable with X-ray\nwavelengths However, for the ball it is about 10\u201319 times the size of\nthe proton, quite beyond experimental measurement SUMMARY\n1 The minimum energy needed by an electron to come out from a metal\nsurface is called the work function of the metal" + }, + { + "Chapter": "9", + "sentence_range": "1965-1968", + "Text": "However, for the ball it is about 10\u201319 times the size of\nthe proton, quite beyond experimental measurement SUMMARY\n1 The minimum energy needed by an electron to come out from a metal\nsurface is called the work function of the metal Energy (greater than\nthe work function (fo) required for electron emission from the metal\nsurface can be supplied by suitably heating or applying strong electric\nfield or irradiating it by light of suitable frequency" + }, + { + "Chapter": "9", + "sentence_range": "1966-1969", + "Text": "SUMMARY\n1 The minimum energy needed by an electron to come out from a metal\nsurface is called the work function of the metal Energy (greater than\nthe work function (fo) required for electron emission from the metal\nsurface can be supplied by suitably heating or applying strong electric\nfield or irradiating it by light of suitable frequency 2" + }, + { + "Chapter": "9", + "sentence_range": "1967-1970", + "Text": "The minimum energy needed by an electron to come out from a metal\nsurface is called the work function of the metal Energy (greater than\nthe work function (fo) required for electron emission from the metal\nsurface can be supplied by suitably heating or applying strong electric\nfield or irradiating it by light of suitable frequency 2 Photoelectric effect is the phenomenon of emission of electrons by metals\nwhen illuminated by light of suitable frequency" + }, + { + "Chapter": "9", + "sentence_range": "1968-1971", + "Text": "Energy (greater than\nthe work function (fo) required for electron emission from the metal\nsurface can be supplied by suitably heating or applying strong electric\nfield or irradiating it by light of suitable frequency 2 Photoelectric effect is the phenomenon of emission of electrons by metals\nwhen illuminated by light of suitable frequency Certain metals respond\nto ultraviolet light while others are sensitive even to the visible light" + }, + { + "Chapter": "9", + "sentence_range": "1969-1972", + "Text": "2 Photoelectric effect is the phenomenon of emission of electrons by metals\nwhen illuminated by light of suitable frequency Certain metals respond\nto ultraviolet light while others are sensitive even to the visible light Photoelectric effect involves conversion of light energy into electrical\nenergy" + }, + { + "Chapter": "9", + "sentence_range": "1970-1973", + "Text": "Photoelectric effect is the phenomenon of emission of electrons by metals\nwhen illuminated by light of suitable frequency Certain metals respond\nto ultraviolet light while others are sensitive even to the visible light Photoelectric effect involves conversion of light energy into electrical\nenergy It follows the law of conservation of energy" + }, + { + "Chapter": "9", + "sentence_range": "1971-1974", + "Text": "Certain metals respond\nto ultraviolet light while others are sensitive even to the visible light Photoelectric effect involves conversion of light energy into electrical\nenergy It follows the law of conservation of energy The photoelectric\nemission is an instantaneous process and possesses certain special\nfeatures" + }, + { + "Chapter": "9", + "sentence_range": "1972-1975", + "Text": "Photoelectric effect involves conversion of light energy into electrical\nenergy It follows the law of conservation of energy The photoelectric\nemission is an instantaneous process and possesses certain special\nfeatures Rationalised 2023-24\n287\nDual Nature of Radiation\nand Matter\n3" + }, + { + "Chapter": "9", + "sentence_range": "1973-1976", + "Text": "It follows the law of conservation of energy The photoelectric\nemission is an instantaneous process and possesses certain special\nfeatures Rationalised 2023-24\n287\nDual Nature of Radiation\nand Matter\n3 Photoelectric current depends on (i) the intensity of incident light, (ii)\nthe potential difference applied between the two electrodes, and (iii)\nthe nature of the emitter material" + }, + { + "Chapter": "9", + "sentence_range": "1974-1977", + "Text": "The photoelectric\nemission is an instantaneous process and possesses certain special\nfeatures Rationalised 2023-24\n287\nDual Nature of Radiation\nand Matter\n3 Photoelectric current depends on (i) the intensity of incident light, (ii)\nthe potential difference applied between the two electrodes, and (iii)\nthe nature of the emitter material 4" + }, + { + "Chapter": "9", + "sentence_range": "1975-1978", + "Text": "Rationalised 2023-24\n287\nDual Nature of Radiation\nand Matter\n3 Photoelectric current depends on (i) the intensity of incident light, (ii)\nthe potential difference applied between the two electrodes, and (iii)\nthe nature of the emitter material 4 The stopping potential (Vo) depends on (i) the frequency of incident\nlight, and (ii) the nature of the emitter material" + }, + { + "Chapter": "9", + "sentence_range": "1976-1979", + "Text": "Photoelectric current depends on (i) the intensity of incident light, (ii)\nthe potential difference applied between the two electrodes, and (iii)\nthe nature of the emitter material 4 The stopping potential (Vo) depends on (i) the frequency of incident\nlight, and (ii) the nature of the emitter material For a given frequency\nof incident light, it is independent of its intensity" + }, + { + "Chapter": "9", + "sentence_range": "1977-1980", + "Text": "4 The stopping potential (Vo) depends on (i) the frequency of incident\nlight, and (ii) the nature of the emitter material For a given frequency\nof incident light, it is independent of its intensity The stopping potential\nis directly related to the maximum kinetic energy of electrons emitted:\ne V0 = (1/2) m v2\nmax = Kmax" + }, + { + "Chapter": "9", + "sentence_range": "1978-1981", + "Text": "The stopping potential (Vo) depends on (i) the frequency of incident\nlight, and (ii) the nature of the emitter material For a given frequency\nof incident light, it is independent of its intensity The stopping potential\nis directly related to the maximum kinetic energy of electrons emitted:\ne V0 = (1/2) m v2\nmax = Kmax 5" + }, + { + "Chapter": "9", + "sentence_range": "1979-1982", + "Text": "For a given frequency\nof incident light, it is independent of its intensity The stopping potential\nis directly related to the maximum kinetic energy of electrons emitted:\ne V0 = (1/2) m v2\nmax = Kmax 5 Below a certain frequency (threshold frequency) n 0, characteristic of\nthe metal, no photoelectric emission takes place, no matter how large\nthe intensity may be" + }, + { + "Chapter": "9", + "sentence_range": "1980-1983", + "Text": "The stopping potential\nis directly related to the maximum kinetic energy of electrons emitted:\ne V0 = (1/2) m v2\nmax = Kmax 5 Below a certain frequency (threshold frequency) n 0, characteristic of\nthe metal, no photoelectric emission takes place, no matter how large\nthe intensity may be 6" + }, + { + "Chapter": "9", + "sentence_range": "1981-1984", + "Text": "5 Below a certain frequency (threshold frequency) n 0, characteristic of\nthe metal, no photoelectric emission takes place, no matter how large\nthe intensity may be 6 The classical wave theory could not explain the main features of\nphotoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "1982-1985", + "Text": "Below a certain frequency (threshold frequency) n 0, characteristic of\nthe metal, no photoelectric emission takes place, no matter how large\nthe intensity may be 6 The classical wave theory could not explain the main features of\nphotoelectric effect Its picture of continuous absorption of energy\nfrom radiation could not explain the independence of Kmax on\nintensity, the existence of no and the instantaneous nature of the\nprocess" + }, + { + "Chapter": "9", + "sentence_range": "1983-1986", + "Text": "6 The classical wave theory could not explain the main features of\nphotoelectric effect Its picture of continuous absorption of energy\nfrom radiation could not explain the independence of Kmax on\nintensity, the existence of no and the instantaneous nature of the\nprocess Einstein explained these features on the basis of photon\npicture of light" + }, + { + "Chapter": "9", + "sentence_range": "1984-1987", + "Text": "The classical wave theory could not explain the main features of\nphotoelectric effect Its picture of continuous absorption of energy\nfrom radiation could not explain the independence of Kmax on\nintensity, the existence of no and the instantaneous nature of the\nprocess Einstein explained these features on the basis of photon\npicture of light According to this, light is composed of discrete\npackets of energy called quanta or photons" + }, + { + "Chapter": "9", + "sentence_range": "1985-1988", + "Text": "Its picture of continuous absorption of energy\nfrom radiation could not explain the independence of Kmax on\nintensity, the existence of no and the instantaneous nature of the\nprocess Einstein explained these features on the basis of photon\npicture of light According to this, light is composed of discrete\npackets of energy called quanta or photons Each photon carries an\nenergy E (= h n) and momentum p (= h/l), which depend on the\nfrequency (n ) of incident light and not on its intensity" + }, + { + "Chapter": "9", + "sentence_range": "1986-1989", + "Text": "Einstein explained these features on the basis of photon\npicture of light According to this, light is composed of discrete\npackets of energy called quanta or photons Each photon carries an\nenergy E (= h n) and momentum p (= h/l), which depend on the\nfrequency (n ) of incident light and not on its intensity Photoelectric\nemission from the metal surface occurs due to absorption of a photon\nby an electron" + }, + { + "Chapter": "9", + "sentence_range": "1987-1990", + "Text": "According to this, light is composed of discrete\npackets of energy called quanta or photons Each photon carries an\nenergy E (= h n) and momentum p (= h/l), which depend on the\nfrequency (n ) of incident light and not on its intensity Photoelectric\nemission from the metal surface occurs due to absorption of a photon\nby an electron 7" + }, + { + "Chapter": "9", + "sentence_range": "1988-1991", + "Text": "Each photon carries an\nenergy E (= h n) and momentum p (= h/l), which depend on the\nfrequency (n ) of incident light and not on its intensity Photoelectric\nemission from the metal surface occurs due to absorption of a photon\nby an electron 7 Einstein\u2019s photoelectric equation is in accordance with the energy\nconservation law as applied to the photon absorption by an electron in\nthe metal" + }, + { + "Chapter": "9", + "sentence_range": "1989-1992", + "Text": "Photoelectric\nemission from the metal surface occurs due to absorption of a photon\nby an electron 7 Einstein\u2019s photoelectric equation is in accordance with the energy\nconservation law as applied to the photon absorption by an electron in\nthe metal The maximum kinetic energy (1/2)m v2\nmax is equal to\nthe photon energy (hn ) minus the work function f0 (= hn0) of the\ntarget metal:\n1\n2 m v2\nmax = V0 e = hn \u2013 f0 = h (n \u2013 n0)\nThis photoelectric equation explains all the features of the photoelectric\neffect" + }, + { + "Chapter": "9", + "sentence_range": "1990-1993", + "Text": "7 Einstein\u2019s photoelectric equation is in accordance with the energy\nconservation law as applied to the photon absorption by an electron in\nthe metal The maximum kinetic energy (1/2)m v2\nmax is equal to\nthe photon energy (hn ) minus the work function f0 (= hn0) of the\ntarget metal:\n1\n2 m v2\nmax = V0 e = hn \u2013 f0 = h (n \u2013 n0)\nThis photoelectric equation explains all the features of the photoelectric\neffect Millikan\u2019s first precise measurements confirmed the Einstein\u2019s\nphotoelectric equation and obtained an accurate value of Planck\u2019s\nconstant h" + }, + { + "Chapter": "9", + "sentence_range": "1991-1994", + "Text": "Einstein\u2019s photoelectric equation is in accordance with the energy\nconservation law as applied to the photon absorption by an electron in\nthe metal The maximum kinetic energy (1/2)m v2\nmax is equal to\nthe photon energy (hn ) minus the work function f0 (= hn0) of the\ntarget metal:\n1\n2 m v2\nmax = V0 e = hn \u2013 f0 = h (n \u2013 n0)\nThis photoelectric equation explains all the features of the photoelectric\neffect Millikan\u2019s first precise measurements confirmed the Einstein\u2019s\nphotoelectric equation and obtained an accurate value of Planck\u2019s\nconstant h This led to the acceptance of particle or photon description\n(nature) of electromagnetic radiation, introduced by Einstein" + }, + { + "Chapter": "9", + "sentence_range": "1992-1995", + "Text": "The maximum kinetic energy (1/2)m v2\nmax is equal to\nthe photon energy (hn ) minus the work function f0 (= hn0) of the\ntarget metal:\n1\n2 m v2\nmax = V0 e = hn \u2013 f0 = h (n \u2013 n0)\nThis photoelectric equation explains all the features of the photoelectric\neffect Millikan\u2019s first precise measurements confirmed the Einstein\u2019s\nphotoelectric equation and obtained an accurate value of Planck\u2019s\nconstant h This led to the acceptance of particle or photon description\n(nature) of electromagnetic radiation, introduced by Einstein 8" + }, + { + "Chapter": "9", + "sentence_range": "1993-1996", + "Text": "Millikan\u2019s first precise measurements confirmed the Einstein\u2019s\nphotoelectric equation and obtained an accurate value of Planck\u2019s\nconstant h This led to the acceptance of particle or photon description\n(nature) of electromagnetic radiation, introduced by Einstein 8 Radiation has dual nature: wave and particle" + }, + { + "Chapter": "9", + "sentence_range": "1994-1997", + "Text": "This led to the acceptance of particle or photon description\n(nature) of electromagnetic radiation, introduced by Einstein 8 Radiation has dual nature: wave and particle The nature of experiment\ndetermines whether a wave or particle description is best suited for\nunderstanding the experimental result" + }, + { + "Chapter": "9", + "sentence_range": "1995-1998", + "Text": "8 Radiation has dual nature: wave and particle The nature of experiment\ndetermines whether a wave or particle description is best suited for\nunderstanding the experimental result Reasoning that radiation and\nmatter should be symmetrical in nature, Louis Victor de Broglie\nattributed a wave-like character to matter (material particles)" + }, + { + "Chapter": "9", + "sentence_range": "1996-1999", + "Text": "Radiation has dual nature: wave and particle The nature of experiment\ndetermines whether a wave or particle description is best suited for\nunderstanding the experimental result Reasoning that radiation and\nmatter should be symmetrical in nature, Louis Victor de Broglie\nattributed a wave-like character to matter (material particles) The waves\nassociated with the moving material particles are called matter waves\nor de Broglie waves" + }, + { + "Chapter": "9", + "sentence_range": "1997-2000", + "Text": "The nature of experiment\ndetermines whether a wave or particle description is best suited for\nunderstanding the experimental result Reasoning that radiation and\nmatter should be symmetrical in nature, Louis Victor de Broglie\nattributed a wave-like character to matter (material particles) The waves\nassociated with the moving material particles are called matter waves\nor de Broglie waves 9" + }, + { + "Chapter": "9", + "sentence_range": "1998-2001", + "Text": "Reasoning that radiation and\nmatter should be symmetrical in nature, Louis Victor de Broglie\nattributed a wave-like character to matter (material particles) The waves\nassociated with the moving material particles are called matter waves\nor de Broglie waves 9 The de Broglie wavelength (l) associated with a moving particle is\nrelated to its momentum p as: l = h/p" + }, + { + "Chapter": "9", + "sentence_range": "1999-2002", + "Text": "The waves\nassociated with the moving material particles are called matter waves\nor de Broglie waves 9 The de Broglie wavelength (l) associated with a moving particle is\nrelated to its momentum p as: l = h/p The dualism of matter is\ninherent in the de Broglie relation which contains a wave concept\n(l) and a particle concept (p)" + }, + { + "Chapter": "9", + "sentence_range": "2000-2003", + "Text": "9 The de Broglie wavelength (l) associated with a moving particle is\nrelated to its momentum p as: l = h/p The dualism of matter is\ninherent in the de Broglie relation which contains a wave concept\n(l) and a particle concept (p) The de Broglie wavelength is\nindependent of the charge and nature of the material particle" + }, + { + "Chapter": "9", + "sentence_range": "2001-2004", + "Text": "The de Broglie wavelength (l) associated with a moving particle is\nrelated to its momentum p as: l = h/p The dualism of matter is\ninherent in the de Broglie relation which contains a wave concept\n(l) and a particle concept (p) The de Broglie wavelength is\nindependent of the charge and nature of the material particle It is\nsignificantly measurable (of the order of the atomic-planes spacing\nin crystals) only in case of sub-atomic particles like electrons,\nprotons, etc" + }, + { + "Chapter": "9", + "sentence_range": "2002-2005", + "Text": "The dualism of matter is\ninherent in the de Broglie relation which contains a wave concept\n(l) and a particle concept (p) The de Broglie wavelength is\nindependent of the charge and nature of the material particle It is\nsignificantly measurable (of the order of the atomic-planes spacing\nin crystals) only in case of sub-atomic particles like electrons,\nprotons, etc (due to smallness of their masses and hence, momenta)" + }, + { + "Chapter": "9", + "sentence_range": "2003-2006", + "Text": "The de Broglie wavelength is\nindependent of the charge and nature of the material particle It is\nsignificantly measurable (of the order of the atomic-planes spacing\nin crystals) only in case of sub-atomic particles like electrons,\nprotons, etc (due to smallness of their masses and hence, momenta) However, it is indeed very small, quite beyond measurement, in case\nof macroscopic objects, commonly encountered in everyday life" + }, + { + "Chapter": "9", + "sentence_range": "2004-2007", + "Text": "It is\nsignificantly measurable (of the order of the atomic-planes spacing\nin crystals) only in case of sub-atomic particles like electrons,\nprotons, etc (due to smallness of their masses and hence, momenta) However, it is indeed very small, quite beyond measurement, in case\nof macroscopic objects, commonly encountered in everyday life Rationalised 2023-24\nPhysics\n288\nPOINTS TO PONDER\n1" + }, + { + "Chapter": "9", + "sentence_range": "2005-2008", + "Text": "(due to smallness of their masses and hence, momenta) However, it is indeed very small, quite beyond measurement, in case\nof macroscopic objects, commonly encountered in everyday life Rationalised 2023-24\nPhysics\n288\nPOINTS TO PONDER\n1 Free electrons in a metal are free in the sense that they move inside the\nmetal in a constant potential (This is only an approximation)" + }, + { + "Chapter": "9", + "sentence_range": "2006-2009", + "Text": "However, it is indeed very small, quite beyond measurement, in case\nof macroscopic objects, commonly encountered in everyday life Rationalised 2023-24\nPhysics\n288\nPOINTS TO PONDER\n1 Free electrons in a metal are free in the sense that they move inside the\nmetal in a constant potential (This is only an approximation) They are\nnot free to move out of the metal" + }, + { + "Chapter": "9", + "sentence_range": "2007-2010", + "Text": "Rationalised 2023-24\nPhysics\n288\nPOINTS TO PONDER\n1 Free electrons in a metal are free in the sense that they move inside the\nmetal in a constant potential (This is only an approximation) They are\nnot free to move out of the metal They need additional energy to get\nout of the metal" + }, + { + "Chapter": "9", + "sentence_range": "2008-2011", + "Text": "Free electrons in a metal are free in the sense that they move inside the\nmetal in a constant potential (This is only an approximation) They are\nnot free to move out of the metal They need additional energy to get\nout of the metal 2" + }, + { + "Chapter": "9", + "sentence_range": "2009-2012", + "Text": "They are\nnot free to move out of the metal They need additional energy to get\nout of the metal 2 Free electrons in a metal do not all have the same energy" + }, + { + "Chapter": "9", + "sentence_range": "2010-2013", + "Text": "They need additional energy to get\nout of the metal 2 Free electrons in a metal do not all have the same energy Like molecules\nin a gas jar, the electrons have a certain energy distribution at a given\ntemperature" + }, + { + "Chapter": "9", + "sentence_range": "2011-2014", + "Text": "2 Free electrons in a metal do not all have the same energy Like molecules\nin a gas jar, the electrons have a certain energy distribution at a given\ntemperature This distribution is different from the usual Maxwell\u2019s\ndistribution that you have learnt in the study of kinetic theory of gases" + }, + { + "Chapter": "9", + "sentence_range": "2012-2015", + "Text": "Free electrons in a metal do not all have the same energy Like molecules\nin a gas jar, the electrons have a certain energy distribution at a given\ntemperature This distribution is different from the usual Maxwell\u2019s\ndistribution that you have learnt in the study of kinetic theory of gases You will learn about it in later courses, but the difference has to do\nwith the fact that electrons obey Pauli\u2019s exclusion principle" + }, + { + "Chapter": "9", + "sentence_range": "2013-2016", + "Text": "Like molecules\nin a gas jar, the electrons have a certain energy distribution at a given\ntemperature This distribution is different from the usual Maxwell\u2019s\ndistribution that you have learnt in the study of kinetic theory of gases You will learn about it in later courses, but the difference has to do\nwith the fact that electrons obey Pauli\u2019s exclusion principle 3" + }, + { + "Chapter": "9", + "sentence_range": "2014-2017", + "Text": "This distribution is different from the usual Maxwell\u2019s\ndistribution that you have learnt in the study of kinetic theory of gases You will learn about it in later courses, but the difference has to do\nwith the fact that electrons obey Pauli\u2019s exclusion principle 3 Because of the energy distribution of free electrons in a metal, the energy\nrequired by an electron to come out of the metal is different for different\nelectrons" + }, + { + "Chapter": "9", + "sentence_range": "2015-2018", + "Text": "You will learn about it in later courses, but the difference has to do\nwith the fact that electrons obey Pauli\u2019s exclusion principle 3 Because of the energy distribution of free electrons in a metal, the energy\nrequired by an electron to come out of the metal is different for different\nelectrons Electrons with higher energy require less additional energy to\ncome out of the metal than those with lower energies" + }, + { + "Chapter": "9", + "sentence_range": "2016-2019", + "Text": "3 Because of the energy distribution of free electrons in a metal, the energy\nrequired by an electron to come out of the metal is different for different\nelectrons Electrons with higher energy require less additional energy to\ncome out of the metal than those with lower energies Work function is\nthe least energy required by an electron to come out of the metal" + }, + { + "Chapter": "9", + "sentence_range": "2017-2020", + "Text": "Because of the energy distribution of free electrons in a metal, the energy\nrequired by an electron to come out of the metal is different for different\nelectrons Electrons with higher energy require less additional energy to\ncome out of the metal than those with lower energies Work function is\nthe least energy required by an electron to come out of the metal 4" + }, + { + "Chapter": "9", + "sentence_range": "2018-2021", + "Text": "Electrons with higher energy require less additional energy to\ncome out of the metal than those with lower energies Work function is\nthe least energy required by an electron to come out of the metal 4 Observations on photoelectric effect imply that in the event of matter-\nlight interaction, absorption of energy takes place in discrete units of hn" + }, + { + "Chapter": "9", + "sentence_range": "2019-2022", + "Text": "Work function is\nthe least energy required by an electron to come out of the metal 4 Observations on photoelectric effect imply that in the event of matter-\nlight interaction, absorption of energy takes place in discrete units of hn This is not quite the same as saying that light consists of particles,\neach of energy hn" + }, + { + "Chapter": "9", + "sentence_range": "2020-2023", + "Text": "4 Observations on photoelectric effect imply that in the event of matter-\nlight interaction, absorption of energy takes place in discrete units of hn This is not quite the same as saying that light consists of particles,\neach of energy hn 5" + }, + { + "Chapter": "9", + "sentence_range": "2021-2024", + "Text": "Observations on photoelectric effect imply that in the event of matter-\nlight interaction, absorption of energy takes place in discrete units of hn This is not quite the same as saying that light consists of particles,\neach of energy hn 5 Observations on the stopping potential (its independence of intensity\nand dependence on frequency) are the crucial discriminator between\nthe wave-picture and photon-picture of photoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "2022-2025", + "Text": "This is not quite the same as saying that light consists of particles,\neach of energy hn 5 Observations on the stopping potential (its independence of intensity\nand dependence on frequency) are the crucial discriminator between\nthe wave-picture and photon-picture of photoelectric effect 6" + }, + { + "Chapter": "9", + "sentence_range": "2023-2026", + "Text": "5 Observations on the stopping potential (its independence of intensity\nand dependence on frequency) are the crucial discriminator between\nthe wave-picture and photon-picture of photoelectric effect 6 The wavelength of a matter wave given by \n\u03bb =ph\n has physical\nsignificance; its phase velocity vp has no physical significance" + }, + { + "Chapter": "9", + "sentence_range": "2024-2027", + "Text": "Observations on the stopping potential (its independence of intensity\nand dependence on frequency) are the crucial discriminator between\nthe wave-picture and photon-picture of photoelectric effect 6 The wavelength of a matter wave given by \n\u03bb =ph\n has physical\nsignificance; its phase velocity vp has no physical significance However,\nthe group velocity of the matter wave is physically meaningful and\nequals the velocity of the particle" + }, + { + "Chapter": "9", + "sentence_range": "2025-2028", + "Text": "6 The wavelength of a matter wave given by \n\u03bb =ph\n has physical\nsignificance; its phase velocity vp has no physical significance However,\nthe group velocity of the matter wave is physically meaningful and\nequals the velocity of the particle Physical\nSymbol\nDimensions\nUnit\nRemarks\nQuantity\nPlanck\u2019s\nh\n[ML2T \u20131]\nJ s\nE = hn\nconstant\nStopping\nV0\n[ML2T \u20133A\u20131]\nV\ne V0= Kmax\npotential\nWork\nf0\n[ML2T \u20132]\nJ; eV\nKmax = E \u2013f0\nfunction\nThreshold\nn0\n[T \u20131]\nHz\nn0 = f0/h\nfrequency\nde Broglie\nl\n[L]\nm\n\uf06c= h/p\nwavelength\nEXERCISES\n11" + }, + { + "Chapter": "9", + "sentence_range": "2026-2029", + "Text": "The wavelength of a matter wave given by \n\u03bb =ph\n has physical\nsignificance; its phase velocity vp has no physical significance However,\nthe group velocity of the matter wave is physically meaningful and\nequals the velocity of the particle Physical\nSymbol\nDimensions\nUnit\nRemarks\nQuantity\nPlanck\u2019s\nh\n[ML2T \u20131]\nJ s\nE = hn\nconstant\nStopping\nV0\n[ML2T \u20133A\u20131]\nV\ne V0= Kmax\npotential\nWork\nf0\n[ML2T \u20132]\nJ; eV\nKmax = E \u2013f0\nfunction\nThreshold\nn0\n[T \u20131]\nHz\nn0 = f0/h\nfrequency\nde Broglie\nl\n[L]\nm\n\uf06c= h/p\nwavelength\nEXERCISES\n11 1\nFind the\n(a) maximum frequency, and\n(b) minimum wavelength of X-rays produced by 30 kV electrons" + }, + { + "Chapter": "9", + "sentence_range": "2027-2030", + "Text": "However,\nthe group velocity of the matter wave is physically meaningful and\nequals the velocity of the particle Physical\nSymbol\nDimensions\nUnit\nRemarks\nQuantity\nPlanck\u2019s\nh\n[ML2T \u20131]\nJ s\nE = hn\nconstant\nStopping\nV0\n[ML2T \u20133A\u20131]\nV\ne V0= Kmax\npotential\nWork\nf0\n[ML2T \u20132]\nJ; eV\nKmax = E \u2013f0\nfunction\nThreshold\nn0\n[T \u20131]\nHz\nn0 = f0/h\nfrequency\nde Broglie\nl\n[L]\nm\n\uf06c= h/p\nwavelength\nEXERCISES\n11 1\nFind the\n(a) maximum frequency, and\n(b) minimum wavelength of X-rays produced by 30 kV electrons Rationalised 2023-24\n289\nDual Nature of Radiation\nand Matter\n11" + }, + { + "Chapter": "9", + "sentence_range": "2028-2031", + "Text": "Physical\nSymbol\nDimensions\nUnit\nRemarks\nQuantity\nPlanck\u2019s\nh\n[ML2T \u20131]\nJ s\nE = hn\nconstant\nStopping\nV0\n[ML2T \u20133A\u20131]\nV\ne V0= Kmax\npotential\nWork\nf0\n[ML2T \u20132]\nJ; eV\nKmax = E \u2013f0\nfunction\nThreshold\nn0\n[T \u20131]\nHz\nn0 = f0/h\nfrequency\nde Broglie\nl\n[L]\nm\n\uf06c= h/p\nwavelength\nEXERCISES\n11 1\nFind the\n(a) maximum frequency, and\n(b) minimum wavelength of X-rays produced by 30 kV electrons Rationalised 2023-24\n289\nDual Nature of Radiation\nand Matter\n11 2\nThe work function of caesium metal is 2" + }, + { + "Chapter": "9", + "sentence_range": "2029-2032", + "Text": "1\nFind the\n(a) maximum frequency, and\n(b) minimum wavelength of X-rays produced by 30 kV electrons Rationalised 2023-24\n289\nDual Nature of Radiation\nand Matter\n11 2\nThe work function of caesium metal is 2 14 eV" + }, + { + "Chapter": "9", + "sentence_range": "2030-2033", + "Text": "Rationalised 2023-24\n289\nDual Nature of Radiation\nand Matter\n11 2\nThe work function of caesium metal is 2 14 eV When light of\nfrequency 6 \u00d71014Hz is incident on the metal surface, photoemission\nof electrons occurs" + }, + { + "Chapter": "9", + "sentence_range": "2031-2034", + "Text": "2\nThe work function of caesium metal is 2 14 eV When light of\nfrequency 6 \u00d71014Hz is incident on the metal surface, photoemission\nof electrons occurs What is the\n(a) maximum kinetic energy of the emitted electrons,\n(b) Stopping potential, and\n(c) maximum speed of the emitted photoelectrons" + }, + { + "Chapter": "9", + "sentence_range": "2032-2035", + "Text": "14 eV When light of\nfrequency 6 \u00d71014Hz is incident on the metal surface, photoemission\nof electrons occurs What is the\n(a) maximum kinetic energy of the emitted electrons,\n(b) Stopping potential, and\n(c) maximum speed of the emitted photoelectrons 11" + }, + { + "Chapter": "9", + "sentence_range": "2033-2036", + "Text": "When light of\nfrequency 6 \u00d71014Hz is incident on the metal surface, photoemission\nof electrons occurs What is the\n(a) maximum kinetic energy of the emitted electrons,\n(b) Stopping potential, and\n(c) maximum speed of the emitted photoelectrons 11 3\nThe photoelectric cut-off voltage in a certain experiment is 1" + }, + { + "Chapter": "9", + "sentence_range": "2034-2037", + "Text": "What is the\n(a) maximum kinetic energy of the emitted electrons,\n(b) Stopping potential, and\n(c) maximum speed of the emitted photoelectrons 11 3\nThe photoelectric cut-off voltage in a certain experiment is 1 5 V" + }, + { + "Chapter": "9", + "sentence_range": "2035-2038", + "Text": "11 3\nThe photoelectric cut-off voltage in a certain experiment is 1 5 V What is the maximum kinetic energy of photoelectrons emitted" + }, + { + "Chapter": "9", + "sentence_range": "2036-2039", + "Text": "3\nThe photoelectric cut-off voltage in a certain experiment is 1 5 V What is the maximum kinetic energy of photoelectrons emitted 11" + }, + { + "Chapter": "9", + "sentence_range": "2037-2040", + "Text": "5 V What is the maximum kinetic energy of photoelectrons emitted 11 4\nMonochromatic light of wavelength 632" + }, + { + "Chapter": "9", + "sentence_range": "2038-2041", + "Text": "What is the maximum kinetic energy of photoelectrons emitted 11 4\nMonochromatic light of wavelength 632 8 nm is produced by a\nhelium-neon laser" + }, + { + "Chapter": "9", + "sentence_range": "2039-2042", + "Text": "11 4\nMonochromatic light of wavelength 632 8 nm is produced by a\nhelium-neon laser The power emitted is 9" + }, + { + "Chapter": "9", + "sentence_range": "2040-2043", + "Text": "4\nMonochromatic light of wavelength 632 8 nm is produced by a\nhelium-neon laser The power emitted is 9 42 mW" + }, + { + "Chapter": "9", + "sentence_range": "2041-2044", + "Text": "8 nm is produced by a\nhelium-neon laser The power emitted is 9 42 mW (a) Find the energy and momentum of each photon in the light beam,\n(b) How many photons per second, on the average, arrive at a target\nirradiated by this beam" + }, + { + "Chapter": "9", + "sentence_range": "2042-2045", + "Text": "The power emitted is 9 42 mW (a) Find the energy and momentum of each photon in the light beam,\n(b) How many photons per second, on the average, arrive at a target\nirradiated by this beam (Assume the beam to have uniform\ncross-section which is less than the target area), and\n(c) How fast does a hydrogen atom have to travel in order to have\nthe same momentum as that of the photon" + }, + { + "Chapter": "9", + "sentence_range": "2043-2046", + "Text": "42 mW (a) Find the energy and momentum of each photon in the light beam,\n(b) How many photons per second, on the average, arrive at a target\nirradiated by this beam (Assume the beam to have uniform\ncross-section which is less than the target area), and\n(c) How fast does a hydrogen atom have to travel in order to have\nthe same momentum as that of the photon 11" + }, + { + "Chapter": "9", + "sentence_range": "2044-2047", + "Text": "(a) Find the energy and momentum of each photon in the light beam,\n(b) How many photons per second, on the average, arrive at a target\nirradiated by this beam (Assume the beam to have uniform\ncross-section which is less than the target area), and\n(c) How fast does a hydrogen atom have to travel in order to have\nthe same momentum as that of the photon 11 5\nIn an experiment on photoelectric effect, the slope of the cut-off voltage\nversus frequency of incident light is found to be 4" + }, + { + "Chapter": "9", + "sentence_range": "2045-2048", + "Text": "(Assume the beam to have uniform\ncross-section which is less than the target area), and\n(c) How fast does a hydrogen atom have to travel in order to have\nthe same momentum as that of the photon 11 5\nIn an experiment on photoelectric effect, the slope of the cut-off voltage\nversus frequency of incident light is found to be 4 12 \u00d7 10\u201315 V s" + }, + { + "Chapter": "9", + "sentence_range": "2046-2049", + "Text": "11 5\nIn an experiment on photoelectric effect, the slope of the cut-off voltage\nversus frequency of incident light is found to be 4 12 \u00d7 10\u201315 V s Calculate\nthe value of Planck\u2019s constant" + }, + { + "Chapter": "9", + "sentence_range": "2047-2050", + "Text": "5\nIn an experiment on photoelectric effect, the slope of the cut-off voltage\nversus frequency of incident light is found to be 4 12 \u00d7 10\u201315 V s Calculate\nthe value of Planck\u2019s constant 11" + }, + { + "Chapter": "9", + "sentence_range": "2048-2051", + "Text": "12 \u00d7 10\u201315 V s Calculate\nthe value of Planck\u2019s constant 11 6\nThe threshold frequency for a certain metal is 3" + }, + { + "Chapter": "9", + "sentence_range": "2049-2052", + "Text": "Calculate\nthe value of Planck\u2019s constant 11 6\nThe threshold frequency for a certain metal is 3 3 \u00d7 1014 Hz" + }, + { + "Chapter": "9", + "sentence_range": "2050-2053", + "Text": "11 6\nThe threshold frequency for a certain metal is 3 3 \u00d7 1014 Hz If light\nof frequency 8" + }, + { + "Chapter": "9", + "sentence_range": "2051-2054", + "Text": "6\nThe threshold frequency for a certain metal is 3 3 \u00d7 1014 Hz If light\nof frequency 8 2 \u00d7 1014 Hz is incident on the metal, predict the cut-\noff voltage for the photoelectric emission" + }, + { + "Chapter": "9", + "sentence_range": "2052-2055", + "Text": "3 \u00d7 1014 Hz If light\nof frequency 8 2 \u00d7 1014 Hz is incident on the metal, predict the cut-\noff voltage for the photoelectric emission 11" + }, + { + "Chapter": "9", + "sentence_range": "2053-2056", + "Text": "If light\nof frequency 8 2 \u00d7 1014 Hz is incident on the metal, predict the cut-\noff voltage for the photoelectric emission 11 7\nThe work function for a certain metal is 4" + }, + { + "Chapter": "9", + "sentence_range": "2054-2057", + "Text": "2 \u00d7 1014 Hz is incident on the metal, predict the cut-\noff voltage for the photoelectric emission 11 7\nThe work function for a certain metal is 4 2 eV" + }, + { + "Chapter": "9", + "sentence_range": "2055-2058", + "Text": "11 7\nThe work function for a certain metal is 4 2 eV Will this metal give\nhotoelectric emission for incident radiation of wavelength 330 nm" + }, + { + "Chapter": "9", + "sentence_range": "2056-2059", + "Text": "7\nThe work function for a certain metal is 4 2 eV Will this metal give\nhotoelectric emission for incident radiation of wavelength 330 nm 11" + }, + { + "Chapter": "9", + "sentence_range": "2057-2060", + "Text": "2 eV Will this metal give\nhotoelectric emission for incident radiation of wavelength 330 nm 11 8\nLight of frequency 7" + }, + { + "Chapter": "9", + "sentence_range": "2058-2061", + "Text": "Will this metal give\nhotoelectric emission for incident radiation of wavelength 330 nm 11 8\nLight of frequency 7 21 \u00d7 1014 Hz is incident on a metal surface" + }, + { + "Chapter": "9", + "sentence_range": "2059-2062", + "Text": "11 8\nLight of frequency 7 21 \u00d7 1014 Hz is incident on a metal surface Electrons with a maximum speed of 6" + }, + { + "Chapter": "9", + "sentence_range": "2060-2063", + "Text": "8\nLight of frequency 7 21 \u00d7 1014 Hz is incident on a metal surface Electrons with a maximum speed of 6 0 \u00d7 105 m/s are ejected from\nthe surface" + }, + { + "Chapter": "9", + "sentence_range": "2061-2064", + "Text": "21 \u00d7 1014 Hz is incident on a metal surface Electrons with a maximum speed of 6 0 \u00d7 105 m/s are ejected from\nthe surface What is the threshold frequency for photoemission of\nelectrons" + }, + { + "Chapter": "9", + "sentence_range": "2062-2065", + "Text": "Electrons with a maximum speed of 6 0 \u00d7 105 m/s are ejected from\nthe surface What is the threshold frequency for photoemission of\nelectrons 11" + }, + { + "Chapter": "9", + "sentence_range": "2063-2066", + "Text": "0 \u00d7 105 m/s are ejected from\nthe surface What is the threshold frequency for photoemission of\nelectrons 11 9\nLight of wavelength 488 nm is produced by an argon laser which is\nused in the photoelectric effect" + }, + { + "Chapter": "9", + "sentence_range": "2064-2067", + "Text": "What is the threshold frequency for photoemission of\nelectrons 11 9\nLight of wavelength 488 nm is produced by an argon laser which is\nused in the photoelectric effect When light from this spectral line is\nincident on the emitter, the stopping (cut-off) potential of\nphotoelectrons is 0" + }, + { + "Chapter": "9", + "sentence_range": "2065-2068", + "Text": "11 9\nLight of wavelength 488 nm is produced by an argon laser which is\nused in the photoelectric effect When light from this spectral line is\nincident on the emitter, the stopping (cut-off) potential of\nphotoelectrons is 0 38 V" + }, + { + "Chapter": "9", + "sentence_range": "2066-2069", + "Text": "9\nLight of wavelength 488 nm is produced by an argon laser which is\nused in the photoelectric effect When light from this spectral line is\nincident on the emitter, the stopping (cut-off) potential of\nphotoelectrons is 0 38 V Find the work function of the material from\nwhich the emitter is made" + }, + { + "Chapter": "9", + "sentence_range": "2067-2070", + "Text": "When light from this spectral line is\nincident on the emitter, the stopping (cut-off) potential of\nphotoelectrons is 0 38 V Find the work function of the material from\nwhich the emitter is made 11" + }, + { + "Chapter": "9", + "sentence_range": "2068-2071", + "Text": "38 V Find the work function of the material from\nwhich the emitter is made 11 10 What is the de Broglie wavelength of\n(a) a bullet of mass 0" + }, + { + "Chapter": "9", + "sentence_range": "2069-2072", + "Text": "Find the work function of the material from\nwhich the emitter is made 11 10 What is the de Broglie wavelength of\n(a) a bullet of mass 0 040 kg travelling at the speed of 1" + }, + { + "Chapter": "9", + "sentence_range": "2070-2073", + "Text": "11 10 What is the de Broglie wavelength of\n(a) a bullet of mass 0 040 kg travelling at the speed of 1 0 km/s,\n(b) a ball of mass 0" + }, + { + "Chapter": "9", + "sentence_range": "2071-2074", + "Text": "10 What is the de Broglie wavelength of\n(a) a bullet of mass 0 040 kg travelling at the speed of 1 0 km/s,\n(b) a ball of mass 0 060 kg moving at a speed of 1" + }, + { + "Chapter": "9", + "sentence_range": "2072-2075", + "Text": "040 kg travelling at the speed of 1 0 km/s,\n(b) a ball of mass 0 060 kg moving at a speed of 1 0 m/s, and\n(c) a dust particle of mass 1" + }, + { + "Chapter": "9", + "sentence_range": "2073-2076", + "Text": "0 km/s,\n(b) a ball of mass 0 060 kg moving at a speed of 1 0 m/s, and\n(c) a dust particle of mass 1 0 \u00d7 10\u20139 kg drifting with a speed of 2" + }, + { + "Chapter": "9", + "sentence_range": "2074-2077", + "Text": "060 kg moving at a speed of 1 0 m/s, and\n(c) a dust particle of mass 1 0 \u00d7 10\u20139 kg drifting with a speed of 2 2\nm/s" + }, + { + "Chapter": "9", + "sentence_range": "2075-2078", + "Text": "0 m/s, and\n(c) a dust particle of mass 1 0 \u00d7 10\u20139 kg drifting with a speed of 2 2\nm/s 11" + }, + { + "Chapter": "9", + "sentence_range": "2076-2079", + "Text": "0 \u00d7 10\u20139 kg drifting with a speed of 2 2\nm/s 11 11 Show that the wavelength of electromagnetic radiation is equal to\nthe de Broglie wavelength of its quantum (photon)" + }, + { + "Chapter": "9", + "sentence_range": "2077-2080", + "Text": "2\nm/s 11 11 Show that the wavelength of electromagnetic radiation is equal to\nthe de Broglie wavelength of its quantum (photon) Rationalised 2023-24\nPhysics\n290\n12" + }, + { + "Chapter": "9", + "sentence_range": "2078-2081", + "Text": "11 11 Show that the wavelength of electromagnetic radiation is equal to\nthe de Broglie wavelength of its quantum (photon) Rationalised 2023-24\nPhysics\n290\n12 1 INTRODUCTION\nBy the nineteenth century, enough evidence had accumulated in favour of\natomic hypothesis of matter" + }, + { + "Chapter": "9", + "sentence_range": "2079-2082", + "Text": "11 Show that the wavelength of electromagnetic radiation is equal to\nthe de Broglie wavelength of its quantum (photon) Rationalised 2023-24\nPhysics\n290\n12 1 INTRODUCTION\nBy the nineteenth century, enough evidence had accumulated in favour of\natomic hypothesis of matter In 1897, the experiments on electric discharge\nthrough gases carried out by the English physicist J" + }, + { + "Chapter": "9", + "sentence_range": "2080-2083", + "Text": "Rationalised 2023-24\nPhysics\n290\n12 1 INTRODUCTION\nBy the nineteenth century, enough evidence had accumulated in favour of\natomic hypothesis of matter In 1897, the experiments on electric discharge\nthrough gases carried out by the English physicist J J" + }, + { + "Chapter": "9", + "sentence_range": "2081-2084", + "Text": "1 INTRODUCTION\nBy the nineteenth century, enough evidence had accumulated in favour of\natomic hypothesis of matter In 1897, the experiments on electric discharge\nthrough gases carried out by the English physicist J J Thomson (1856 \u2013\n1940) revealed that atoms of different elements contain negatively charged\nconstituents (electrons) that are identical for all atoms" + }, + { + "Chapter": "9", + "sentence_range": "2082-2085", + "Text": "In 1897, the experiments on electric discharge\nthrough gases carried out by the English physicist J J Thomson (1856 \u2013\n1940) revealed that atoms of different elements contain negatively charged\nconstituents (electrons) that are identical for all atoms However, atoms on a\nwhole are electrically neutral" + }, + { + "Chapter": "9", + "sentence_range": "2083-2086", + "Text": "J Thomson (1856 \u2013\n1940) revealed that atoms of different elements contain negatively charged\nconstituents (electrons) that are identical for all atoms However, atoms on a\nwhole are electrically neutral Therefore, an atom must also contain some\npositive charge to neutralise the negative charge of the electrons" + }, + { + "Chapter": "9", + "sentence_range": "2084-2087", + "Text": "Thomson (1856 \u2013\n1940) revealed that atoms of different elements contain negatively charged\nconstituents (electrons) that are identical for all atoms However, atoms on a\nwhole are electrically neutral Therefore, an atom must also contain some\npositive charge to neutralise the negative charge of the electrons But what\nis the arrangement of the positive charge and the electrons inside the atom" + }, + { + "Chapter": "9", + "sentence_range": "2085-2088", + "Text": "However, atoms on a\nwhole are electrically neutral Therefore, an atom must also contain some\npositive charge to neutralise the negative charge of the electrons But what\nis the arrangement of the positive charge and the electrons inside the atom In other words, what is the structure of an atom" + }, + { + "Chapter": "9", + "sentence_range": "2086-2089", + "Text": "Therefore, an atom must also contain some\npositive charge to neutralise the negative charge of the electrons But what\nis the arrangement of the positive charge and the electrons inside the atom In other words, what is the structure of an atom The first model of atom was proposed by J" + }, + { + "Chapter": "9", + "sentence_range": "2087-2090", + "Text": "But what\nis the arrangement of the positive charge and the electrons inside the atom In other words, what is the structure of an atom The first model of atom was proposed by J J" + }, + { + "Chapter": "9", + "sentence_range": "2088-2091", + "Text": "In other words, what is the structure of an atom The first model of atom was proposed by J J Thomson in 1898" + }, + { + "Chapter": "9", + "sentence_range": "2089-2092", + "Text": "The first model of atom was proposed by J J Thomson in 1898 According to this model, the positive charge of the atom is uniformly\ndistributed throughout the volume of the atom and the negatively charged\nelectrons are embedded in it like seeds in a watermelon" + }, + { + "Chapter": "9", + "sentence_range": "2090-2093", + "Text": "J Thomson in 1898 According to this model, the positive charge of the atom is uniformly\ndistributed throughout the volume of the atom and the negatively charged\nelectrons are embedded in it like seeds in a watermelon This model was\npicturesquely called plum pudding model of the atom" + }, + { + "Chapter": "9", + "sentence_range": "2091-2094", + "Text": "Thomson in 1898 According to this model, the positive charge of the atom is uniformly\ndistributed throughout the volume of the atom and the negatively charged\nelectrons are embedded in it like seeds in a watermelon This model was\npicturesquely called plum pudding model of the atom However\nsubsequent studies on atoms, as described in this chapter, showed that\nthe distribution of the electrons and positive charges are very different\nfrom that proposed in this model" + }, + { + "Chapter": "9", + "sentence_range": "2092-2095", + "Text": "According to this model, the positive charge of the atom is uniformly\ndistributed throughout the volume of the atom and the negatively charged\nelectrons are embedded in it like seeds in a watermelon This model was\npicturesquely called plum pudding model of the atom However\nsubsequent studies on atoms, as described in this chapter, showed that\nthe distribution of the electrons and positive charges are very different\nfrom that proposed in this model We know that condensed matter (solids and liquids) and dense gases at\nall temperatures emit electromagnetic radiation in which a continuous\ndistribution of several wavelengths is present, though with different\nintensities" + }, + { + "Chapter": "9", + "sentence_range": "2093-2096", + "Text": "This model was\npicturesquely called plum pudding model of the atom However\nsubsequent studies on atoms, as described in this chapter, showed that\nthe distribution of the electrons and positive charges are very different\nfrom that proposed in this model We know that condensed matter (solids and liquids) and dense gases at\nall temperatures emit electromagnetic radiation in which a continuous\ndistribution of several wavelengths is present, though with different\nintensities This radiation is considered to be due to oscillations of atoms\nChapter Twelve\nATOMS\nRationalised 2023-24\n291\nAtoms\nand molecules, governed by the interaction of each atom or\nmolecule with its neighbours" + }, + { + "Chapter": "9", + "sentence_range": "2094-2097", + "Text": "However\nsubsequent studies on atoms, as described in this chapter, showed that\nthe distribution of the electrons and positive charges are very different\nfrom that proposed in this model We know that condensed matter (solids and liquids) and dense gases at\nall temperatures emit electromagnetic radiation in which a continuous\ndistribution of several wavelengths is present, though with different\nintensities This radiation is considered to be due to oscillations of atoms\nChapter Twelve\nATOMS\nRationalised 2023-24\n291\nAtoms\nand molecules, governed by the interaction of each atom or\nmolecule with its neighbours In contrast, light emitted from\nrarefied gases heated in a flame, or excited electrically in a\nglow tube such as the familiar neon sign or mercury vapour\nlight has only certain discrete wavelengths" + }, + { + "Chapter": "9", + "sentence_range": "2095-2098", + "Text": "We know that condensed matter (solids and liquids) and dense gases at\nall temperatures emit electromagnetic radiation in which a continuous\ndistribution of several wavelengths is present, though with different\nintensities This radiation is considered to be due to oscillations of atoms\nChapter Twelve\nATOMS\nRationalised 2023-24\n291\nAtoms\nand molecules, governed by the interaction of each atom or\nmolecule with its neighbours In contrast, light emitted from\nrarefied gases heated in a flame, or excited electrically in a\nglow tube such as the familiar neon sign or mercury vapour\nlight has only certain discrete wavelengths The spectrum\nappears as a series of bright lines" + }, + { + "Chapter": "9", + "sentence_range": "2096-2099", + "Text": "This radiation is considered to be due to oscillations of atoms\nChapter Twelve\nATOMS\nRationalised 2023-24\n291\nAtoms\nand molecules, governed by the interaction of each atom or\nmolecule with its neighbours In contrast, light emitted from\nrarefied gases heated in a flame, or excited electrically in a\nglow tube such as the familiar neon sign or mercury vapour\nlight has only certain discrete wavelengths The spectrum\nappears as a series of bright lines In such gases, the\naverage spacing between atoms is large" + }, + { + "Chapter": "9", + "sentence_range": "2097-2100", + "Text": "In contrast, light emitted from\nrarefied gases heated in a flame, or excited electrically in a\nglow tube such as the familiar neon sign or mercury vapour\nlight has only certain discrete wavelengths The spectrum\nappears as a series of bright lines In such gases, the\naverage spacing between atoms is large Hence, the\nradiation emitted can be considered due to individual atoms\nrather than because of interactions between atoms or\nmolecules" + }, + { + "Chapter": "9", + "sentence_range": "2098-2101", + "Text": "The spectrum\nappears as a series of bright lines In such gases, the\naverage spacing between atoms is large Hence, the\nradiation emitted can be considered due to individual atoms\nrather than because of interactions between atoms or\nmolecules In the early nineteenth century it was also established\nthat each element is associated with a characteristic\nspectrum of radiation, for example, hydrogen always gives\na set of lines with fixed relative position between the lines" + }, + { + "Chapter": "9", + "sentence_range": "2099-2102", + "Text": "In such gases, the\naverage spacing between atoms is large Hence, the\nradiation emitted can be considered due to individual atoms\nrather than because of interactions between atoms or\nmolecules In the early nineteenth century it was also established\nthat each element is associated with a characteristic\nspectrum of radiation, for example, hydrogen always gives\na set of lines with fixed relative position between the lines This fact suggested an intimate relationship between the\ninternal structure of an atom and the spectrum of\nradiation emitted by it" + }, + { + "Chapter": "9", + "sentence_range": "2100-2103", + "Text": "Hence, the\nradiation emitted can be considered due to individual atoms\nrather than because of interactions between atoms or\nmolecules In the early nineteenth century it was also established\nthat each element is associated with a characteristic\nspectrum of radiation, for example, hydrogen always gives\na set of lines with fixed relative position between the lines This fact suggested an intimate relationship between the\ninternal structure of an atom and the spectrum of\nradiation emitted by it In 1885, Johann Jakob Balmer\n(1825 \u2013 1898) obtained a simple empirical formula which\ngave the wavelengths of a group of lines emitted by atomic\nhydrogen" + }, + { + "Chapter": "9", + "sentence_range": "2101-2104", + "Text": "In the early nineteenth century it was also established\nthat each element is associated with a characteristic\nspectrum of radiation, for example, hydrogen always gives\na set of lines with fixed relative position between the lines This fact suggested an intimate relationship between the\ninternal structure of an atom and the spectrum of\nradiation emitted by it In 1885, Johann Jakob Balmer\n(1825 \u2013 1898) obtained a simple empirical formula which\ngave the wavelengths of a group of lines emitted by atomic\nhydrogen Since hydrogen is simplest of the elements\nknown, we shall consider its spectrum in detail in this\nchapter" + }, + { + "Chapter": "9", + "sentence_range": "2102-2105", + "Text": "This fact suggested an intimate relationship between the\ninternal structure of an atom and the spectrum of\nradiation emitted by it In 1885, Johann Jakob Balmer\n(1825 \u2013 1898) obtained a simple empirical formula which\ngave the wavelengths of a group of lines emitted by atomic\nhydrogen Since hydrogen is simplest of the elements\nknown, we shall consider its spectrum in detail in this\nchapter Ernst Rutherford (1871\u20131937), a former research\nstudent of J" + }, + { + "Chapter": "9", + "sentence_range": "2103-2106", + "Text": "In 1885, Johann Jakob Balmer\n(1825 \u2013 1898) obtained a simple empirical formula which\ngave the wavelengths of a group of lines emitted by atomic\nhydrogen Since hydrogen is simplest of the elements\nknown, we shall consider its spectrum in detail in this\nchapter Ernst Rutherford (1871\u20131937), a former research\nstudent of J J" + }, + { + "Chapter": "9", + "sentence_range": "2104-2107", + "Text": "Since hydrogen is simplest of the elements\nknown, we shall consider its spectrum in detail in this\nchapter Ernst Rutherford (1871\u20131937), a former research\nstudent of J J Thomson, was engaged in experiments on\na-particles emitted by some radioactive elements" + }, + { + "Chapter": "9", + "sentence_range": "2105-2108", + "Text": "Ernst Rutherford (1871\u20131937), a former research\nstudent of J J Thomson, was engaged in experiments on\na-particles emitted by some radioactive elements In 1906,\nhe proposed a classic experiment of scattering of these\na-particles by atoms to investigate the atomic structure" + }, + { + "Chapter": "9", + "sentence_range": "2106-2109", + "Text": "J Thomson, was engaged in experiments on\na-particles emitted by some radioactive elements In 1906,\nhe proposed a classic experiment of scattering of these\na-particles by atoms to investigate the atomic structure This experiment was later performed around 1911 by Hans\nGeiger (1882\u20131945) and Ernst Marsden (1889\u20131970, who\nwas 20 year-old student and had not yet earned his\nbachelor\u2019s degree)" + }, + { + "Chapter": "9", + "sentence_range": "2107-2110", + "Text": "Thomson, was engaged in experiments on\na-particles emitted by some radioactive elements In 1906,\nhe proposed a classic experiment of scattering of these\na-particles by atoms to investigate the atomic structure This experiment was later performed around 1911 by Hans\nGeiger (1882\u20131945) and Ernst Marsden (1889\u20131970, who\nwas 20 year-old student and had not yet earned his\nbachelor\u2019s degree) The details are discussed in Section\n12" + }, + { + "Chapter": "9", + "sentence_range": "2108-2111", + "Text": "In 1906,\nhe proposed a classic experiment of scattering of these\na-particles by atoms to investigate the atomic structure This experiment was later performed around 1911 by Hans\nGeiger (1882\u20131945) and Ernst Marsden (1889\u20131970, who\nwas 20 year-old student and had not yet earned his\nbachelor\u2019s degree) The details are discussed in Section\n12 2" + }, + { + "Chapter": "9", + "sentence_range": "2109-2112", + "Text": "This experiment was later performed around 1911 by Hans\nGeiger (1882\u20131945) and Ernst Marsden (1889\u20131970, who\nwas 20 year-old student and had not yet earned his\nbachelor\u2019s degree) The details are discussed in Section\n12 2 The explanation of the results led to the birth of\nRutherford\u2019s planetary model of atom (also called the\nnuclear model of the atom)" + }, + { + "Chapter": "9", + "sentence_range": "2110-2113", + "Text": "The details are discussed in Section\n12 2 The explanation of the results led to the birth of\nRutherford\u2019s planetary model of atom (also called the\nnuclear model of the atom) According to this the entire\npositive charge and most of the mass of the atom is\nconcentrated in a small volume called the nucleus with electrons revolving\naround the nucleus just as planets revolve around the sun" + }, + { + "Chapter": "9", + "sentence_range": "2111-2114", + "Text": "2 The explanation of the results led to the birth of\nRutherford\u2019s planetary model of atom (also called the\nnuclear model of the atom) According to this the entire\npositive charge and most of the mass of the atom is\nconcentrated in a small volume called the nucleus with electrons revolving\naround the nucleus just as planets revolve around the sun Rutherford\u2019s nuclear model was a major step towards how we see\nthe atom today" + }, + { + "Chapter": "9", + "sentence_range": "2112-2115", + "Text": "The explanation of the results led to the birth of\nRutherford\u2019s planetary model of atom (also called the\nnuclear model of the atom) According to this the entire\npositive charge and most of the mass of the atom is\nconcentrated in a small volume called the nucleus with electrons revolving\naround the nucleus just as planets revolve around the sun Rutherford\u2019s nuclear model was a major step towards how we see\nthe atom today However, it could not explain why atoms emit light of\nonly discrete wavelengths" + }, + { + "Chapter": "9", + "sentence_range": "2113-2116", + "Text": "According to this the entire\npositive charge and most of the mass of the atom is\nconcentrated in a small volume called the nucleus with electrons revolving\naround the nucleus just as planets revolve around the sun Rutherford\u2019s nuclear model was a major step towards how we see\nthe atom today However, it could not explain why atoms emit light of\nonly discrete wavelengths How could an atom as simple as hydrogen,\nconsisting of a single electron and a single proton, emit a complex\nspectrum of specific wavelengths" + }, + { + "Chapter": "9", + "sentence_range": "2114-2117", + "Text": "Rutherford\u2019s nuclear model was a major step towards how we see\nthe atom today However, it could not explain why atoms emit light of\nonly discrete wavelengths How could an atom as simple as hydrogen,\nconsisting of a single electron and a single proton, emit a complex\nspectrum of specific wavelengths In the classical picture of an atom, the\nelectron revolves round the nucleus much like the way a planet revolves\nround the sun" + }, + { + "Chapter": "9", + "sentence_range": "2115-2118", + "Text": "However, it could not explain why atoms emit light of\nonly discrete wavelengths How could an atom as simple as hydrogen,\nconsisting of a single electron and a single proton, emit a complex\nspectrum of specific wavelengths In the classical picture of an atom, the\nelectron revolves round the nucleus much like the way a planet revolves\nround the sun However, we shall see that there are some serious\ndifficulties in accepting such a model" + }, + { + "Chapter": "9", + "sentence_range": "2116-2119", + "Text": "How could an atom as simple as hydrogen,\nconsisting of a single electron and a single proton, emit a complex\nspectrum of specific wavelengths In the classical picture of an atom, the\nelectron revolves round the nucleus much like the way a planet revolves\nround the sun However, we shall see that there are some serious\ndifficulties in accepting such a model 12" + }, + { + "Chapter": "9", + "sentence_range": "2117-2120", + "Text": "In the classical picture of an atom, the\nelectron revolves round the nucleus much like the way a planet revolves\nround the sun However, we shall see that there are some serious\ndifficulties in accepting such a model 12 2 ALPHA-PARTICLE SCATTERING AND\nRUTHERFORD\u2019S NUCLEAR MODEL OF ATOM\nAt the suggestion of Ernst Rutherford, in 1911, H" + }, + { + "Chapter": "9", + "sentence_range": "2118-2121", + "Text": "However, we shall see that there are some serious\ndifficulties in accepting such a model 12 2 ALPHA-PARTICLE SCATTERING AND\nRUTHERFORD\u2019S NUCLEAR MODEL OF ATOM\nAt the suggestion of Ernst Rutherford, in 1911, H Geiger and E" + }, + { + "Chapter": "9", + "sentence_range": "2119-2122", + "Text": "12 2 ALPHA-PARTICLE SCATTERING AND\nRUTHERFORD\u2019S NUCLEAR MODEL OF ATOM\nAt the suggestion of Ernst Rutherford, in 1911, H Geiger and E Marsden\nperformed some experiments" + }, + { + "Chapter": "9", + "sentence_range": "2120-2123", + "Text": "2 ALPHA-PARTICLE SCATTERING AND\nRUTHERFORD\u2019S NUCLEAR MODEL OF ATOM\nAt the suggestion of Ernst Rutherford, in 1911, H Geiger and E Marsden\nperformed some experiments In one of their experiments, as shown in\nErnst Rutherford (1871 \u2013\n1937) New Zealand born,\nBritish physicist who did\npioneering \nwork \non\nradioactive radiation" + }, + { + "Chapter": "9", + "sentence_range": "2121-2124", + "Text": "Geiger and E Marsden\nperformed some experiments In one of their experiments, as shown in\nErnst Rutherford (1871 \u2013\n1937) New Zealand born,\nBritish physicist who did\npioneering \nwork \non\nradioactive radiation He\ndiscovered alpha-rays and\nbeta-rays" + }, + { + "Chapter": "9", + "sentence_range": "2122-2125", + "Text": "Marsden\nperformed some experiments In one of their experiments, as shown in\nErnst Rutherford (1871 \u2013\n1937) New Zealand born,\nBritish physicist who did\npioneering \nwork \non\nradioactive radiation He\ndiscovered alpha-rays and\nbeta-rays Along \nwith\nFederick Soddy, he created\nthe modern theory of\nradioactivity" + }, + { + "Chapter": "9", + "sentence_range": "2123-2126", + "Text": "In one of their experiments, as shown in\nErnst Rutherford (1871 \u2013\n1937) New Zealand born,\nBritish physicist who did\npioneering \nwork \non\nradioactive radiation He\ndiscovered alpha-rays and\nbeta-rays Along \nwith\nFederick Soddy, he created\nthe modern theory of\nradioactivity He studied\nthe \u2018emanation\u2019 of thorium\nand discovered a new noble\ngas, an isotope of radon,\nnow known as thoron" + }, + { + "Chapter": "9", + "sentence_range": "2124-2127", + "Text": "He\ndiscovered alpha-rays and\nbeta-rays Along \nwith\nFederick Soddy, he created\nthe modern theory of\nradioactivity He studied\nthe \u2018emanation\u2019 of thorium\nand discovered a new noble\ngas, an isotope of radon,\nnow known as thoron By\nscattering alpha-rays from\nthe \nmetal \nfoils, \nhe\ndiscovered the atomic\nnucleus and proposed the\nplenatery model of the\natom" + }, + { + "Chapter": "9", + "sentence_range": "2125-2128", + "Text": "Along \nwith\nFederick Soddy, he created\nthe modern theory of\nradioactivity He studied\nthe \u2018emanation\u2019 of thorium\nand discovered a new noble\ngas, an isotope of radon,\nnow known as thoron By\nscattering alpha-rays from\nthe \nmetal \nfoils, \nhe\ndiscovered the atomic\nnucleus and proposed the\nplenatery model of the\natom He also estimated the\napproximate size of the\nnucleus" + }, + { + "Chapter": "9", + "sentence_range": "2126-2129", + "Text": "He studied\nthe \u2018emanation\u2019 of thorium\nand discovered a new noble\ngas, an isotope of radon,\nnow known as thoron By\nscattering alpha-rays from\nthe \nmetal \nfoils, \nhe\ndiscovered the atomic\nnucleus and proposed the\nplenatery model of the\natom He also estimated the\napproximate size of the\nnucleus ERNST RUTHERFORD (1871 \u2013 1937)\nRationalised 2023-24\nPhysics\n292\nFig" + }, + { + "Chapter": "9", + "sentence_range": "2127-2130", + "Text": "By\nscattering alpha-rays from\nthe \nmetal \nfoils, \nhe\ndiscovered the atomic\nnucleus and proposed the\nplenatery model of the\natom He also estimated the\napproximate size of the\nnucleus ERNST RUTHERFORD (1871 \u2013 1937)\nRationalised 2023-24\nPhysics\n292\nFig 12" + }, + { + "Chapter": "9", + "sentence_range": "2128-2131", + "Text": "He also estimated the\napproximate size of the\nnucleus ERNST RUTHERFORD (1871 \u2013 1937)\nRationalised 2023-24\nPhysics\n292\nFig 12 1, they directed a beam of\n5" + }, + { + "Chapter": "9", + "sentence_range": "2129-2132", + "Text": "ERNST RUTHERFORD (1871 \u2013 1937)\nRationalised 2023-24\nPhysics\n292\nFig 12 1, they directed a beam of\n5 5 MeV a-particles emitted from a\n214\n83Bi radioactive source at a thin metal\nfoil made of gold" + }, + { + "Chapter": "9", + "sentence_range": "2130-2133", + "Text": "12 1, they directed a beam of\n5 5 MeV a-particles emitted from a\n214\n83Bi radioactive source at a thin metal\nfoil made of gold Figure 12" + }, + { + "Chapter": "9", + "sentence_range": "2131-2134", + "Text": "1, they directed a beam of\n5 5 MeV a-particles emitted from a\n214\n83Bi radioactive source at a thin metal\nfoil made of gold Figure 12 2 shows a\nschematic diagram of this experiment" + }, + { + "Chapter": "9", + "sentence_range": "2132-2135", + "Text": "5 MeV a-particles emitted from a\n214\n83Bi radioactive source at a thin metal\nfoil made of gold Figure 12 2 shows a\nschematic diagram of this experiment Alpha-particles emitted by a 214\n83Bi\nradioactive source were collimated into\na narrow beam by their passage\nthrough lead bricks" + }, + { + "Chapter": "9", + "sentence_range": "2133-2136", + "Text": "Figure 12 2 shows a\nschematic diagram of this experiment Alpha-particles emitted by a 214\n83Bi\nradioactive source were collimated into\na narrow beam by their passage\nthrough lead bricks The beam was\nallowed to fall on a thin foil of gold of\nthickness 2" + }, + { + "Chapter": "9", + "sentence_range": "2134-2137", + "Text": "2 shows a\nschematic diagram of this experiment Alpha-particles emitted by a 214\n83Bi\nradioactive source were collimated into\na narrow beam by their passage\nthrough lead bricks The beam was\nallowed to fall on a thin foil of gold of\nthickness 2 1 \u00d7 10\u20137 m" + }, + { + "Chapter": "9", + "sentence_range": "2135-2138", + "Text": "Alpha-particles emitted by a 214\n83Bi\nradioactive source were collimated into\na narrow beam by their passage\nthrough lead bricks The beam was\nallowed to fall on a thin foil of gold of\nthickness 2 1 \u00d7 10\u20137 m The scattered\nalpha-particles were observed through\na rotatable detector consisting of zinc\nsulphide screen and a microscope" + }, + { + "Chapter": "9", + "sentence_range": "2136-2139", + "Text": "The beam was\nallowed to fall on a thin foil of gold of\nthickness 2 1 \u00d7 10\u20137 m The scattered\nalpha-particles were observed through\na rotatable detector consisting of zinc\nsulphide screen and a microscope The\nscattered alpha-particles on striking\nthe screen produced brief light flashes\nor scintillations" + }, + { + "Chapter": "9", + "sentence_range": "2137-2140", + "Text": "1 \u00d7 10\u20137 m The scattered\nalpha-particles were observed through\na rotatable detector consisting of zinc\nsulphide screen and a microscope The\nscattered alpha-particles on striking\nthe screen produced brief light flashes\nor scintillations These flashes may be\nviewed through a microscope and the\ndistribution of the number of scattered\nparticles may be studied as a function\nof angle of scattering" + }, + { + "Chapter": "9", + "sentence_range": "2138-2141", + "Text": "The scattered\nalpha-particles were observed through\na rotatable detector consisting of zinc\nsulphide screen and a microscope The\nscattered alpha-particles on striking\nthe screen produced brief light flashes\nor scintillations These flashes may be\nviewed through a microscope and the\ndistribution of the number of scattered\nparticles may be studied as a function\nof angle of scattering FIGURE 12" + }, + { + "Chapter": "9", + "sentence_range": "2139-2142", + "Text": "The\nscattered alpha-particles on striking\nthe screen produced brief light flashes\nor scintillations These flashes may be\nviewed through a microscope and the\ndistribution of the number of scattered\nparticles may be studied as a function\nof angle of scattering FIGURE 12 2 Schematic arrangement of the Geiger-Marsden experiment" + }, + { + "Chapter": "9", + "sentence_range": "2140-2143", + "Text": "These flashes may be\nviewed through a microscope and the\ndistribution of the number of scattered\nparticles may be studied as a function\nof angle of scattering FIGURE 12 2 Schematic arrangement of the Geiger-Marsden experiment A typical graph of the total number of a-particles scattered at different\nangles, in a given interval of time, is shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "2141-2144", + "Text": "FIGURE 12 2 Schematic arrangement of the Geiger-Marsden experiment A typical graph of the total number of a-particles scattered at different\nangles, in a given interval of time, is shown in Fig 12" + }, + { + "Chapter": "9", + "sentence_range": "2142-2145", + "Text": "2 Schematic arrangement of the Geiger-Marsden experiment A typical graph of the total number of a-particles scattered at different\nangles, in a given interval of time, is shown in Fig 12 3" + }, + { + "Chapter": "9", + "sentence_range": "2143-2146", + "Text": "A typical graph of the total number of a-particles scattered at different\nangles, in a given interval of time, is shown in Fig 12 3 The dots in this\nfigure represent the data points and the solid curve is the theoretical\nprediction based on the assumption that the target atom has a small,\ndense, positively charged nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2144-2147", + "Text": "12 3 The dots in this\nfigure represent the data points and the solid curve is the theoretical\nprediction based on the assumption that the target atom has a small,\ndense, positively charged nucleus Many of the a-particles pass through\nthe foil" + }, + { + "Chapter": "9", + "sentence_range": "2145-2148", + "Text": "3 The dots in this\nfigure represent the data points and the solid curve is the theoretical\nprediction based on the assumption that the target atom has a small,\ndense, positively charged nucleus Many of the a-particles pass through\nthe foil It means that they do not suffer any collisions" + }, + { + "Chapter": "9", + "sentence_range": "2146-2149", + "Text": "The dots in this\nfigure represent the data points and the solid curve is the theoretical\nprediction based on the assumption that the target atom has a small,\ndense, positively charged nucleus Many of the a-particles pass through\nthe foil It means that they do not suffer any collisions Only about 0" + }, + { + "Chapter": "9", + "sentence_range": "2147-2150", + "Text": "Many of the a-particles pass through\nthe foil It means that they do not suffer any collisions Only about 0 14%\nof the incident a-particles scatter by more than 1\u00b0; and about 1 in 8000\ndeflect by more than 90\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "2148-2151", + "Text": "It means that they do not suffer any collisions Only about 0 14%\nof the incident a-particles scatter by more than 1\u00b0; and about 1 in 8000\ndeflect by more than 90\u00b0 Rutherford argued that, to deflect the a-particle\nbackwards, it must experience a large repulsive force" + }, + { + "Chapter": "9", + "sentence_range": "2149-2152", + "Text": "Only about 0 14%\nof the incident a-particles scatter by more than 1\u00b0; and about 1 in 8000\ndeflect by more than 90\u00b0 Rutherford argued that, to deflect the a-particle\nbackwards, it must experience a large repulsive force This force could\nFIGURE 12" + }, + { + "Chapter": "9", + "sentence_range": "2150-2153", + "Text": "14%\nof the incident a-particles scatter by more than 1\u00b0; and about 1 in 8000\ndeflect by more than 90\u00b0 Rutherford argued that, to deflect the a-particle\nbackwards, it must experience a large repulsive force This force could\nFIGURE 12 1 Geiger-Marsden scattering experiment" + }, + { + "Chapter": "9", + "sentence_range": "2151-2154", + "Text": "Rutherford argued that, to deflect the a-particle\nbackwards, it must experience a large repulsive force This force could\nFIGURE 12 1 Geiger-Marsden scattering experiment The entire apparatus is placed in a vacuum chamber\n(not shown in this figure)" + }, + { + "Chapter": "9", + "sentence_range": "2152-2155", + "Text": "This force could\nFIGURE 12 1 Geiger-Marsden scattering experiment The entire apparatus is placed in a vacuum chamber\n(not shown in this figure) Rationalised 2023-24\n293\nAtoms\nbe provided if the greater part of the\nmass of the atom and its positive charge\nwere concentrated tightly at its centre" + }, + { + "Chapter": "9", + "sentence_range": "2153-2156", + "Text": "1 Geiger-Marsden scattering experiment The entire apparatus is placed in a vacuum chamber\n(not shown in this figure) Rationalised 2023-24\n293\nAtoms\nbe provided if the greater part of the\nmass of the atom and its positive charge\nwere concentrated tightly at its centre Then the incoming a-particle could get\nvery close to the positive charge without\npenetrating it, and such a close\nencounter would result in a large\ndeflection" + }, + { + "Chapter": "9", + "sentence_range": "2154-2157", + "Text": "The entire apparatus is placed in a vacuum chamber\n(not shown in this figure) Rationalised 2023-24\n293\nAtoms\nbe provided if the greater part of the\nmass of the atom and its positive charge\nwere concentrated tightly at its centre Then the incoming a-particle could get\nvery close to the positive charge without\npenetrating it, and such a close\nencounter would result in a large\ndeflection This agreement supported\nthe hypothesis of the nuclear atom" + }, + { + "Chapter": "9", + "sentence_range": "2155-2158", + "Text": "Rationalised 2023-24\n293\nAtoms\nbe provided if the greater part of the\nmass of the atom and its positive charge\nwere concentrated tightly at its centre Then the incoming a-particle could get\nvery close to the positive charge without\npenetrating it, and such a close\nencounter would result in a large\ndeflection This agreement supported\nthe hypothesis of the nuclear atom This\nis why Rutherford is credited with the\ndiscovery of the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2156-2159", + "Text": "Then the incoming a-particle could get\nvery close to the positive charge without\npenetrating it, and such a close\nencounter would result in a large\ndeflection This agreement supported\nthe hypothesis of the nuclear atom This\nis why Rutherford is credited with the\ndiscovery of the nucleus In Rutherford\u2019s nuclear model of\nthe atom, the entire positive charge and\nmost of the mass of the atom are\nconcentrated in the nucleus with the\nelectrons some distance away" + }, + { + "Chapter": "9", + "sentence_range": "2157-2160", + "Text": "This agreement supported\nthe hypothesis of the nuclear atom This\nis why Rutherford is credited with the\ndiscovery of the nucleus In Rutherford\u2019s nuclear model of\nthe atom, the entire positive charge and\nmost of the mass of the atom are\nconcentrated in the nucleus with the\nelectrons some distance away The\nelectrons would be moving in orbits\nabout the nucleus just as the planets\ndo around the sun" + }, + { + "Chapter": "9", + "sentence_range": "2158-2161", + "Text": "This\nis why Rutherford is credited with the\ndiscovery of the nucleus In Rutherford\u2019s nuclear model of\nthe atom, the entire positive charge and\nmost of the mass of the atom are\nconcentrated in the nucleus with the\nelectrons some distance away The\nelectrons would be moving in orbits\nabout the nucleus just as the planets\ndo around the sun Rutherford\u2019s\nexperiments suggested the size of\nthe nucleus to be about 10\u201315 m to\n10\u201314 m" + }, + { + "Chapter": "9", + "sentence_range": "2159-2162", + "Text": "In Rutherford\u2019s nuclear model of\nthe atom, the entire positive charge and\nmost of the mass of the atom are\nconcentrated in the nucleus with the\nelectrons some distance away The\nelectrons would be moving in orbits\nabout the nucleus just as the planets\ndo around the sun Rutherford\u2019s\nexperiments suggested the size of\nthe nucleus to be about 10\u201315 m to\n10\u201314 m From kinetic theory, the size\nof an atom was known to be 10\u201310 m,\nabout 10,000 to 100,000 times larger\nthan the size of the nucleus (see Chapter 10, Section 10" + }, + { + "Chapter": "9", + "sentence_range": "2160-2163", + "Text": "The\nelectrons would be moving in orbits\nabout the nucleus just as the planets\ndo around the sun Rutherford\u2019s\nexperiments suggested the size of\nthe nucleus to be about 10\u201315 m to\n10\u201314 m From kinetic theory, the size\nof an atom was known to be 10\u201310 m,\nabout 10,000 to 100,000 times larger\nthan the size of the nucleus (see Chapter 10, Section 10 6 in Class XI\nPhysics textbook)" + }, + { + "Chapter": "9", + "sentence_range": "2161-2164", + "Text": "Rutherford\u2019s\nexperiments suggested the size of\nthe nucleus to be about 10\u201315 m to\n10\u201314 m From kinetic theory, the size\nof an atom was known to be 10\u201310 m,\nabout 10,000 to 100,000 times larger\nthan the size of the nucleus (see Chapter 10, Section 10 6 in Class XI\nPhysics textbook) Thus, the electrons would seem to be at a distance\nfrom the nucleus of about 10,000 to 100,000 times the size of the nucleus\nitself" + }, + { + "Chapter": "9", + "sentence_range": "2162-2165", + "Text": "From kinetic theory, the size\nof an atom was known to be 10\u201310 m,\nabout 10,000 to 100,000 times larger\nthan the size of the nucleus (see Chapter 10, Section 10 6 in Class XI\nPhysics textbook) Thus, the electrons would seem to be at a distance\nfrom the nucleus of about 10,000 to 100,000 times the size of the nucleus\nitself Thus, most of an atom is empty space" + }, + { + "Chapter": "9", + "sentence_range": "2163-2166", + "Text": "6 in Class XI\nPhysics textbook) Thus, the electrons would seem to be at a distance\nfrom the nucleus of about 10,000 to 100,000 times the size of the nucleus\nitself Thus, most of an atom is empty space With the atom being largely\nempty space, it is easy to see why most a-particles go right through a\nthin metal foil" + }, + { + "Chapter": "9", + "sentence_range": "2164-2167", + "Text": "Thus, the electrons would seem to be at a distance\nfrom the nucleus of about 10,000 to 100,000 times the size of the nucleus\nitself Thus, most of an atom is empty space With the atom being largely\nempty space, it is easy to see why most a-particles go right through a\nthin metal foil However, when a-particle happens to come near a nucleus,\nthe intense electric field there scatters it through a large angle" + }, + { + "Chapter": "9", + "sentence_range": "2165-2168", + "Text": "Thus, most of an atom is empty space With the atom being largely\nempty space, it is easy to see why most a-particles go right through a\nthin metal foil However, when a-particle happens to come near a nucleus,\nthe intense electric field there scatters it through a large angle The atomic\nelectrons, being so light, do not appreciably affect the a-particles" + }, + { + "Chapter": "9", + "sentence_range": "2166-2169", + "Text": "With the atom being largely\nempty space, it is easy to see why most a-particles go right through a\nthin metal foil However, when a-particle happens to come near a nucleus,\nthe intense electric field there scatters it through a large angle The atomic\nelectrons, being so light, do not appreciably affect the a-particles The scattering data shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "2167-2170", + "Text": "However, when a-particle happens to come near a nucleus,\nthe intense electric field there scatters it through a large angle The atomic\nelectrons, being so light, do not appreciably affect the a-particles The scattering data shown in Fig 12" + }, + { + "Chapter": "9", + "sentence_range": "2168-2171", + "Text": "The atomic\nelectrons, being so light, do not appreciably affect the a-particles The scattering data shown in Fig 12 3 can be analysed by employing\nRutherford\u2019s nuclear model of the atom" + }, + { + "Chapter": "9", + "sentence_range": "2169-2172", + "Text": "The scattering data shown in Fig 12 3 can be analysed by employing\nRutherford\u2019s nuclear model of the atom As the gold foil is very thin, it\ncan be assumed that a-particles will suffer not more than one scattering\nduring their passage through it" + }, + { + "Chapter": "9", + "sentence_range": "2170-2173", + "Text": "12 3 can be analysed by employing\nRutherford\u2019s nuclear model of the atom As the gold foil is very thin, it\ncan be assumed that a-particles will suffer not more than one scattering\nduring their passage through it Therefore, computation of the trajectory\nof an alpha-particle scattered by a single nucleus is enough" + }, + { + "Chapter": "9", + "sentence_range": "2171-2174", + "Text": "3 can be analysed by employing\nRutherford\u2019s nuclear model of the atom As the gold foil is very thin, it\ncan be assumed that a-particles will suffer not more than one scattering\nduring their passage through it Therefore, computation of the trajectory\nof an alpha-particle scattered by a single nucleus is enough Alpha-\nparticles are nuclei of helium atoms and, therefore, carry two units, 2e,\nof positive charge and have the mass of the helium atom" + }, + { + "Chapter": "9", + "sentence_range": "2172-2175", + "Text": "As the gold foil is very thin, it\ncan be assumed that a-particles will suffer not more than one scattering\nduring their passage through it Therefore, computation of the trajectory\nof an alpha-particle scattered by a single nucleus is enough Alpha-\nparticles are nuclei of helium atoms and, therefore, carry two units, 2e,\nof positive charge and have the mass of the helium atom The charge of\nthe gold nucleus is Ze, where Z is the atomic number of the atom; for\ngold Z = 79" + }, + { + "Chapter": "9", + "sentence_range": "2173-2176", + "Text": "Therefore, computation of the trajectory\nof an alpha-particle scattered by a single nucleus is enough Alpha-\nparticles are nuclei of helium atoms and, therefore, carry two units, 2e,\nof positive charge and have the mass of the helium atom The charge of\nthe gold nucleus is Ze, where Z is the atomic number of the atom; for\ngold Z = 79 Since the nucleus of gold is about 50 times heavier than an\na-particle, it is reasonable to assume that it remains stationary\nthroughout the scattering process" + }, + { + "Chapter": "9", + "sentence_range": "2174-2177", + "Text": "Alpha-\nparticles are nuclei of helium atoms and, therefore, carry two units, 2e,\nof positive charge and have the mass of the helium atom The charge of\nthe gold nucleus is Ze, where Z is the atomic number of the atom; for\ngold Z = 79 Since the nucleus of gold is about 50 times heavier than an\na-particle, it is reasonable to assume that it remains stationary\nthroughout the scattering process Under these assumptions, the\ntrajectory of an alpha-particle can be computed employing Newton\u2019s\nsecond law of motion and the Coulomb\u2019s law for electrostatic\nforce of repulsion between the alpha-particle and the positively\ncharged nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2175-2178", + "Text": "The charge of\nthe gold nucleus is Ze, where Z is the atomic number of the atom; for\ngold Z = 79 Since the nucleus of gold is about 50 times heavier than an\na-particle, it is reasonable to assume that it remains stationary\nthroughout the scattering process Under these assumptions, the\ntrajectory of an alpha-particle can be computed employing Newton\u2019s\nsecond law of motion and the Coulomb\u2019s law for electrostatic\nforce of repulsion between the alpha-particle and the positively\ncharged nucleus FIGURE 12" + }, + { + "Chapter": "9", + "sentence_range": "2176-2179", + "Text": "Since the nucleus of gold is about 50 times heavier than an\na-particle, it is reasonable to assume that it remains stationary\nthroughout the scattering process Under these assumptions, the\ntrajectory of an alpha-particle can be computed employing Newton\u2019s\nsecond law of motion and the Coulomb\u2019s law for electrostatic\nforce of repulsion between the alpha-particle and the positively\ncharged nucleus FIGURE 12 3 Experimental data points (shown by\ndots) on scattering of a-particles by a thin foil at\ndifferent angles obtained by Geiger and Marsden\nusing the setup shown in Figs" + }, + { + "Chapter": "9", + "sentence_range": "2177-2180", + "Text": "Under these assumptions, the\ntrajectory of an alpha-particle can be computed employing Newton\u2019s\nsecond law of motion and the Coulomb\u2019s law for electrostatic\nforce of repulsion between the alpha-particle and the positively\ncharged nucleus FIGURE 12 3 Experimental data points (shown by\ndots) on scattering of a-particles by a thin foil at\ndifferent angles obtained by Geiger and Marsden\nusing the setup shown in Figs 12" + }, + { + "Chapter": "9", + "sentence_range": "2178-2181", + "Text": "FIGURE 12 3 Experimental data points (shown by\ndots) on scattering of a-particles by a thin foil at\ndifferent angles obtained by Geiger and Marsden\nusing the setup shown in Figs 12 1 and\n12" + }, + { + "Chapter": "9", + "sentence_range": "2179-2182", + "Text": "3 Experimental data points (shown by\ndots) on scattering of a-particles by a thin foil at\ndifferent angles obtained by Geiger and Marsden\nusing the setup shown in Figs 12 1 and\n12 2" + }, + { + "Chapter": "9", + "sentence_range": "2180-2183", + "Text": "12 1 and\n12 2 Rutherford\u2019s nuclear model predicts the solid\ncurve which is seen to be in good agreement with\nexperiment" + }, + { + "Chapter": "9", + "sentence_range": "2181-2184", + "Text": "1 and\n12 2 Rutherford\u2019s nuclear model predicts the solid\ncurve which is seen to be in good agreement with\nexperiment Rationalised 2023-24\nPhysics\n294\n EXAMPLE 12" + }, + { + "Chapter": "9", + "sentence_range": "2182-2185", + "Text": "2 Rutherford\u2019s nuclear model predicts the solid\ncurve which is seen to be in good agreement with\nexperiment Rationalised 2023-24\nPhysics\n294\n EXAMPLE 12 1\nThe magnitude of this force is\n2\n0\n(2 )(\n)\n1\n4\ne\nZe\nF\nr\n\u03b5\n=\n\u03c0\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2183-2186", + "Text": "Rutherford\u2019s nuclear model predicts the solid\ncurve which is seen to be in good agreement with\nexperiment Rationalised 2023-24\nPhysics\n294\n EXAMPLE 12 1\nThe magnitude of this force is\n2\n0\n(2 )(\n)\n1\n4\ne\nZe\nF\nr\n\u03b5\n=\n\u03c0\n(12 1)\nwhere r is the distance between the a-particle and the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2184-2187", + "Text": "Rationalised 2023-24\nPhysics\n294\n EXAMPLE 12 1\nThe magnitude of this force is\n2\n0\n(2 )(\n)\n1\n4\ne\nZe\nF\nr\n\u03b5\n=\n\u03c0\n(12 1)\nwhere r is the distance between the a-particle and the nucleus The force\nis directed along the line joining the a-particle and the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2185-2188", + "Text": "1\nThe magnitude of this force is\n2\n0\n(2 )(\n)\n1\n4\ne\nZe\nF\nr\n\u03b5\n=\n\u03c0\n(12 1)\nwhere r is the distance between the a-particle and the nucleus The force\nis directed along the line joining the a-particle and the nucleus The\nmagnitude and direction of the force on an a-particle continuously\nchanges as it approaches the nucleus and recedes away from it" + }, + { + "Chapter": "9", + "sentence_range": "2186-2189", + "Text": "1)\nwhere r is the distance between the a-particle and the nucleus The force\nis directed along the line joining the a-particle and the nucleus The\nmagnitude and direction of the force on an a-particle continuously\nchanges as it approaches the nucleus and recedes away from it 12" + }, + { + "Chapter": "9", + "sentence_range": "2187-2190", + "Text": "The force\nis directed along the line joining the a-particle and the nucleus The\nmagnitude and direction of the force on an a-particle continuously\nchanges as it approaches the nucleus and recedes away from it 12 2" + }, + { + "Chapter": "9", + "sentence_range": "2188-2191", + "Text": "The\nmagnitude and direction of the force on an a-particle continuously\nchanges as it approaches the nucleus and recedes away from it 12 2 1 Alpha-particle trajectory\nThe trajectory traced by an a-particle depends on the impact parameter,\nb of collision" + }, + { + "Chapter": "9", + "sentence_range": "2189-2192", + "Text": "12 2 1 Alpha-particle trajectory\nThe trajectory traced by an a-particle depends on the impact parameter,\nb of collision The impact parameter is the perpendicular distance of the\ninitial velocity vector of the a-particle from the centre of the nucleus (Fig" + }, + { + "Chapter": "9", + "sentence_range": "2190-2193", + "Text": "2 1 Alpha-particle trajectory\nThe trajectory traced by an a-particle depends on the impact parameter,\nb of collision The impact parameter is the perpendicular distance of the\ninitial velocity vector of the a-particle from the centre of the nucleus (Fig 12" + }, + { + "Chapter": "9", + "sentence_range": "2191-2194", + "Text": "1 Alpha-particle trajectory\nThe trajectory traced by an a-particle depends on the impact parameter,\nb of collision The impact parameter is the perpendicular distance of the\ninitial velocity vector of the a-particle from the centre of the nucleus (Fig 12 4)" + }, + { + "Chapter": "9", + "sentence_range": "2192-2195", + "Text": "The impact parameter is the perpendicular distance of the\ninitial velocity vector of the a-particle from the centre of the nucleus (Fig 12 4) A given beam of a-particles has a\ndistribution of impact parameters b, so that\nthe beam is scattered in various directions\nwith different probabilities (Fig" + }, + { + "Chapter": "9", + "sentence_range": "2193-2196", + "Text": "12 4) A given beam of a-particles has a\ndistribution of impact parameters b, so that\nthe beam is scattered in various directions\nwith different probabilities (Fig 12" + }, + { + "Chapter": "9", + "sentence_range": "2194-2197", + "Text": "4) A given beam of a-particles has a\ndistribution of impact parameters b, so that\nthe beam is scattered in various directions\nwith different probabilities (Fig 12 4)" + }, + { + "Chapter": "9", + "sentence_range": "2195-2198", + "Text": "A given beam of a-particles has a\ndistribution of impact parameters b, so that\nthe beam is scattered in various directions\nwith different probabilities (Fig 12 4) (In\na beam, all particles have nearly same\nkinetic energy" + }, + { + "Chapter": "9", + "sentence_range": "2196-2199", + "Text": "12 4) (In\na beam, all particles have nearly same\nkinetic energy ) It is seen that an a-particle\nclose to the nucleus (small impact\nparameter) suffers large scattering" + }, + { + "Chapter": "9", + "sentence_range": "2197-2200", + "Text": "4) (In\na beam, all particles have nearly same\nkinetic energy ) It is seen that an a-particle\nclose to the nucleus (small impact\nparameter) suffers large scattering In case\nof head-on collision, the impact parameter\nis minimum and the a-particle rebounds\nback (q @ p)" + }, + { + "Chapter": "9", + "sentence_range": "2198-2201", + "Text": "(In\na beam, all particles have nearly same\nkinetic energy ) It is seen that an a-particle\nclose to the nucleus (small impact\nparameter) suffers large scattering In case\nof head-on collision, the impact parameter\nis minimum and the a-particle rebounds\nback (q @ p) For a large impact parameter,\nthe a-particle goes nearly undeviated and\nhas a small deflection (q @ 0)" + }, + { + "Chapter": "9", + "sentence_range": "2199-2202", + "Text": ") It is seen that an a-particle\nclose to the nucleus (small impact\nparameter) suffers large scattering In case\nof head-on collision, the impact parameter\nis minimum and the a-particle rebounds\nback (q @ p) For a large impact parameter,\nthe a-particle goes nearly undeviated and\nhas a small deflection (q @ 0) The fact that only a small fraction of the\nnumber of incident particles rebound back\nindicates that the number of a-particles\nundergoing head on collision is small" + }, + { + "Chapter": "9", + "sentence_range": "2200-2203", + "Text": "In case\nof head-on collision, the impact parameter\nis minimum and the a-particle rebounds\nback (q @ p) For a large impact parameter,\nthe a-particle goes nearly undeviated and\nhas a small deflection (q @ 0) The fact that only a small fraction of the\nnumber of incident particles rebound back\nindicates that the number of a-particles\nundergoing head on collision is small This,\nin turn, implies that the mass and positive charge of the atom is\nconcentrated in a small volume" + }, + { + "Chapter": "9", + "sentence_range": "2201-2204", + "Text": "For a large impact parameter,\nthe a-particle goes nearly undeviated and\nhas a small deflection (q @ 0) The fact that only a small fraction of the\nnumber of incident particles rebound back\nindicates that the number of a-particles\nundergoing head on collision is small This,\nin turn, implies that the mass and positive charge of the atom is\nconcentrated in a small volume Rutherford scattering therefore, is a\npowerful way to determine an upper limit to the size of the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2202-2205", + "Text": "The fact that only a small fraction of the\nnumber of incident particles rebound back\nindicates that the number of a-particles\nundergoing head on collision is small This,\nin turn, implies that the mass and positive charge of the atom is\nconcentrated in a small volume Rutherford scattering therefore, is a\npowerful way to determine an upper limit to the size of the nucleus FIGURE 12" + }, + { + "Chapter": "9", + "sentence_range": "2203-2206", + "Text": "This,\nin turn, implies that the mass and positive charge of the atom is\nconcentrated in a small volume Rutherford scattering therefore, is a\npowerful way to determine an upper limit to the size of the nucleus FIGURE 12 4 Trajectory of a-particles in the\ncoulomb field of a target nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2204-2207", + "Text": "Rutherford scattering therefore, is a\npowerful way to determine an upper limit to the size of the nucleus FIGURE 12 4 Trajectory of a-particles in the\ncoulomb field of a target nucleus The impact\nparameter, b and scattering angle q\nare also depicted" + }, + { + "Chapter": "9", + "sentence_range": "2205-2208", + "Text": "FIGURE 12 4 Trajectory of a-particles in the\ncoulomb field of a target nucleus The impact\nparameter, b and scattering angle q\nare also depicted Example 12" + }, + { + "Chapter": "9", + "sentence_range": "2206-2209", + "Text": "4 Trajectory of a-particles in the\ncoulomb field of a target nucleus The impact\nparameter, b and scattering angle q\nare also depicted Example 12 1 In the Rutherford\u2019s nuclear model of the atom, the\nnucleus (radius about 10\u201315 m) is analogous to the sun about which\nthe electron move in orbit (radius \u00bb 10\u201310 m) like the earth orbits\naround the sun" + }, + { + "Chapter": "9", + "sentence_range": "2207-2210", + "Text": "The impact\nparameter, b and scattering angle q\nare also depicted Example 12 1 In the Rutherford\u2019s nuclear model of the atom, the\nnucleus (radius about 10\u201315 m) is analogous to the sun about which\nthe electron move in orbit (radius \u00bb 10\u201310 m) like the earth orbits\naround the sun If the dimensions of the solar system had the same\nproportions as those of the atom, would the earth be closer to or\nfarther away from the sun than actually it is" + }, + { + "Chapter": "9", + "sentence_range": "2208-2211", + "Text": "Example 12 1 In the Rutherford\u2019s nuclear model of the atom, the\nnucleus (radius about 10\u201315 m) is analogous to the sun about which\nthe electron move in orbit (radius \u00bb 10\u201310 m) like the earth orbits\naround the sun If the dimensions of the solar system had the same\nproportions as those of the atom, would the earth be closer to or\nfarther away from the sun than actually it is The radius of earth\u2019s\norbit is about 1" + }, + { + "Chapter": "9", + "sentence_range": "2209-2212", + "Text": "1 In the Rutherford\u2019s nuclear model of the atom, the\nnucleus (radius about 10\u201315 m) is analogous to the sun about which\nthe electron move in orbit (radius \u00bb 10\u201310 m) like the earth orbits\naround the sun If the dimensions of the solar system had the same\nproportions as those of the atom, would the earth be closer to or\nfarther away from the sun than actually it is The radius of earth\u2019s\norbit is about 1 5 \u00b4 1011 m" + }, + { + "Chapter": "9", + "sentence_range": "2210-2213", + "Text": "If the dimensions of the solar system had the same\nproportions as those of the atom, would the earth be closer to or\nfarther away from the sun than actually it is The radius of earth\u2019s\norbit is about 1 5 \u00b4 1011 m The radius of sun is taken as 7 \u00b4 108 m" + }, + { + "Chapter": "9", + "sentence_range": "2211-2214", + "Text": "The radius of earth\u2019s\norbit is about 1 5 \u00b4 1011 m The radius of sun is taken as 7 \u00b4 108 m Solution The ratio of the radius of electron\u2019s orbit to the radius of\nnucleus is (10\u201310 m)/(10\u201315 m) = 105, that is, the radius of the electron\u2019s\norbit is 105 times larger than the radius of nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2212-2215", + "Text": "5 \u00b4 1011 m The radius of sun is taken as 7 \u00b4 108 m Solution The ratio of the radius of electron\u2019s orbit to the radius of\nnucleus is (10\u201310 m)/(10\u201315 m) = 105, that is, the radius of the electron\u2019s\norbit is 105 times larger than the radius of nucleus If the radius of\nthe earth\u2019s orbit around the sun were 105 times larger than the radius\nof the sun, the radius of the earth\u2019s orbit would be 105 \u00b4 7 \u00b4 108 m =\n7 \u00b4 1013 m" + }, + { + "Chapter": "9", + "sentence_range": "2213-2216", + "Text": "The radius of sun is taken as 7 \u00b4 108 m Solution The ratio of the radius of electron\u2019s orbit to the radius of\nnucleus is (10\u201310 m)/(10\u201315 m) = 105, that is, the radius of the electron\u2019s\norbit is 105 times larger than the radius of nucleus If the radius of\nthe earth\u2019s orbit around the sun were 105 times larger than the radius\nof the sun, the radius of the earth\u2019s orbit would be 105 \u00b4 7 \u00b4 108 m =\n7 \u00b4 1013 m This is more than 100 times greater than the actual\norbital radius of earth" + }, + { + "Chapter": "9", + "sentence_range": "2214-2217", + "Text": "Solution The ratio of the radius of electron\u2019s orbit to the radius of\nnucleus is (10\u201310 m)/(10\u201315 m) = 105, that is, the radius of the electron\u2019s\norbit is 105 times larger than the radius of nucleus If the radius of\nthe earth\u2019s orbit around the sun were 105 times larger than the radius\nof the sun, the radius of the earth\u2019s orbit would be 105 \u00b4 7 \u00b4 108 m =\n7 \u00b4 1013 m This is more than 100 times greater than the actual\norbital radius of earth Thus, the earth would be much farther away\nfrom the sun" + }, + { + "Chapter": "9", + "sentence_range": "2215-2218", + "Text": "If the radius of\nthe earth\u2019s orbit around the sun were 105 times larger than the radius\nof the sun, the radius of the earth\u2019s orbit would be 105 \u00b4 7 \u00b4 108 m =\n7 \u00b4 1013 m This is more than 100 times greater than the actual\norbital radius of earth Thus, the earth would be much farther away\nfrom the sun It implies that an atom contains a much greater fraction of empty\nspace than our solar system does" + }, + { + "Chapter": "9", + "sentence_range": "2216-2219", + "Text": "This is more than 100 times greater than the actual\norbital radius of earth Thus, the earth would be much farther away\nfrom the sun It implies that an atom contains a much greater fraction of empty\nspace than our solar system does Rationalised 2023-24\n295\nAtoms\n EXAMPLE 12" + }, + { + "Chapter": "9", + "sentence_range": "2217-2220", + "Text": "Thus, the earth would be much farther away\nfrom the sun It implies that an atom contains a much greater fraction of empty\nspace than our solar system does Rationalised 2023-24\n295\nAtoms\n EXAMPLE 12 2\nExample 12" + }, + { + "Chapter": "9", + "sentence_range": "2218-2221", + "Text": "It implies that an atom contains a much greater fraction of empty\nspace than our solar system does Rationalised 2023-24\n295\nAtoms\n EXAMPLE 12 2\nExample 12 2 In a Geiger-Marsden experiment, what is the distance\nof closest approach to the nucleus of a 7" + }, + { + "Chapter": "9", + "sentence_range": "2219-2222", + "Text": "Rationalised 2023-24\n295\nAtoms\n EXAMPLE 12 2\nExample 12 2 In a Geiger-Marsden experiment, what is the distance\nof closest approach to the nucleus of a 7 7 MeV a-particle before it\ncomes momentarily to rest and reverses its direction" + }, + { + "Chapter": "9", + "sentence_range": "2220-2223", + "Text": "2\nExample 12 2 In a Geiger-Marsden experiment, what is the distance\nof closest approach to the nucleus of a 7 7 MeV a-particle before it\ncomes momentarily to rest and reverses its direction Solution The key idea here is that throughout the scattering process,\nthe total mechanical energy of the system consisting of an a-particle\nand a gold nucleus is conserved" + }, + { + "Chapter": "9", + "sentence_range": "2221-2224", + "Text": "2 In a Geiger-Marsden experiment, what is the distance\nof closest approach to the nucleus of a 7 7 MeV a-particle before it\ncomes momentarily to rest and reverses its direction Solution The key idea here is that throughout the scattering process,\nthe total mechanical energy of the system consisting of an a-particle\nand a gold nucleus is conserved The system\u2019s initial mechanical\nenergy is Ei, before the particle and nucleus interact, and it is equal\nto its mechanical energy Ef when the a-particle momentarily stops" + }, + { + "Chapter": "9", + "sentence_range": "2222-2225", + "Text": "7 MeV a-particle before it\ncomes momentarily to rest and reverses its direction Solution The key idea here is that throughout the scattering process,\nthe total mechanical energy of the system consisting of an a-particle\nand a gold nucleus is conserved The system\u2019s initial mechanical\nenergy is Ei, before the particle and nucleus interact, and it is equal\nto its mechanical energy Ef when the a-particle momentarily stops The initial energy Ei is just the kinetic energy K of the incoming\na- particle" + }, + { + "Chapter": "9", + "sentence_range": "2223-2226", + "Text": "Solution The key idea here is that throughout the scattering process,\nthe total mechanical energy of the system consisting of an a-particle\nand a gold nucleus is conserved The system\u2019s initial mechanical\nenergy is Ei, before the particle and nucleus interact, and it is equal\nto its mechanical energy Ef when the a-particle momentarily stops The initial energy Ei is just the kinetic energy K of the incoming\na- particle The final energy Ef is just the electric potential energy U\nof the system" + }, + { + "Chapter": "9", + "sentence_range": "2224-2227", + "Text": "The system\u2019s initial mechanical\nenergy is Ei, before the particle and nucleus interact, and it is equal\nto its mechanical energy Ef when the a-particle momentarily stops The initial energy Ei is just the kinetic energy K of the incoming\na- particle The final energy Ef is just the electric potential energy U\nof the system The potential energy U can be calculated from\nEq" + }, + { + "Chapter": "9", + "sentence_range": "2225-2228", + "Text": "The initial energy Ei is just the kinetic energy K of the incoming\na- particle The final energy Ef is just the electric potential energy U\nof the system The potential energy U can be calculated from\nEq (12" + }, + { + "Chapter": "9", + "sentence_range": "2226-2229", + "Text": "The final energy Ef is just the electric potential energy U\nof the system The potential energy U can be calculated from\nEq (12 1)" + }, + { + "Chapter": "9", + "sentence_range": "2227-2230", + "Text": "The potential energy U can be calculated from\nEq (12 1) Let d be the centre-to-centre distance between the a-particle and\nthe gold nucleus when the a-particle is at its stopping point" + }, + { + "Chapter": "9", + "sentence_range": "2228-2231", + "Text": "(12 1) Let d be the centre-to-centre distance between the a-particle and\nthe gold nucleus when the a-particle is at its stopping point Then\nwe can write the conservation of energy Ei = Ef as\n2\n0\n0\n1\n(2 )(\n)\n2\n4\n4\ne Ze\nZe\nK\nd\nd\n\u03b5\n\u03b5\n=\n=\n\u03c0\n\u03c0\nThus the distance of closest approach d is given by\n2\n0\n2\n4\nZe\nd\n\u03b5K\n=\n\u03c0\nThe maximum kinetic energy found in a-particles of natural origin is\n7" + }, + { + "Chapter": "9", + "sentence_range": "2229-2232", + "Text": "1) Let d be the centre-to-centre distance between the a-particle and\nthe gold nucleus when the a-particle is at its stopping point Then\nwe can write the conservation of energy Ei = Ef as\n2\n0\n0\n1\n(2 )(\n)\n2\n4\n4\ne Ze\nZe\nK\nd\nd\n\u03b5\n\u03b5\n=\n=\n\u03c0\n\u03c0\nThus the distance of closest approach d is given by\n2\n0\n2\n4\nZe\nd\n\u03b5K\n=\n\u03c0\nThe maximum kinetic energy found in a-particles of natural origin is\n7 7 MeV or 1" + }, + { + "Chapter": "9", + "sentence_range": "2230-2233", + "Text": "Let d be the centre-to-centre distance between the a-particle and\nthe gold nucleus when the a-particle is at its stopping point Then\nwe can write the conservation of energy Ei = Ef as\n2\n0\n0\n1\n(2 )(\n)\n2\n4\n4\ne Ze\nZe\nK\nd\nd\n\u03b5\n\u03b5\n=\n=\n\u03c0\n\u03c0\nThus the distance of closest approach d is given by\n2\n0\n2\n4\nZe\nd\n\u03b5K\n=\n\u03c0\nThe maximum kinetic energy found in a-particles of natural origin is\n7 7 MeV or 1 2 \u00d7 10\u201312 J" + }, + { + "Chapter": "9", + "sentence_range": "2231-2234", + "Text": "Then\nwe can write the conservation of energy Ei = Ef as\n2\n0\n0\n1\n(2 )(\n)\n2\n4\n4\ne Ze\nZe\nK\nd\nd\n\u03b5\n\u03b5\n=\n=\n\u03c0\n\u03c0\nThus the distance of closest approach d is given by\n2\n0\n2\n4\nZe\nd\n\u03b5K\n=\n\u03c0\nThe maximum kinetic energy found in a-particles of natural origin is\n7 7 MeV or 1 2 \u00d7 10\u201312 J Since 1/4pe0 = 9" + }, + { + "Chapter": "9", + "sentence_range": "2232-2235", + "Text": "7 MeV or 1 2 \u00d7 10\u201312 J Since 1/4pe0 = 9 0 \u00d7 109 N m2/C2" + }, + { + "Chapter": "9", + "sentence_range": "2233-2236", + "Text": "2 \u00d7 10\u201312 J Since 1/4pe0 = 9 0 \u00d7 109 N m2/C2 Therefore\nwith e = 1" + }, + { + "Chapter": "9", + "sentence_range": "2234-2237", + "Text": "Since 1/4pe0 = 9 0 \u00d7 109 N m2/C2 Therefore\nwith e = 1 6 \u00d7 10\u201319 C, we have,\n9\n2\n2\n\u201319\n2\n12\n(2)(9" + }, + { + "Chapter": "9", + "sentence_range": "2235-2238", + "Text": "0 \u00d7 109 N m2/C2 Therefore\nwith e = 1 6 \u00d7 10\u201319 C, we have,\n9\n2\n2\n\u201319\n2\n12\n(2)(9 0\n10 Nm /\n)(1" + }, + { + "Chapter": "9", + "sentence_range": "2236-2239", + "Text": "Therefore\nwith e = 1 6 \u00d7 10\u201319 C, we have,\n9\n2\n2\n\u201319\n2\n12\n(2)(9 0\n10 Nm /\n)(1 6\n10\n) Z\n1" + }, + { + "Chapter": "9", + "sentence_range": "2237-2240", + "Text": "6 \u00d7 10\u201319 C, we have,\n9\n2\n2\n\u201319\n2\n12\n(2)(9 0\n10 Nm /\n)(1 6\n10\n) Z\n1 2\n10\nJ\nC\nC\nd\n\u2212\n\u00d7\n\u00d7\n=\n\u00d7\n = 3" + }, + { + "Chapter": "9", + "sentence_range": "2238-2241", + "Text": "0\n10 Nm /\n)(1 6\n10\n) Z\n1 2\n10\nJ\nC\nC\nd\n\u2212\n\u00d7\n\u00d7\n=\n\u00d7\n = 3 84 \u00d7 10\u201316 Z m\nThe atomic number of foil material gold is Z = 79, so that\nd (Au) = 3" + }, + { + "Chapter": "9", + "sentence_range": "2239-2242", + "Text": "6\n10\n) Z\n1 2\n10\nJ\nC\nC\nd\n\u2212\n\u00d7\n\u00d7\n=\n\u00d7\n = 3 84 \u00d7 10\u201316 Z m\nThe atomic number of foil material gold is Z = 79, so that\nd (Au) = 3 0 \u00d7 10\u201314 m = 30 fm" + }, + { + "Chapter": "9", + "sentence_range": "2240-2243", + "Text": "2\n10\nJ\nC\nC\nd\n\u2212\n\u00d7\n\u00d7\n=\n\u00d7\n = 3 84 \u00d7 10\u201316 Z m\nThe atomic number of foil material gold is Z = 79, so that\nd (Au) = 3 0 \u00d7 10\u201314 m = 30 fm (1 fm (i" + }, + { + "Chapter": "9", + "sentence_range": "2241-2244", + "Text": "84 \u00d7 10\u201316 Z m\nThe atomic number of foil material gold is Z = 79, so that\nd (Au) = 3 0 \u00d7 10\u201314 m = 30 fm (1 fm (i e" + }, + { + "Chapter": "9", + "sentence_range": "2242-2245", + "Text": "0 \u00d7 10\u201314 m = 30 fm (1 fm (i e fermi) = 10\u201315 m" + }, + { + "Chapter": "9", + "sentence_range": "2243-2246", + "Text": "(1 fm (i e fermi) = 10\u201315 m )\nThe radius of gold nucleus is, therefore, less than 3" + }, + { + "Chapter": "9", + "sentence_range": "2244-2247", + "Text": "e fermi) = 10\u201315 m )\nThe radius of gold nucleus is, therefore, less than 3 0 \u00d7 10\u201314 m" + }, + { + "Chapter": "9", + "sentence_range": "2245-2248", + "Text": "fermi) = 10\u201315 m )\nThe radius of gold nucleus is, therefore, less than 3 0 \u00d7 10\u201314 m This\nis not in very good agreement with the observed result as the actual\nradius of gold nucleus is 6 fm" + }, + { + "Chapter": "9", + "sentence_range": "2246-2249", + "Text": ")\nThe radius of gold nucleus is, therefore, less than 3 0 \u00d7 10\u201314 m This\nis not in very good agreement with the observed result as the actual\nradius of gold nucleus is 6 fm The cause of discrepancy is that the\ndistance of closest approach is considerably larger than the sum of\nthe radii of the gold nucleus and the a-particle" + }, + { + "Chapter": "9", + "sentence_range": "2247-2250", + "Text": "0 \u00d7 10\u201314 m This\nis not in very good agreement with the observed result as the actual\nradius of gold nucleus is 6 fm The cause of discrepancy is that the\ndistance of closest approach is considerably larger than the sum of\nthe radii of the gold nucleus and the a-particle Thus, the a-particle\nreverses its motion without ever actually touching the gold nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2248-2251", + "Text": "This\nis not in very good agreement with the observed result as the actual\nradius of gold nucleus is 6 fm The cause of discrepancy is that the\ndistance of closest approach is considerably larger than the sum of\nthe radii of the gold nucleus and the a-particle Thus, the a-particle\nreverses its motion without ever actually touching the gold nucleus 12" + }, + { + "Chapter": "9", + "sentence_range": "2249-2252", + "Text": "The cause of discrepancy is that the\ndistance of closest approach is considerably larger than the sum of\nthe radii of the gold nucleus and the a-particle Thus, the a-particle\nreverses its motion without ever actually touching the gold nucleus 12 2" + }, + { + "Chapter": "9", + "sentence_range": "2250-2253", + "Text": "Thus, the a-particle\nreverses its motion without ever actually touching the gold nucleus 12 2 2 Electron orbits\nThe Rutherford nuclear model of the atom which involves classical\nconcepts, pictures the atom as an electrically neutral sphere consisting\nof a very small, massive and positively charged nucleus at the centre\nsurrounded by the revolving electrons in their respective dynamically\nstable orbits" + }, + { + "Chapter": "9", + "sentence_range": "2251-2254", + "Text": "12 2 2 Electron orbits\nThe Rutherford nuclear model of the atom which involves classical\nconcepts, pictures the atom as an electrically neutral sphere consisting\nof a very small, massive and positively charged nucleus at the centre\nsurrounded by the revolving electrons in their respective dynamically\nstable orbits The electrostatic force of attraction, Fe between the revolving\nelectrons and the nucleus provides the requisite centripetal force (Fc) to\nkeep them in their orbits" + }, + { + "Chapter": "9", + "sentence_range": "2252-2255", + "Text": "2 2 Electron orbits\nThe Rutherford nuclear model of the atom which involves classical\nconcepts, pictures the atom as an electrically neutral sphere consisting\nof a very small, massive and positively charged nucleus at the centre\nsurrounded by the revolving electrons in their respective dynamically\nstable orbits The electrostatic force of attraction, Fe between the revolving\nelectrons and the nucleus provides the requisite centripetal force (Fc) to\nkeep them in their orbits Thus, for a dynamically stable orbit in a\nhydrogen atom\n Fe = Fc\n2\n2\n2\n0\n1\n4 \u03b5\n=\n\u03c0\ne\nmv\nr\nr\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2253-2256", + "Text": "2 Electron orbits\nThe Rutherford nuclear model of the atom which involves classical\nconcepts, pictures the atom as an electrically neutral sphere consisting\nof a very small, massive and positively charged nucleus at the centre\nsurrounded by the revolving electrons in their respective dynamically\nstable orbits The electrostatic force of attraction, Fe between the revolving\nelectrons and the nucleus provides the requisite centripetal force (Fc) to\nkeep them in their orbits Thus, for a dynamically stable orbit in a\nhydrogen atom\n Fe = Fc\n2\n2\n2\n0\n1\n4 \u03b5\n=\n\u03c0\ne\nmv\nr\nr\n(12 2)\nRationalised 2023-24\nPhysics\n296\nThus the relation between the orbit radius and the electron\nvelocity is\n2\n2\n0\n4\ne\nr\n\u03b5mv\n=\n\u03c0\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2254-2257", + "Text": "The electrostatic force of attraction, Fe between the revolving\nelectrons and the nucleus provides the requisite centripetal force (Fc) to\nkeep them in their orbits Thus, for a dynamically stable orbit in a\nhydrogen atom\n Fe = Fc\n2\n2\n2\n0\n1\n4 \u03b5\n=\n\u03c0\ne\nmv\nr\nr\n(12 2)\nRationalised 2023-24\nPhysics\n296\nThus the relation between the orbit radius and the electron\nvelocity is\n2\n2\n0\n4\ne\nr\n\u03b5mv\n=\n\u03c0\n(12 3)\nThe kinetic energy (K) and electrostatic potential energy (U) of the electron\nin hydrogen atom are\n2\n2\n2\n0\n0\n1\n and \n2\n8\n4\ne\ne\nK\nmv\nU\nr\nr\n\u03b5\n\u03b5\n=\n=\n= \u2212\n\u03c0\n\u03c0\n(The negative sign in U signifies that the electrostatic force is in the \u2013r\ndirection" + }, + { + "Chapter": "9", + "sentence_range": "2255-2258", + "Text": "Thus, for a dynamically stable orbit in a\nhydrogen atom\n Fe = Fc\n2\n2\n2\n0\n1\n4 \u03b5\n=\n\u03c0\ne\nmv\nr\nr\n(12 2)\nRationalised 2023-24\nPhysics\n296\nThus the relation between the orbit radius and the electron\nvelocity is\n2\n2\n0\n4\ne\nr\n\u03b5mv\n=\n\u03c0\n(12 3)\nThe kinetic energy (K) and electrostatic potential energy (U) of the electron\nin hydrogen atom are\n2\n2\n2\n0\n0\n1\n and \n2\n8\n4\ne\ne\nK\nmv\nU\nr\nr\n\u03b5\n\u03b5\n=\n=\n= \u2212\n\u03c0\n\u03c0\n(The negative sign in U signifies that the electrostatic force is in the \u2013r\ndirection ) Thus the total energy E of the electron in a hydrogen atom is\n2\n2\n0\n0\n8\n4\ne\ne\nE\nK\nU\nr\nr\n\u03b5\n\u03b5\n=\n+\n=\n\u2212\n\u03c0\n\u03c0\n \n2\n0\n8\ne\n\u03b5r\n= \u2212\n\u03c0\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2256-2259", + "Text": "2)\nRationalised 2023-24\nPhysics\n296\nThus the relation between the orbit radius and the electron\nvelocity is\n2\n2\n0\n4\ne\nr\n\u03b5mv\n=\n\u03c0\n(12 3)\nThe kinetic energy (K) and electrostatic potential energy (U) of the electron\nin hydrogen atom are\n2\n2\n2\n0\n0\n1\n and \n2\n8\n4\ne\ne\nK\nmv\nU\nr\nr\n\u03b5\n\u03b5\n=\n=\n= \u2212\n\u03c0\n\u03c0\n(The negative sign in U signifies that the electrostatic force is in the \u2013r\ndirection ) Thus the total energy E of the electron in a hydrogen atom is\n2\n2\n0\n0\n8\n4\ne\ne\nE\nK\nU\nr\nr\n\u03b5\n\u03b5\n=\n+\n=\n\u2212\n\u03c0\n\u03c0\n \n2\n0\n8\ne\n\u03b5r\n= \u2212\n\u03c0\n(12 4)\nThe total energy of the electron is negative" + }, + { + "Chapter": "9", + "sentence_range": "2257-2260", + "Text": "3)\nThe kinetic energy (K) and electrostatic potential energy (U) of the electron\nin hydrogen atom are\n2\n2\n2\n0\n0\n1\n and \n2\n8\n4\ne\ne\nK\nmv\nU\nr\nr\n\u03b5\n\u03b5\n=\n=\n= \u2212\n\u03c0\n\u03c0\n(The negative sign in U signifies that the electrostatic force is in the \u2013r\ndirection ) Thus the total energy E of the electron in a hydrogen atom is\n2\n2\n0\n0\n8\n4\ne\ne\nE\nK\nU\nr\nr\n\u03b5\n\u03b5\n=\n+\n=\n\u2212\n\u03c0\n\u03c0\n \n2\n0\n8\ne\n\u03b5r\n= \u2212\n\u03c0\n(12 4)\nThe total energy of the electron is negative This implies the fact that\nthe electron is bound to the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2258-2261", + "Text": ") Thus the total energy E of the electron in a hydrogen atom is\n2\n2\n0\n0\n8\n4\ne\ne\nE\nK\nU\nr\nr\n\u03b5\n\u03b5\n=\n+\n=\n\u2212\n\u03c0\n\u03c0\n \n2\n0\n8\ne\n\u03b5r\n= \u2212\n\u03c0\n(12 4)\nThe total energy of the electron is negative This implies the fact that\nthe electron is bound to the nucleus If E were positive, an electron will\nnot follow a closed orbit around the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2259-2262", + "Text": "4)\nThe total energy of the electron is negative This implies the fact that\nthe electron is bound to the nucleus If E were positive, an electron will\nnot follow a closed orbit around the nucleus 12" + }, + { + "Chapter": "9", + "sentence_range": "2260-2263", + "Text": "This implies the fact that\nthe electron is bound to the nucleus If E were positive, an electron will\nnot follow a closed orbit around the nucleus 12 3 ATOMIC SPECTRA\nAs mentioned in Section 12" + }, + { + "Chapter": "9", + "sentence_range": "2261-2264", + "Text": "If E were positive, an electron will\nnot follow a closed orbit around the nucleus 12 3 ATOMIC SPECTRA\nAs mentioned in Section 12 1, each element has a characteristic spectrum\nof radiation, which it emits" + }, + { + "Chapter": "9", + "sentence_range": "2262-2265", + "Text": "12 3 ATOMIC SPECTRA\nAs mentioned in Section 12 1, each element has a characteristic spectrum\nof radiation, which it emits When an atomic gas or vapour is excited at\nlow pressure, usually by passing an electric current through it, the emitted\nradiation has a spectrum which contains certain specific wavelengths\nonly" + }, + { + "Chapter": "9", + "sentence_range": "2263-2266", + "Text": "3 ATOMIC SPECTRA\nAs mentioned in Section 12 1, each element has a characteristic spectrum\nof radiation, which it emits When an atomic gas or vapour is excited at\nlow pressure, usually by passing an electric current through it, the emitted\nradiation has a spectrum which contains certain specific wavelengths\nonly A spectrum of this kind is termed as emission line spectrum and it\n EXAMPLE 12" + }, + { + "Chapter": "9", + "sentence_range": "2264-2267", + "Text": "1, each element has a characteristic spectrum\nof radiation, which it emits When an atomic gas or vapour is excited at\nlow pressure, usually by passing an electric current through it, the emitted\nradiation has a spectrum which contains certain specific wavelengths\nonly A spectrum of this kind is termed as emission line spectrum and it\n EXAMPLE 12 3\nExample 12" + }, + { + "Chapter": "9", + "sentence_range": "2265-2268", + "Text": "When an atomic gas or vapour is excited at\nlow pressure, usually by passing an electric current through it, the emitted\nradiation has a spectrum which contains certain specific wavelengths\nonly A spectrum of this kind is termed as emission line spectrum and it\n EXAMPLE 12 3\nExample 12 3 It is found experimentally that 13" + }, + { + "Chapter": "9", + "sentence_range": "2266-2269", + "Text": "A spectrum of this kind is termed as emission line spectrum and it\n EXAMPLE 12 3\nExample 12 3 It is found experimentally that 13 6 eV energy is\nrequired to separate a hydrogen atom into a proton and an electron" + }, + { + "Chapter": "9", + "sentence_range": "2267-2270", + "Text": "3\nExample 12 3 It is found experimentally that 13 6 eV energy is\nrequired to separate a hydrogen atom into a proton and an electron Compute the orbital radius and the velocity of the electron in a\nhydrogen atom" + }, + { + "Chapter": "9", + "sentence_range": "2268-2271", + "Text": "3 It is found experimentally that 13 6 eV energy is\nrequired to separate a hydrogen atom into a proton and an electron Compute the orbital radius and the velocity of the electron in a\nhydrogen atom Solution Total energy of the electron in hydrogen atom is \u201313" + }, + { + "Chapter": "9", + "sentence_range": "2269-2272", + "Text": "6 eV energy is\nrequired to separate a hydrogen atom into a proton and an electron Compute the orbital radius and the velocity of the electron in a\nhydrogen atom Solution Total energy of the electron in hydrogen atom is \u201313 6 eV =\n\u201313" + }, + { + "Chapter": "9", + "sentence_range": "2270-2273", + "Text": "Compute the orbital radius and the velocity of the electron in a\nhydrogen atom Solution Total energy of the electron in hydrogen atom is \u201313 6 eV =\n\u201313 6 \u00d7 1" + }, + { + "Chapter": "9", + "sentence_range": "2271-2274", + "Text": "Solution Total energy of the electron in hydrogen atom is \u201313 6 eV =\n\u201313 6 \u00d7 1 6 \u00d7 10\u201319 J = \u20132" + }, + { + "Chapter": "9", + "sentence_range": "2272-2275", + "Text": "6 eV =\n\u201313 6 \u00d7 1 6 \u00d7 10\u201319 J = \u20132 2 \u00d710\u201318 J" + }, + { + "Chapter": "9", + "sentence_range": "2273-2276", + "Text": "6 \u00d7 1 6 \u00d7 10\u201319 J = \u20132 2 \u00d710\u201318 J Thus from Eq" + }, + { + "Chapter": "9", + "sentence_range": "2274-2277", + "Text": "6 \u00d7 10\u201319 J = \u20132 2 \u00d710\u201318 J Thus from Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2275-2278", + "Text": "2 \u00d710\u201318 J Thus from Eq (12 4), we have\n2\n18\n0\n2" + }, + { + "Chapter": "9", + "sentence_range": "2276-2279", + "Text": "Thus from Eq (12 4), we have\n2\n18\n0\n2 2\n10\n J\n8 \u03b5\n\u2212\n= \u2212\n= \u2212\n\u00d7\ne\u03c0\nE\nr\nThis gives the orbital radius\n2\n9\n2\n2\n19\n2\n18\n0\n(9\n10 N m /C )(1" + }, + { + "Chapter": "9", + "sentence_range": "2277-2280", + "Text": "(12 4), we have\n2\n18\n0\n2 2\n10\n J\n8 \u03b5\n\u2212\n= \u2212\n= \u2212\n\u00d7\ne\u03c0\nE\nr\nThis gives the orbital radius\n2\n9\n2\n2\n19\n2\n18\n0\n(9\n10 N m /C )(1 6 \n10\nC)\n \n8\n(2)(\u20132" + }, + { + "Chapter": "9", + "sentence_range": "2278-2281", + "Text": "4), we have\n2\n18\n0\n2 2\n10\n J\n8 \u03b5\n\u2212\n= \u2212\n= \u2212\n\u00d7\ne\u03c0\nE\nr\nThis gives the orbital radius\n2\n9\n2\n2\n19\n2\n18\n0\n(9\n10 N m /C )(1 6 \n10\nC)\n \n8\n(2)(\u20132 2\n10\n J)\ne\nr\nE\n\u03b5\n\u2212\n\u2212\n\u00d7\n\u00d7\n= \u2212\n= \u2212\n\u03c0\n\u00d7\n = 5" + }, + { + "Chapter": "9", + "sentence_range": "2279-2282", + "Text": "2\n10\n J\n8 \u03b5\n\u2212\n= \u2212\n= \u2212\n\u00d7\ne\u03c0\nE\nr\nThis gives the orbital radius\n2\n9\n2\n2\n19\n2\n18\n0\n(9\n10 N m /C )(1 6 \n10\nC)\n \n8\n(2)(\u20132 2\n10\n J)\ne\nr\nE\n\u03b5\n\u2212\n\u2212\n\u00d7\n\u00d7\n= \u2212\n= \u2212\n\u03c0\n\u00d7\n = 5 3 \u00d7 10\u201311 m" + }, + { + "Chapter": "9", + "sentence_range": "2280-2283", + "Text": "6 \n10\nC)\n \n8\n(2)(\u20132 2\n10\n J)\ne\nr\nE\n\u03b5\n\u2212\n\u2212\n\u00d7\n\u00d7\n= \u2212\n= \u2212\n\u03c0\n\u00d7\n = 5 3 \u00d7 10\u201311 m The velocity of the revolving electron can be computed from Eq" + }, + { + "Chapter": "9", + "sentence_range": "2281-2284", + "Text": "2\n10\n J)\ne\nr\nE\n\u03b5\n\u2212\n\u2212\n\u00d7\n\u00d7\n= \u2212\n= \u2212\n\u03c0\n\u00d7\n = 5 3 \u00d7 10\u201311 m The velocity of the revolving electron can be computed from Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2282-2285", + "Text": "3 \u00d7 10\u201311 m The velocity of the revolving electron can be computed from Eq (12 3)\nwith m = 9" + }, + { + "Chapter": "9", + "sentence_range": "2283-2286", + "Text": "The velocity of the revolving electron can be computed from Eq (12 3)\nwith m = 9 1 \u00d7 10\u201331 kg,\n6\n0\n2" + }, + { + "Chapter": "9", + "sentence_range": "2284-2287", + "Text": "(12 3)\nwith m = 9 1 \u00d7 10\u201331 kg,\n6\n0\n2 2\n10 m/s" + }, + { + "Chapter": "9", + "sentence_range": "2285-2288", + "Text": "3)\nwith m = 9 1 \u00d7 10\u201331 kg,\n6\n0\n2 2\n10 m/s 4\ne\nv\n\u03b5mr\n=\n=\n\u00d7\n\u03c0\nRationalised 2023-24\n297\nAtoms\nconsists of bright lines on a\ndark \nbackground" + }, + { + "Chapter": "9", + "sentence_range": "2286-2289", + "Text": "1 \u00d7 10\u201331 kg,\n6\n0\n2 2\n10 m/s 4\ne\nv\n\u03b5mr\n=\n=\n\u00d7\n\u03c0\nRationalised 2023-24\n297\nAtoms\nconsists of bright lines on a\ndark \nbackground The\nspectrum emitted by atomic\nhydrogen \nis \nshown \nin\nFig" + }, + { + "Chapter": "9", + "sentence_range": "2287-2290", + "Text": "2\n10 m/s 4\ne\nv\n\u03b5mr\n=\n=\n\u00d7\n\u03c0\nRationalised 2023-24\n297\nAtoms\nconsists of bright lines on a\ndark \nbackground The\nspectrum emitted by atomic\nhydrogen \nis \nshown \nin\nFig 12" + }, + { + "Chapter": "9", + "sentence_range": "2288-2291", + "Text": "4\ne\nv\n\u03b5mr\n=\n=\n\u00d7\n\u03c0\nRationalised 2023-24\n297\nAtoms\nconsists of bright lines on a\ndark \nbackground The\nspectrum emitted by atomic\nhydrogen \nis \nshown \nin\nFig 12 5" + }, + { + "Chapter": "9", + "sentence_range": "2289-2292", + "Text": "The\nspectrum emitted by atomic\nhydrogen \nis \nshown \nin\nFig 12 5 Study of emission\nline spectra of a material can\ntherefore serve as a type of\n\u201cfingerprint\u201d for identification\nof the gas" + }, + { + "Chapter": "9", + "sentence_range": "2290-2293", + "Text": "12 5 Study of emission\nline spectra of a material can\ntherefore serve as a type of\n\u201cfingerprint\u201d for identification\nof the gas When white light\npasses through a gas and we\nanalyse the transmitted light\nusing a spectrometer we find\nsome dark lines in the\nspectrum" + }, + { + "Chapter": "9", + "sentence_range": "2291-2294", + "Text": "5 Study of emission\nline spectra of a material can\ntherefore serve as a type of\n\u201cfingerprint\u201d for identification\nof the gas When white light\npasses through a gas and we\nanalyse the transmitted light\nusing a spectrometer we find\nsome dark lines in the\nspectrum These dark lines\ncorrespond precisely to those wavelengths which were found in the\nemission line spectrum of the gas" + }, + { + "Chapter": "9", + "sentence_range": "2292-2295", + "Text": "Study of emission\nline spectra of a material can\ntherefore serve as a type of\n\u201cfingerprint\u201d for identification\nof the gas When white light\npasses through a gas and we\nanalyse the transmitted light\nusing a spectrometer we find\nsome dark lines in the\nspectrum These dark lines\ncorrespond precisely to those wavelengths which were found in the\nemission line spectrum of the gas This is called the absorption spectrum\nof the material of the gas" + }, + { + "Chapter": "9", + "sentence_range": "2293-2296", + "Text": "When white light\npasses through a gas and we\nanalyse the transmitted light\nusing a spectrometer we find\nsome dark lines in the\nspectrum These dark lines\ncorrespond precisely to those wavelengths which were found in the\nemission line spectrum of the gas This is called the absorption spectrum\nof the material of the gas 12" + }, + { + "Chapter": "9", + "sentence_range": "2294-2297", + "Text": "These dark lines\ncorrespond precisely to those wavelengths which were found in the\nemission line spectrum of the gas This is called the absorption spectrum\nof the material of the gas 12 4 BOHR MODEL OF THE HYDROGEN\n ATOM\nThe model of the atom proposed by Rutherford assumes\nthat the atom, consisting of a central nucleus and\nrevolving electron is stable much like sun-planet system\nwhich the model imitates" + }, + { + "Chapter": "9", + "sentence_range": "2295-2298", + "Text": "This is called the absorption spectrum\nof the material of the gas 12 4 BOHR MODEL OF THE HYDROGEN\n ATOM\nThe model of the atom proposed by Rutherford assumes\nthat the atom, consisting of a central nucleus and\nrevolving electron is stable much like sun-planet system\nwhich the model imitates However, there are some\nfundamental differences between the two situations" + }, + { + "Chapter": "9", + "sentence_range": "2296-2299", + "Text": "12 4 BOHR MODEL OF THE HYDROGEN\n ATOM\nThe model of the atom proposed by Rutherford assumes\nthat the atom, consisting of a central nucleus and\nrevolving electron is stable much like sun-planet system\nwhich the model imitates However, there are some\nfundamental differences between the two situations While the planetary system is held by gravitational\nforce, the nucleus-electron system being charged\nobjects, interact by Coulomb\u2019s Law of force" + }, + { + "Chapter": "9", + "sentence_range": "2297-2300", + "Text": "4 BOHR MODEL OF THE HYDROGEN\n ATOM\nThe model of the atom proposed by Rutherford assumes\nthat the atom, consisting of a central nucleus and\nrevolving electron is stable much like sun-planet system\nwhich the model imitates However, there are some\nfundamental differences between the two situations While the planetary system is held by gravitational\nforce, the nucleus-electron system being charged\nobjects, interact by Coulomb\u2019s Law of force We know\nthat an object which moves in a circle is being\nconstantly accelerated \u2013 the acceleration being\ncentripetal in nature" + }, + { + "Chapter": "9", + "sentence_range": "2298-2301", + "Text": "However, there are some\nfundamental differences between the two situations While the planetary system is held by gravitational\nforce, the nucleus-electron system being charged\nobjects, interact by Coulomb\u2019s Law of force We know\nthat an object which moves in a circle is being\nconstantly accelerated \u2013 the acceleration being\ncentripetal in nature According to classical\nelectromagnetic theory, an accelerating charged particle\nemits radiation in the form of electromagnetic waves" + }, + { + "Chapter": "9", + "sentence_range": "2299-2302", + "Text": "While the planetary system is held by gravitational\nforce, the nucleus-electron system being charged\nobjects, interact by Coulomb\u2019s Law of force We know\nthat an object which moves in a circle is being\nconstantly accelerated \u2013 the acceleration being\ncentripetal in nature According to classical\nelectromagnetic theory, an accelerating charged particle\nemits radiation in the form of electromagnetic waves The energy of an accelerating electron should therefore,\ncontinuously decrease" + }, + { + "Chapter": "9", + "sentence_range": "2300-2303", + "Text": "We know\nthat an object which moves in a circle is being\nconstantly accelerated \u2013 the acceleration being\ncentripetal in nature According to classical\nelectromagnetic theory, an accelerating charged particle\nemits radiation in the form of electromagnetic waves The energy of an accelerating electron should therefore,\ncontinuously decrease The electron would spiral\ninward and eventually fall into the nucleus (Fig" + }, + { + "Chapter": "9", + "sentence_range": "2301-2304", + "Text": "According to classical\nelectromagnetic theory, an accelerating charged particle\nemits radiation in the form of electromagnetic waves The energy of an accelerating electron should therefore,\ncontinuously decrease The electron would spiral\ninward and eventually fall into the nucleus (Fig 12" + }, + { + "Chapter": "9", + "sentence_range": "2302-2305", + "Text": "The energy of an accelerating electron should therefore,\ncontinuously decrease The electron would spiral\ninward and eventually fall into the nucleus (Fig 12 6)" + }, + { + "Chapter": "9", + "sentence_range": "2303-2306", + "Text": "The electron would spiral\ninward and eventually fall into the nucleus (Fig 12 6) Thus, such an atom can not be stable" + }, + { + "Chapter": "9", + "sentence_range": "2304-2307", + "Text": "12 6) Thus, such an atom can not be stable Further,\naccording to the classical electromagnetic theory, the\nfrequency of the electromagnetic waves emitted by the\nrevolving electrons is equal to the frequency of\nrevolution" + }, + { + "Chapter": "9", + "sentence_range": "2305-2308", + "Text": "6) Thus, such an atom can not be stable Further,\naccording to the classical electromagnetic theory, the\nfrequency of the electromagnetic waves emitted by the\nrevolving electrons is equal to the frequency of\nrevolution As the electrons spiral inwards, their angular\nvelocities and hence their frequencies would change\ncontinuously, and so will the frequency of the light\nemitted" + }, + { + "Chapter": "9", + "sentence_range": "2306-2309", + "Text": "Thus, such an atom can not be stable Further,\naccording to the classical electromagnetic theory, the\nfrequency of the electromagnetic waves emitted by the\nrevolving electrons is equal to the frequency of\nrevolution As the electrons spiral inwards, their angular\nvelocities and hence their frequencies would change\ncontinuously, and so will the frequency of the light\nemitted Thus, they would emit a continuous spectrum,\nin contradiction to the line spectrum actually observed" + }, + { + "Chapter": "9", + "sentence_range": "2307-2310", + "Text": "Further,\naccording to the classical electromagnetic theory, the\nfrequency of the electromagnetic waves emitted by the\nrevolving electrons is equal to the frequency of\nrevolution As the electrons spiral inwards, their angular\nvelocities and hence their frequencies would change\ncontinuously, and so will the frequency of the light\nemitted Thus, they would emit a continuous spectrum,\nin contradiction to the line spectrum actually observed Clearly Rutherford model tells only a part of the story\nimplying that the classical ideas are not sufficient to\nexplain the atomic structure" + }, + { + "Chapter": "9", + "sentence_range": "2308-2311", + "Text": "As the electrons spiral inwards, their angular\nvelocities and hence their frequencies would change\ncontinuously, and so will the frequency of the light\nemitted Thus, they would emit a continuous spectrum,\nin contradiction to the line spectrum actually observed Clearly Rutherford model tells only a part of the story\nimplying that the classical ideas are not sufficient to\nexplain the atomic structure FIGURE 12" + }, + { + "Chapter": "9", + "sentence_range": "2309-2312", + "Text": "Thus, they would emit a continuous spectrum,\nin contradiction to the line spectrum actually observed Clearly Rutherford model tells only a part of the story\nimplying that the classical ideas are not sufficient to\nexplain the atomic structure FIGURE 12 5 Emission lines in the spectrum of hydrogen" + }, + { + "Chapter": "9", + "sentence_range": "2310-2313", + "Text": "Clearly Rutherford model tells only a part of the story\nimplying that the classical ideas are not sufficient to\nexplain the atomic structure FIGURE 12 5 Emission lines in the spectrum of hydrogen Niels Henrik David Bohr\n(1885 \u2013 1962) Danish\nphysicist who explained the\nspectrum of hydrogen atom\nbased on quantum ideas" + }, + { + "Chapter": "9", + "sentence_range": "2311-2314", + "Text": "FIGURE 12 5 Emission lines in the spectrum of hydrogen Niels Henrik David Bohr\n(1885 \u2013 1962) Danish\nphysicist who explained the\nspectrum of hydrogen atom\nbased on quantum ideas He gave a theory of nuclear\nfission based on the liquid-\ndrop model of nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2312-2315", + "Text": "5 Emission lines in the spectrum of hydrogen Niels Henrik David Bohr\n(1885 \u2013 1962) Danish\nphysicist who explained the\nspectrum of hydrogen atom\nbased on quantum ideas He gave a theory of nuclear\nfission based on the liquid-\ndrop model of nucleus Bohr contributed to the\nclarification of conceptual\nproblems \nin \nquantum\nmechanics, in particular by\nproposing the comple-\nmentary principle" + }, + { + "Chapter": "9", + "sentence_range": "2313-2316", + "Text": "Niels Henrik David Bohr\n(1885 \u2013 1962) Danish\nphysicist who explained the\nspectrum of hydrogen atom\nbased on quantum ideas He gave a theory of nuclear\nfission based on the liquid-\ndrop model of nucleus Bohr contributed to the\nclarification of conceptual\nproblems \nin \nquantum\nmechanics, in particular by\nproposing the comple-\nmentary principle NIELS HENRIK DAVID BOHR (1885 \u2013 1962)\nRationalised 2023-24\nPhysics\n298\n EXAMPLE 12" + }, + { + "Chapter": "9", + "sentence_range": "2314-2317", + "Text": "He gave a theory of nuclear\nfission based on the liquid-\ndrop model of nucleus Bohr contributed to the\nclarification of conceptual\nproblems \nin \nquantum\nmechanics, in particular by\nproposing the comple-\nmentary principle NIELS HENRIK DAVID BOHR (1885 \u2013 1962)\nRationalised 2023-24\nPhysics\n298\n EXAMPLE 12 4\nFIGURE 12" + }, + { + "Chapter": "9", + "sentence_range": "2315-2318", + "Text": "Bohr contributed to the\nclarification of conceptual\nproblems \nin \nquantum\nmechanics, in particular by\nproposing the comple-\nmentary principle NIELS HENRIK DAVID BOHR (1885 \u2013 1962)\nRationalised 2023-24\nPhysics\n298\n EXAMPLE 12 4\nFIGURE 12 6 An accelerated atomic electron must spiral into the\nnucleus as it loses energy" + }, + { + "Chapter": "9", + "sentence_range": "2316-2319", + "Text": "NIELS HENRIK DAVID BOHR (1885 \u2013 1962)\nRationalised 2023-24\nPhysics\n298\n EXAMPLE 12 4\nFIGURE 12 6 An accelerated atomic electron must spiral into the\nnucleus as it loses energy Example 12" + }, + { + "Chapter": "9", + "sentence_range": "2317-2320", + "Text": "4\nFIGURE 12 6 An accelerated atomic electron must spiral into the\nnucleus as it loses energy Example 12 4 According to the classical electromagnetic theory,\ncalculate the initial frequency of the light emitted by the electron\nrevolving around a proton in hydrogen atom" + }, + { + "Chapter": "9", + "sentence_range": "2318-2321", + "Text": "6 An accelerated atomic electron must spiral into the\nnucleus as it loses energy Example 12 4 According to the classical electromagnetic theory,\ncalculate the initial frequency of the light emitted by the electron\nrevolving around a proton in hydrogen atom Solution From Example 12" + }, + { + "Chapter": "9", + "sentence_range": "2319-2322", + "Text": "Example 12 4 According to the classical electromagnetic theory,\ncalculate the initial frequency of the light emitted by the electron\nrevolving around a proton in hydrogen atom Solution From Example 12 3 we know that velocity of electron moving\naround a proton in hydrogen atom in an orbit of radius 5" + }, + { + "Chapter": "9", + "sentence_range": "2320-2323", + "Text": "4 According to the classical electromagnetic theory,\ncalculate the initial frequency of the light emitted by the electron\nrevolving around a proton in hydrogen atom Solution From Example 12 3 we know that velocity of electron moving\naround a proton in hydrogen atom in an orbit of radius 5 3 \u00d7 10\u201311 m\nis 2" + }, + { + "Chapter": "9", + "sentence_range": "2321-2324", + "Text": "Solution From Example 12 3 we know that velocity of electron moving\naround a proton in hydrogen atom in an orbit of radius 5 3 \u00d7 10\u201311 m\nis 2 2 \u00d7 10\u20136 m/s" + }, + { + "Chapter": "9", + "sentence_range": "2322-2325", + "Text": "3 we know that velocity of electron moving\naround a proton in hydrogen atom in an orbit of radius 5 3 \u00d7 10\u201311 m\nis 2 2 \u00d7 10\u20136 m/s Thus, the frequency of the electron moving around\nthe proton is\n(\n)\n6\n1\n11\n2" + }, + { + "Chapter": "9", + "sentence_range": "2323-2326", + "Text": "3 \u00d7 10\u201311 m\nis 2 2 \u00d7 10\u20136 m/s Thus, the frequency of the electron moving around\nthe proton is\n(\n)\n6\n1\n11\n2 2\n10 m s\n2\n2\n5" + }, + { + "Chapter": "9", + "sentence_range": "2324-2327", + "Text": "2 \u00d7 10\u20136 m/s Thus, the frequency of the electron moving around\nthe proton is\n(\n)\n6\n1\n11\n2 2\n10 m s\n2\n2\n5 3\n10\n m\nv\nr\n\u03bd\n\u2212\n\u2212\n\u00d7\n=\n=\n\u03c0\n\u03c0\n\u00d7\n\u00bb 6" + }, + { + "Chapter": "9", + "sentence_range": "2325-2328", + "Text": "Thus, the frequency of the electron moving around\nthe proton is\n(\n)\n6\n1\n11\n2 2\n10 m s\n2\n2\n5 3\n10\n m\nv\nr\n\u03bd\n\u2212\n\u2212\n\u00d7\n=\n=\n\u03c0\n\u03c0\n\u00d7\n\u00bb 6 6 \u00d7 1015 Hz" + }, + { + "Chapter": "9", + "sentence_range": "2326-2329", + "Text": "2\n10 m s\n2\n2\n5 3\n10\n m\nv\nr\n\u03bd\n\u2212\n\u2212\n\u00d7\n=\n=\n\u03c0\n\u03c0\n\u00d7\n\u00bb 6 6 \u00d7 1015 Hz According to the classical electromagnetic theory we know that the\nfrequency of the electromagnetic waves emitted by the revolving\nelectrons is equal to the frequency of its revolution around the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2327-2330", + "Text": "3\n10\n m\nv\nr\n\u03bd\n\u2212\n\u2212\n\u00d7\n=\n=\n\u03c0\n\u03c0\n\u00d7\n\u00bb 6 6 \u00d7 1015 Hz According to the classical electromagnetic theory we know that the\nfrequency of the electromagnetic waves emitted by the revolving\nelectrons is equal to the frequency of its revolution around the nucleus Thus the initial frequency of the light emitted is 6" + }, + { + "Chapter": "9", + "sentence_range": "2328-2331", + "Text": "6 \u00d7 1015 Hz According to the classical electromagnetic theory we know that the\nfrequency of the electromagnetic waves emitted by the revolving\nelectrons is equal to the frequency of its revolution around the nucleus Thus the initial frequency of the light emitted is 6 6 \u00d7 1015 Hz" + }, + { + "Chapter": "9", + "sentence_range": "2329-2332", + "Text": "According to the classical electromagnetic theory we know that the\nfrequency of the electromagnetic waves emitted by the revolving\nelectrons is equal to the frequency of its revolution around the nucleus Thus the initial frequency of the light emitted is 6 6 \u00d7 1015 Hz It was Niels Bohr (1885 \u2013 1962) who made certain modifications in\nthis model by adding the ideas of the newly developing quantum\nhypothesis" + }, + { + "Chapter": "9", + "sentence_range": "2330-2333", + "Text": "Thus the initial frequency of the light emitted is 6 6 \u00d7 1015 Hz It was Niels Bohr (1885 \u2013 1962) who made certain modifications in\nthis model by adding the ideas of the newly developing quantum\nhypothesis Niels Bohr studied in Rutherford\u2019s laboratory for several\nmonths in 1912 and he was convinced about the validity of Rutherford\nnuclear model" + }, + { + "Chapter": "9", + "sentence_range": "2331-2334", + "Text": "6 \u00d7 1015 Hz It was Niels Bohr (1885 \u2013 1962) who made certain modifications in\nthis model by adding the ideas of the newly developing quantum\nhypothesis Niels Bohr studied in Rutherford\u2019s laboratory for several\nmonths in 1912 and he was convinced about the validity of Rutherford\nnuclear model Faced with the dilemma as discussed above, Bohr, in\n1913, concluded that in spite of the success of electromagnetic theory in\nexplaining large-scale phenomena, it could not be applied to the processes\nat the atomic scale" + }, + { + "Chapter": "9", + "sentence_range": "2332-2335", + "Text": "It was Niels Bohr (1885 \u2013 1962) who made certain modifications in\nthis model by adding the ideas of the newly developing quantum\nhypothesis Niels Bohr studied in Rutherford\u2019s laboratory for several\nmonths in 1912 and he was convinced about the validity of Rutherford\nnuclear model Faced with the dilemma as discussed above, Bohr, in\n1913, concluded that in spite of the success of electromagnetic theory in\nexplaining large-scale phenomena, it could not be applied to the processes\nat the atomic scale It became clear that a fairly radical departure from\nthe established principles of classical mechanics and electromagnetism\nwould be needed to understand the structure of atoms and the relation\nof atomic structure to atomic spectra" + }, + { + "Chapter": "9", + "sentence_range": "2333-2336", + "Text": "Niels Bohr studied in Rutherford\u2019s laboratory for several\nmonths in 1912 and he was convinced about the validity of Rutherford\nnuclear model Faced with the dilemma as discussed above, Bohr, in\n1913, concluded that in spite of the success of electromagnetic theory in\nexplaining large-scale phenomena, it could not be applied to the processes\nat the atomic scale It became clear that a fairly radical departure from\nthe established principles of classical mechanics and electromagnetism\nwould be needed to understand the structure of atoms and the relation\nof atomic structure to atomic spectra Bohr combined classical and early\nquantum concepts and gave his theory in the form of three postulates" + }, + { + "Chapter": "9", + "sentence_range": "2334-2337", + "Text": "Faced with the dilemma as discussed above, Bohr, in\n1913, concluded that in spite of the success of electromagnetic theory in\nexplaining large-scale phenomena, it could not be applied to the processes\nat the atomic scale It became clear that a fairly radical departure from\nthe established principles of classical mechanics and electromagnetism\nwould be needed to understand the structure of atoms and the relation\nof atomic structure to atomic spectra Bohr combined classical and early\nquantum concepts and gave his theory in the form of three postulates These are :\n(i)\nBohr\u2019s first postulate was that an electron in an atom could revolve\nin certain stable orbits without the emission of radiant energy,\ncontrary to the predictions of electromagnetic theory" + }, + { + "Chapter": "9", + "sentence_range": "2335-2338", + "Text": "It became clear that a fairly radical departure from\nthe established principles of classical mechanics and electromagnetism\nwould be needed to understand the structure of atoms and the relation\nof atomic structure to atomic spectra Bohr combined classical and early\nquantum concepts and gave his theory in the form of three postulates These are :\n(i)\nBohr\u2019s first postulate was that an electron in an atom could revolve\nin certain stable orbits without the emission of radiant energy,\ncontrary to the predictions of electromagnetic theory According to\nthis postulate, each atom has certain definite stable states in which it\nRationalised 2023-24\n299\nAtoms\ncan exist, and each possible state has definite total energy" + }, + { + "Chapter": "9", + "sentence_range": "2336-2339", + "Text": "Bohr combined classical and early\nquantum concepts and gave his theory in the form of three postulates These are :\n(i)\nBohr\u2019s first postulate was that an electron in an atom could revolve\nin certain stable orbits without the emission of radiant energy,\ncontrary to the predictions of electromagnetic theory According to\nthis postulate, each atom has certain definite stable states in which it\nRationalised 2023-24\n299\nAtoms\ncan exist, and each possible state has definite total energy These are\ncalled the stationary states of the atom" + }, + { + "Chapter": "9", + "sentence_range": "2337-2340", + "Text": "These are :\n(i)\nBohr\u2019s first postulate was that an electron in an atom could revolve\nin certain stable orbits without the emission of radiant energy,\ncontrary to the predictions of electromagnetic theory According to\nthis postulate, each atom has certain definite stable states in which it\nRationalised 2023-24\n299\nAtoms\ncan exist, and each possible state has definite total energy These are\ncalled the stationary states of the atom (ii) Bohr\u2019s second postulate defines these stable orbits" + }, + { + "Chapter": "9", + "sentence_range": "2338-2341", + "Text": "According to\nthis postulate, each atom has certain definite stable states in which it\nRationalised 2023-24\n299\nAtoms\ncan exist, and each possible state has definite total energy These are\ncalled the stationary states of the atom (ii) Bohr\u2019s second postulate defines these stable orbits This postulate\nstates that the electron revolves around the nucleus only in those\norbits for which the angular momentum is some integral multiple of\nh/2p where h is the Planck\u2019s constant (= 6" + }, + { + "Chapter": "9", + "sentence_range": "2339-2342", + "Text": "These are\ncalled the stationary states of the atom (ii) Bohr\u2019s second postulate defines these stable orbits This postulate\nstates that the electron revolves around the nucleus only in those\norbits for which the angular momentum is some integral multiple of\nh/2p where h is the Planck\u2019s constant (= 6 6 \u00b4 10\u201334 J s)" + }, + { + "Chapter": "9", + "sentence_range": "2340-2343", + "Text": "(ii) Bohr\u2019s second postulate defines these stable orbits This postulate\nstates that the electron revolves around the nucleus only in those\norbits for which the angular momentum is some integral multiple of\nh/2p where h is the Planck\u2019s constant (= 6 6 \u00b4 10\u201334 J s) Thus the\nangular momentum (L) of the orbiting electron is quantised" + }, + { + "Chapter": "9", + "sentence_range": "2341-2344", + "Text": "This postulate\nstates that the electron revolves around the nucleus only in those\norbits for which the angular momentum is some integral multiple of\nh/2p where h is the Planck\u2019s constant (= 6 6 \u00b4 10\u201334 J s) Thus the\nangular momentum (L) of the orbiting electron is quantised That is\nL = nh/2p\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2342-2345", + "Text": "6 \u00b4 10\u201334 J s) Thus the\nangular momentum (L) of the orbiting electron is quantised That is\nL = nh/2p\n(12 5)\n(iii) Bohr\u2019s third postulate incorporated into atomic theory the early\nquantum concepts that had been developed by Planck and Einstein" + }, + { + "Chapter": "9", + "sentence_range": "2343-2346", + "Text": "Thus the\nangular momentum (L) of the orbiting electron is quantised That is\nL = nh/2p\n(12 5)\n(iii) Bohr\u2019s third postulate incorporated into atomic theory the early\nquantum concepts that had been developed by Planck and Einstein It states that an electron might make a transition from one of its\nspecified non-radiating orbits to another of lower energy" + }, + { + "Chapter": "9", + "sentence_range": "2344-2347", + "Text": "That is\nL = nh/2p\n(12 5)\n(iii) Bohr\u2019s third postulate incorporated into atomic theory the early\nquantum concepts that had been developed by Planck and Einstein It states that an electron might make a transition from one of its\nspecified non-radiating orbits to another of lower energy When it\ndoes so, a photon is emitted having energy equal to the energy\ndifference between the initial and final states" + }, + { + "Chapter": "9", + "sentence_range": "2345-2348", + "Text": "5)\n(iii) Bohr\u2019s third postulate incorporated into atomic theory the early\nquantum concepts that had been developed by Planck and Einstein It states that an electron might make a transition from one of its\nspecified non-radiating orbits to another of lower energy When it\ndoes so, a photon is emitted having energy equal to the energy\ndifference between the initial and final states The frequency of the\nemitted photon is then given by\nhn = Ei \u2013 Ef\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2346-2349", + "Text": "It states that an electron might make a transition from one of its\nspecified non-radiating orbits to another of lower energy When it\ndoes so, a photon is emitted having energy equal to the energy\ndifference between the initial and final states The frequency of the\nemitted photon is then given by\nhn = Ei \u2013 Ef\n(12 6)\nwhere Ei and Ef are the energies of the initial and final states and Ei > Ef" + }, + { + "Chapter": "9", + "sentence_range": "2347-2350", + "Text": "When it\ndoes so, a photon is emitted having energy equal to the energy\ndifference between the initial and final states The frequency of the\nemitted photon is then given by\nhn = Ei \u2013 Ef\n(12 6)\nwhere Ei and Ef are the energies of the initial and final states and Ei > Ef For a hydrogen atom, Eq" + }, + { + "Chapter": "9", + "sentence_range": "2348-2351", + "Text": "The frequency of the\nemitted photon is then given by\nhn = Ei \u2013 Ef\n(12 6)\nwhere Ei and Ef are the energies of the initial and final states and Ei > Ef For a hydrogen atom, Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2349-2352", + "Text": "6)\nwhere Ei and Ef are the energies of the initial and final states and Ei > Ef For a hydrogen atom, Eq (12 4) gives the expression to determine\nthe energies of different energy states" + }, + { + "Chapter": "9", + "sentence_range": "2350-2353", + "Text": "For a hydrogen atom, Eq (12 4) gives the expression to determine\nthe energies of different energy states But then this equation requires\nthe radius r of the electron orbit" + }, + { + "Chapter": "9", + "sentence_range": "2351-2354", + "Text": "(12 4) gives the expression to determine\nthe energies of different energy states But then this equation requires\nthe radius r of the electron orbit To calculate r, Bohr\u2019s second postulate\nabout the angular momentum of the electron\u2013the quantisation\ncondition \u2013 is used" + }, + { + "Chapter": "9", + "sentence_range": "2352-2355", + "Text": "4) gives the expression to determine\nthe energies of different energy states But then this equation requires\nthe radius r of the electron orbit To calculate r, Bohr\u2019s second postulate\nabout the angular momentum of the electron\u2013the quantisation\ncondition \u2013 is used The radius of nth possible orbit thus found is\n2\n2\n0\n42\n2\nn\nn\nh\nr\nm\ne\n\u03b5\n \n \n\u03c0\n \n \n=\n \n \n \n \n\u03c0 \n \n \n(12" + }, + { + "Chapter": "9", + "sentence_range": "2353-2356", + "Text": "But then this equation requires\nthe radius r of the electron orbit To calculate r, Bohr\u2019s second postulate\nabout the angular momentum of the electron\u2013the quantisation\ncondition \u2013 is used The radius of nth possible orbit thus found is\n2\n2\n0\n42\n2\nn\nn\nh\nr\nm\ne\n\u03b5\n \n \n\u03c0\n \n \n=\n \n \n \n \n\u03c0 \n \n \n(12 7)\nThe total energy of the electron in the stationary states of the hydrogen\natom can be obtained by substituting the value of orbital radius in\nEq" + }, + { + "Chapter": "9", + "sentence_range": "2354-2357", + "Text": "To calculate r, Bohr\u2019s second postulate\nabout the angular momentum of the electron\u2013the quantisation\ncondition \u2013 is used The radius of nth possible orbit thus found is\n2\n2\n0\n42\n2\nn\nn\nh\nr\nm\ne\n\u03b5\n \n \n\u03c0\n \n \n=\n \n \n \n \n\u03c0 \n \n \n(12 7)\nThe total energy of the electron in the stationary states of the hydrogen\natom can be obtained by substituting the value of orbital radius in\nEq (12" + }, + { + "Chapter": "9", + "sentence_range": "2355-2358", + "Text": "The radius of nth possible orbit thus found is\n2\n2\n0\n42\n2\nn\nn\nh\nr\nm\ne\n\u03b5\n \n \n\u03c0\n \n \n=\n \n \n \n \n\u03c0 \n \n \n(12 7)\nThe total energy of the electron in the stationary states of the hydrogen\natom can be obtained by substituting the value of orbital radius in\nEq (12 4) as\n2\n2\n2\n2\n0\n0\n2\n8\n4\nn\ne\nm\ne\nE\nh\nn\n\u03b5\n\u03b5\n \n \n \n \n\u03c0\n \n \n \n= \u2212\n \n \n \n \n \n \n \n \n \n \n\u03c0\n\u03c0\n \n \n \n \nor \n4\n2\n2\n2\n0\n8\nn\nme\nE\nn\n\u03b5h\n= \u2212\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2356-2359", + "Text": "7)\nThe total energy of the electron in the stationary states of the hydrogen\natom can be obtained by substituting the value of orbital radius in\nEq (12 4) as\n2\n2\n2\n2\n0\n0\n2\n8\n4\nn\ne\nm\ne\nE\nh\nn\n\u03b5\n\u03b5\n \n \n \n \n\u03c0\n \n \n \n= \u2212\n \n \n \n \n \n \n \n \n \n \n\u03c0\n\u03c0\n \n \n \n \nor \n4\n2\n2\n2\n0\n8\nn\nme\nE\nn\n\u03b5h\n= \u2212\n(12 8)\nSubstituting values, Eq" + }, + { + "Chapter": "9", + "sentence_range": "2357-2360", + "Text": "(12 4) as\n2\n2\n2\n2\n0\n0\n2\n8\n4\nn\ne\nm\ne\nE\nh\nn\n\u03b5\n\u03b5\n \n \n \n \n\u03c0\n \n \n \n= \u2212\n \n \n \n \n \n \n \n \n \n \n\u03c0\n\u03c0\n \n \n \n \nor \n4\n2\n2\n2\n0\n8\nn\nme\nE\nn\n\u03b5h\n= \u2212\n(12 8)\nSubstituting values, Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2358-2361", + "Text": "4) as\n2\n2\n2\n2\n0\n0\n2\n8\n4\nn\ne\nm\ne\nE\nh\nn\n\u03b5\n\u03b5\n \n \n \n \n\u03c0\n \n \n \n= \u2212\n \n \n \n \n \n \n \n \n \n \n\u03c0\n\u03c0\n \n \n \n \nor \n4\n2\n2\n2\n0\n8\nn\nme\nE\nn\n\u03b5h\n= \u2212\n(12 8)\nSubstituting values, Eq (12 8) yields\n18\n2" + }, + { + "Chapter": "9", + "sentence_range": "2359-2362", + "Text": "8)\nSubstituting values, Eq (12 8) yields\n18\n2 182\n10\nJ\nEn\nn\n\u2212\n\u00d7\n= \u2212\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2360-2363", + "Text": "(12 8) yields\n18\n2 182\n10\nJ\nEn\nn\n\u2212\n\u00d7\n= \u2212\n(12 9)\nAtomic energies are often expressed in electron volts (eV) rather than\njoules" + }, + { + "Chapter": "9", + "sentence_range": "2361-2364", + "Text": "8) yields\n18\n2 182\n10\nJ\nEn\nn\n\u2212\n\u00d7\n= \u2212\n(12 9)\nAtomic energies are often expressed in electron volts (eV) rather than\njoules Since 1 eV = 1" + }, + { + "Chapter": "9", + "sentence_range": "2362-2365", + "Text": "182\n10\nJ\nEn\nn\n\u2212\n\u00d7\n= \u2212\n(12 9)\nAtomic energies are often expressed in electron volts (eV) rather than\njoules Since 1 eV = 1 6 \u00b4 10\u201319 J, Eq" + }, + { + "Chapter": "9", + "sentence_range": "2363-2366", + "Text": "9)\nAtomic energies are often expressed in electron volts (eV) rather than\njoules Since 1 eV = 1 6 \u00b4 10\u201319 J, Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2364-2367", + "Text": "Since 1 eV = 1 6 \u00b4 10\u201319 J, Eq (12 9) can be rewritten as\n2\n13" + }, + { + "Chapter": "9", + "sentence_range": "2365-2368", + "Text": "6 \u00b4 10\u201319 J, Eq (12 9) can be rewritten as\n2\n13 6 eV\nEn\n= \u2212n\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2366-2369", + "Text": "(12 9) can be rewritten as\n2\n13 6 eV\nEn\n= \u2212n\n(12 10)\nThe negative sign of the total energy of an electron moving in an orbit\nmeans that the electron is bound with the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2367-2370", + "Text": "9) can be rewritten as\n2\n13 6 eV\nEn\n= \u2212n\n(12 10)\nThe negative sign of the total energy of an electron moving in an orbit\nmeans that the electron is bound with the nucleus Energy will thus be\nrequired to remove the electron from the hydrogen atom to a distance\ninfinitely far away from its nucleus (or proton in hydrogen atom)" + }, + { + "Chapter": "9", + "sentence_range": "2368-2371", + "Text": "6 eV\nEn\n= \u2212n\n(12 10)\nThe negative sign of the total energy of an electron moving in an orbit\nmeans that the electron is bound with the nucleus Energy will thus be\nrequired to remove the electron from the hydrogen atom to a distance\ninfinitely far away from its nucleus (or proton in hydrogen atom) Rationalised 2023-24\nPhysics\n300\n12" + }, + { + "Chapter": "9", + "sentence_range": "2369-2372", + "Text": "10)\nThe negative sign of the total energy of an electron moving in an orbit\nmeans that the electron is bound with the nucleus Energy will thus be\nrequired to remove the electron from the hydrogen atom to a distance\ninfinitely far away from its nucleus (or proton in hydrogen atom) Rationalised 2023-24\nPhysics\n300\n12 4" + }, + { + "Chapter": "9", + "sentence_range": "2370-2373", + "Text": "Energy will thus be\nrequired to remove the electron from the hydrogen atom to a distance\ninfinitely far away from its nucleus (or proton in hydrogen atom) Rationalised 2023-24\nPhysics\n300\n12 4 1 Energy levels\nThe energy of an atom is the least (largest negative value)\nwhen its electron is revolving in an orbit closest to the\nnucleus i" + }, + { + "Chapter": "9", + "sentence_range": "2371-2374", + "Text": "Rationalised 2023-24\nPhysics\n300\n12 4 1 Energy levels\nThe energy of an atom is the least (largest negative value)\nwhen its electron is revolving in an orbit closest to the\nnucleus i e" + }, + { + "Chapter": "9", + "sentence_range": "2372-2375", + "Text": "4 1 Energy levels\nThe energy of an atom is the least (largest negative value)\nwhen its electron is revolving in an orbit closest to the\nnucleus i e , the one for which n = 1" + }, + { + "Chapter": "9", + "sentence_range": "2373-2376", + "Text": "1 Energy levels\nThe energy of an atom is the least (largest negative value)\nwhen its electron is revolving in an orbit closest to the\nnucleus i e , the one for which n = 1 For n = 2, 3," + }, + { + "Chapter": "9", + "sentence_range": "2374-2377", + "Text": "e , the one for which n = 1 For n = 2, 3, the\nabsolute value of the energy E is smaller, hence the energy\nis progressively larger in the outer orbits" + }, + { + "Chapter": "9", + "sentence_range": "2375-2378", + "Text": ", the one for which n = 1 For n = 2, 3, the\nabsolute value of the energy E is smaller, hence the energy\nis progressively larger in the outer orbits The lowest state\nof the atom, called the ground state, is that of the lowest\nenergy, with the electron revolving in the orbit of smallest\nradius, the Bohr radius, a 0" + }, + { + "Chapter": "9", + "sentence_range": "2376-2379", + "Text": "For n = 2, 3, the\nabsolute value of the energy E is smaller, hence the energy\nis progressively larger in the outer orbits The lowest state\nof the atom, called the ground state, is that of the lowest\nenergy, with the electron revolving in the orbit of smallest\nradius, the Bohr radius, a 0 The energy of this state (n = 1),\nE1 is \u201313" + }, + { + "Chapter": "9", + "sentence_range": "2377-2380", + "Text": "the\nabsolute value of the energy E is smaller, hence the energy\nis progressively larger in the outer orbits The lowest state\nof the atom, called the ground state, is that of the lowest\nenergy, with the electron revolving in the orbit of smallest\nradius, the Bohr radius, a 0 The energy of this state (n = 1),\nE1 is \u201313 6 eV" + }, + { + "Chapter": "9", + "sentence_range": "2378-2381", + "Text": "The lowest state\nof the atom, called the ground state, is that of the lowest\nenergy, with the electron revolving in the orbit of smallest\nradius, the Bohr radius, a 0 The energy of this state (n = 1),\nE1 is \u201313 6 eV Therefore, the minimum energy required to\nfree the electron from the ground state of the hydrogen atom\nis 13" + }, + { + "Chapter": "9", + "sentence_range": "2379-2382", + "Text": "The energy of this state (n = 1),\nE1 is \u201313 6 eV Therefore, the minimum energy required to\nfree the electron from the ground state of the hydrogen atom\nis 13 6 eV" + }, + { + "Chapter": "9", + "sentence_range": "2380-2383", + "Text": "6 eV Therefore, the minimum energy required to\nfree the electron from the ground state of the hydrogen atom\nis 13 6 eV It is called the ionisation energy of the hydrogen\natom" + }, + { + "Chapter": "9", + "sentence_range": "2381-2384", + "Text": "Therefore, the minimum energy required to\nfree the electron from the ground state of the hydrogen atom\nis 13 6 eV It is called the ionisation energy of the hydrogen\natom This prediction of the Bohr\u2019s model is in excellent\nagreement with the experimental value of ionisation energy" + }, + { + "Chapter": "9", + "sentence_range": "2382-2385", + "Text": "6 eV It is called the ionisation energy of the hydrogen\natom This prediction of the Bohr\u2019s model is in excellent\nagreement with the experimental value of ionisation energy At room temperature, most of the hydrogen atoms are\nin ground state" + }, + { + "Chapter": "9", + "sentence_range": "2383-2386", + "Text": "It is called the ionisation energy of the hydrogen\natom This prediction of the Bohr\u2019s model is in excellent\nagreement with the experimental value of ionisation energy At room temperature, most of the hydrogen atoms are\nin ground state When a hydrogen atom receives energy\nby processes such as electron collisions, the atom may\nacquire sufficient energy to raise the electron to higher\nenergy states" + }, + { + "Chapter": "9", + "sentence_range": "2384-2387", + "Text": "This prediction of the Bohr\u2019s model is in excellent\nagreement with the experimental value of ionisation energy At room temperature, most of the hydrogen atoms are\nin ground state When a hydrogen atom receives energy\nby processes such as electron collisions, the atom may\nacquire sufficient energy to raise the electron to higher\nenergy states The atom is then said to be in an excited\nstate" + }, + { + "Chapter": "9", + "sentence_range": "2385-2388", + "Text": "At room temperature, most of the hydrogen atoms are\nin ground state When a hydrogen atom receives energy\nby processes such as electron collisions, the atom may\nacquire sufficient energy to raise the electron to higher\nenergy states The atom is then said to be in an excited\nstate From Eq" + }, + { + "Chapter": "9", + "sentence_range": "2386-2389", + "Text": "When a hydrogen atom receives energy\nby processes such as electron collisions, the atom may\nacquire sufficient energy to raise the electron to higher\nenergy states The atom is then said to be in an excited\nstate From Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2387-2390", + "Text": "The atom is then said to be in an excited\nstate From Eq (12 10), for n = 2; the energy E2 is\n\u20133" + }, + { + "Chapter": "9", + "sentence_range": "2388-2391", + "Text": "From Eq (12 10), for n = 2; the energy E2 is\n\u20133 40 eV" + }, + { + "Chapter": "9", + "sentence_range": "2389-2392", + "Text": "(12 10), for n = 2; the energy E2 is\n\u20133 40 eV It means that the energy required to excite an\nelectron in hydrogen atom to its first excited state, is an\nenergy equal to E2 \u2013 E1 = \u20133" + }, + { + "Chapter": "9", + "sentence_range": "2390-2393", + "Text": "10), for n = 2; the energy E2 is\n\u20133 40 eV It means that the energy required to excite an\nelectron in hydrogen atom to its first excited state, is an\nenergy equal to E2 \u2013 E1 = \u20133 40 eV \u2013 (\u201313" + }, + { + "Chapter": "9", + "sentence_range": "2391-2394", + "Text": "40 eV It means that the energy required to excite an\nelectron in hydrogen atom to its first excited state, is an\nenergy equal to E2 \u2013 E1 = \u20133 40 eV \u2013 (\u201313 6) eV = 10" + }, + { + "Chapter": "9", + "sentence_range": "2392-2395", + "Text": "It means that the energy required to excite an\nelectron in hydrogen atom to its first excited state, is an\nenergy equal to E2 \u2013 E1 = \u20133 40 eV \u2013 (\u201313 6) eV = 10 2 eV" + }, + { + "Chapter": "9", + "sentence_range": "2393-2396", + "Text": "40 eV \u2013 (\u201313 6) eV = 10 2 eV Similarly, E3 = \u20131" + }, + { + "Chapter": "9", + "sentence_range": "2394-2397", + "Text": "6) eV = 10 2 eV Similarly, E3 = \u20131 51 eV and E3 \u2013 E1 = 12" + }, + { + "Chapter": "9", + "sentence_range": "2395-2398", + "Text": "2 eV Similarly, E3 = \u20131 51 eV and E3 \u2013 E1 = 12 09 eV, or to excite\nthe hydrogen atom from its ground state (n = 1) to second\nexcited state (n = 3), 12" + }, + { + "Chapter": "9", + "sentence_range": "2396-2399", + "Text": "Similarly, E3 = \u20131 51 eV and E3 \u2013 E1 = 12 09 eV, or to excite\nthe hydrogen atom from its ground state (n = 1) to second\nexcited state (n = 3), 12 09 eV energy is required, and so\non" + }, + { + "Chapter": "9", + "sentence_range": "2397-2400", + "Text": "51 eV and E3 \u2013 E1 = 12 09 eV, or to excite\nthe hydrogen atom from its ground state (n = 1) to second\nexcited state (n = 3), 12 09 eV energy is required, and so\non From these excited states the electron can then fall back\nto a state of lower energy, emitting a photon in the process" + }, + { + "Chapter": "9", + "sentence_range": "2398-2401", + "Text": "09 eV, or to excite\nthe hydrogen atom from its ground state (n = 1) to second\nexcited state (n = 3), 12 09 eV energy is required, and so\non From these excited states the electron can then fall back\nto a state of lower energy, emitting a photon in the process Thus, as the excitation of hydrogen atom increases (that is\nas n increases) the value of minimum energy required to\nfree the electron from the excited atom decreases" + }, + { + "Chapter": "9", + "sentence_range": "2399-2402", + "Text": "09 eV energy is required, and so\non From these excited states the electron can then fall back\nto a state of lower energy, emitting a photon in the process Thus, as the excitation of hydrogen atom increases (that is\nas n increases) the value of minimum energy required to\nfree the electron from the excited atom decreases The energy level diagram* for the stationary states of a\nhydrogen atom, computed from Eq" + }, + { + "Chapter": "9", + "sentence_range": "2400-2403", + "Text": "From these excited states the electron can then fall back\nto a state of lower energy, emitting a photon in the process Thus, as the excitation of hydrogen atom increases (that is\nas n increases) the value of minimum energy required to\nfree the electron from the excited atom decreases The energy level diagram* for the stationary states of a\nhydrogen atom, computed from Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2401-2404", + "Text": "Thus, as the excitation of hydrogen atom increases (that is\nas n increases) the value of minimum energy required to\nfree the electron from the excited atom decreases The energy level diagram* for the stationary states of a\nhydrogen atom, computed from Eq (12 10), is given in\nFig" + }, + { + "Chapter": "9", + "sentence_range": "2402-2405", + "Text": "The energy level diagram* for the stationary states of a\nhydrogen atom, computed from Eq (12 10), is given in\nFig 12" + }, + { + "Chapter": "9", + "sentence_range": "2403-2406", + "Text": "(12 10), is given in\nFig 12 7" + }, + { + "Chapter": "9", + "sentence_range": "2404-2407", + "Text": "10), is given in\nFig 12 7 The principal quantum number n labels the stationary\nstates in the ascending order of energy" + }, + { + "Chapter": "9", + "sentence_range": "2405-2408", + "Text": "12 7 The principal quantum number n labels the stationary\nstates in the ascending order of energy In this diagram, the highest\nenergy state corresponds to n =\u00a5 in Eq, (12" + }, + { + "Chapter": "9", + "sentence_range": "2406-2409", + "Text": "7 The principal quantum number n labels the stationary\nstates in the ascending order of energy In this diagram, the highest\nenergy state corresponds to n =\u00a5 in Eq, (12 10) and has an energy\nof 0 eV" + }, + { + "Chapter": "9", + "sentence_range": "2407-2410", + "Text": "The principal quantum number n labels the stationary\nstates in the ascending order of energy In this diagram, the highest\nenergy state corresponds to n =\u00a5 in Eq, (12 10) and has an energy\nof 0 eV This is the energy of the atom when the electron is\ncompletely removed (r = \u00a5) from the nucleus and is at rest" + }, + { + "Chapter": "9", + "sentence_range": "2408-2411", + "Text": "In this diagram, the highest\nenergy state corresponds to n =\u00a5 in Eq, (12 10) and has an energy\nof 0 eV This is the energy of the atom when the electron is\ncompletely removed (r = \u00a5) from the nucleus and is at rest Observe how\nthe energies of the excited states come closer and closer together as\nn increases" + }, + { + "Chapter": "9", + "sentence_range": "2409-2412", + "Text": "10) and has an energy\nof 0 eV This is the energy of the atom when the electron is\ncompletely removed (r = \u00a5) from the nucleus and is at rest Observe how\nthe energies of the excited states come closer and closer together as\nn increases 12" + }, + { + "Chapter": "9", + "sentence_range": "2410-2413", + "Text": "This is the energy of the atom when the electron is\ncompletely removed (r = \u00a5) from the nucleus and is at rest Observe how\nthe energies of the excited states come closer and closer together as\nn increases 12 5 THE LINE SPECTRA OF THE HYDROGEN ATOM\nAccording to the third postulate of Bohr\u2019s model, when an atom makes a\ntransition from the higher energy state with quantum number ni to the\nlower energy state with quantum number nf (nf < ni), the difference of\nenergy is carried away by a photon of frequency nif such that\nFIGURE 12" + }, + { + "Chapter": "9", + "sentence_range": "2411-2414", + "Text": "Observe how\nthe energies of the excited states come closer and closer together as\nn increases 12 5 THE LINE SPECTRA OF THE HYDROGEN ATOM\nAccording to the third postulate of Bohr\u2019s model, when an atom makes a\ntransition from the higher energy state with quantum number ni to the\nlower energy state with quantum number nf (nf < ni), the difference of\nenergy is carried away by a photon of frequency nif such that\nFIGURE 12 7 The energy level\ndiagram for the hydrogen atom" + }, + { + "Chapter": "9", + "sentence_range": "2412-2415", + "Text": "12 5 THE LINE SPECTRA OF THE HYDROGEN ATOM\nAccording to the third postulate of Bohr\u2019s model, when an atom makes a\ntransition from the higher energy state with quantum number ni to the\nlower energy state with quantum number nf (nf < ni), the difference of\nenergy is carried away by a photon of frequency nif such that\nFIGURE 12 7 The energy level\ndiagram for the hydrogen atom The electron in a hydrogen atom\nat room temperature spends\nmost of its time in the ground\nstate" + }, + { + "Chapter": "9", + "sentence_range": "2413-2416", + "Text": "5 THE LINE SPECTRA OF THE HYDROGEN ATOM\nAccording to the third postulate of Bohr\u2019s model, when an atom makes a\ntransition from the higher energy state with quantum number ni to the\nlower energy state with quantum number nf (nf < ni), the difference of\nenergy is carried away by a photon of frequency nif such that\nFIGURE 12 7 The energy level\ndiagram for the hydrogen atom The electron in a hydrogen atom\nat room temperature spends\nmost of its time in the ground\nstate To ionise a hydrogen\natom an electron from the\nground state, 13" + }, + { + "Chapter": "9", + "sentence_range": "2414-2417", + "Text": "7 The energy level\ndiagram for the hydrogen atom The electron in a hydrogen atom\nat room temperature spends\nmost of its time in the ground\nstate To ionise a hydrogen\natom an electron from the\nground state, 13 6 eV of energy\nmust be supplied" + }, + { + "Chapter": "9", + "sentence_range": "2415-2418", + "Text": "The electron in a hydrogen atom\nat room temperature spends\nmost of its time in the ground\nstate To ionise a hydrogen\natom an electron from the\nground state, 13 6 eV of energy\nmust be supplied (The horizontal\nlines specify the presence of\nallowed energy states" + }, + { + "Chapter": "9", + "sentence_range": "2416-2419", + "Text": "To ionise a hydrogen\natom an electron from the\nground state, 13 6 eV of energy\nmust be supplied (The horizontal\nlines specify the presence of\nallowed energy states )\n*\nAn electron can have any total energy above E = 0 eV" + }, + { + "Chapter": "9", + "sentence_range": "2417-2420", + "Text": "6 eV of energy\nmust be supplied (The horizontal\nlines specify the presence of\nallowed energy states )\n*\nAn electron can have any total energy above E = 0 eV In such situations the\nelectron is free" + }, + { + "Chapter": "9", + "sentence_range": "2418-2421", + "Text": "(The horizontal\nlines specify the presence of\nallowed energy states )\n*\nAn electron can have any total energy above E = 0 eV In such situations the\nelectron is free Thus there is a continuum of energy states above E = 0 eV, as\nshown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "2419-2422", + "Text": ")\n*\nAn electron can have any total energy above E = 0 eV In such situations the\nelectron is free Thus there is a continuum of energy states above E = 0 eV, as\nshown in Fig 12" + }, + { + "Chapter": "9", + "sentence_range": "2420-2423", + "Text": "In such situations the\nelectron is free Thus there is a continuum of energy states above E = 0 eV, as\nshown in Fig 12 7" + }, + { + "Chapter": "9", + "sentence_range": "2421-2424", + "Text": "Thus there is a continuum of energy states above E = 0 eV, as\nshown in Fig 12 7 Rationalised 2023-24\n301\nAtoms\nhvif = Eni \u2013 Enf\n(12" + }, + { + "Chapter": "9", + "sentence_range": "2422-2425", + "Text": "12 7 Rationalised 2023-24\n301\nAtoms\nhvif = Eni \u2013 Enf\n(12 11)\nSince both nf and ni are integers, this immediately shows that in\ntransitions between different atomic levels, light is radiated in various\ndiscrete frequencies" + }, + { + "Chapter": "9", + "sentence_range": "2423-2426", + "Text": "7 Rationalised 2023-24\n301\nAtoms\nhvif = Eni \u2013 Enf\n(12 11)\nSince both nf and ni are integers, this immediately shows that in\ntransitions between different atomic levels, light is radiated in various\ndiscrete frequencies The various lines in the atomic spectra are produced when electrons\njump from higher energy state to a lower energy state and photons are\nemitted" + }, + { + "Chapter": "9", + "sentence_range": "2424-2427", + "Text": "Rationalised 2023-24\n301\nAtoms\nhvif = Eni \u2013 Enf\n(12 11)\nSince both nf and ni are integers, this immediately shows that in\ntransitions between different atomic levels, light is radiated in various\ndiscrete frequencies The various lines in the atomic spectra are produced when electrons\njump from higher energy state to a lower energy state and photons are\nemitted These spectral lines are called emission lines" + }, + { + "Chapter": "9", + "sentence_range": "2425-2428", + "Text": "11)\nSince both nf and ni are integers, this immediately shows that in\ntransitions between different atomic levels, light is radiated in various\ndiscrete frequencies The various lines in the atomic spectra are produced when electrons\njump from higher energy state to a lower energy state and photons are\nemitted These spectral lines are called emission lines But when an atom\nabsorbs a photon that has precisely the same energy needed by the\nelectron in a lower energy state to make transitions to a higher energy\nstate, the process is called absorption" + }, + { + "Chapter": "9", + "sentence_range": "2426-2429", + "Text": "The various lines in the atomic spectra are produced when electrons\njump from higher energy state to a lower energy state and photons are\nemitted These spectral lines are called emission lines But when an atom\nabsorbs a photon that has precisely the same energy needed by the\nelectron in a lower energy state to make transitions to a higher energy\nstate, the process is called absorption Thus if photons with a continuous\nrange of frequencies pass through a rarefied gas and then are analysed\nwith a spectrometer, a series of dark spectral absorption lines appear in\nthe continuous spectrum" + }, + { + "Chapter": "9", + "sentence_range": "2427-2430", + "Text": "These spectral lines are called emission lines But when an atom\nabsorbs a photon that has precisely the same energy needed by the\nelectron in a lower energy state to make transitions to a higher energy\nstate, the process is called absorption Thus if photons with a continuous\nrange of frequencies pass through a rarefied gas and then are analysed\nwith a spectrometer, a series of dark spectral absorption lines appear in\nthe continuous spectrum The dark lines indicate the frequencies that\nhave been absorbed by the atoms of the gas" + }, + { + "Chapter": "9", + "sentence_range": "2428-2431", + "Text": "But when an atom\nabsorbs a photon that has precisely the same energy needed by the\nelectron in a lower energy state to make transitions to a higher energy\nstate, the process is called absorption Thus if photons with a continuous\nrange of frequencies pass through a rarefied gas and then are analysed\nwith a spectrometer, a series of dark spectral absorption lines appear in\nthe continuous spectrum The dark lines indicate the frequencies that\nhave been absorbed by the atoms of the gas The explanation of the hydrogen atom spectrum provided by Bohr\u2019s\nmodel was a brilliant achievement, which greatly stimulated progress\ntowards the modern quantum theory" + }, + { + "Chapter": "9", + "sentence_range": "2429-2432", + "Text": "Thus if photons with a continuous\nrange of frequencies pass through a rarefied gas and then are analysed\nwith a spectrometer, a series of dark spectral absorption lines appear in\nthe continuous spectrum The dark lines indicate the frequencies that\nhave been absorbed by the atoms of the gas The explanation of the hydrogen atom spectrum provided by Bohr\u2019s\nmodel was a brilliant achievement, which greatly stimulated progress\ntowards the modern quantum theory In 1922, Bohr was awarded Nobel\nPrize in Physics" + }, + { + "Chapter": "9", + "sentence_range": "2430-2433", + "Text": "The dark lines indicate the frequencies that\nhave been absorbed by the atoms of the gas The explanation of the hydrogen atom spectrum provided by Bohr\u2019s\nmodel was a brilliant achievement, which greatly stimulated progress\ntowards the modern quantum theory In 1922, Bohr was awarded Nobel\nPrize in Physics 12" + }, + { + "Chapter": "9", + "sentence_range": "2431-2434", + "Text": "The explanation of the hydrogen atom spectrum provided by Bohr\u2019s\nmodel was a brilliant achievement, which greatly stimulated progress\ntowards the modern quantum theory In 1922, Bohr was awarded Nobel\nPrize in Physics 12 6 DE BROGLIE\u2019S EXPLANATION OF BOHR\u2019S\nSECOND POSTULATE OF QUANTISATION\nOf all the postulates, Bohr made in his model of the atom,\nperhaps the most puzzling is his second postulate" + }, + { + "Chapter": "9", + "sentence_range": "2432-2435", + "Text": "In 1922, Bohr was awarded Nobel\nPrize in Physics 12 6 DE BROGLIE\u2019S EXPLANATION OF BOHR\u2019S\nSECOND POSTULATE OF QUANTISATION\nOf all the postulates, Bohr made in his model of the atom,\nperhaps the most puzzling is his second postulate It states\nthat the angular momentum of the electron orbiting around\nthe nucleus is quantised (that is, Ln = nh/2p; n = 1, 2, 3 \u2026)" + }, + { + "Chapter": "9", + "sentence_range": "2433-2436", + "Text": "12 6 DE BROGLIE\u2019S EXPLANATION OF BOHR\u2019S\nSECOND POSTULATE OF QUANTISATION\nOf all the postulates, Bohr made in his model of the atom,\nperhaps the most puzzling is his second postulate It states\nthat the angular momentum of the electron orbiting around\nthe nucleus is quantised (that is, Ln = nh/2p; n = 1, 2, 3 \u2026) Why should the angular momentum have only those values\nthat are integral multiples of h/2p" + }, + { + "Chapter": "9", + "sentence_range": "2434-2437", + "Text": "6 DE BROGLIE\u2019S EXPLANATION OF BOHR\u2019S\nSECOND POSTULATE OF QUANTISATION\nOf all the postulates, Bohr made in his model of the atom,\nperhaps the most puzzling is his second postulate It states\nthat the angular momentum of the electron orbiting around\nthe nucleus is quantised (that is, Ln = nh/2p; n = 1, 2, 3 \u2026) Why should the angular momentum have only those values\nthat are integral multiples of h/2p The French physicist Louis\nde Broglie explained this puzzle in 1923, ten years after Bohr\nproposed his model" + }, + { + "Chapter": "9", + "sentence_range": "2435-2438", + "Text": "It states\nthat the angular momentum of the electron orbiting around\nthe nucleus is quantised (that is, Ln = nh/2p; n = 1, 2, 3 \u2026) Why should the angular momentum have only those values\nthat are integral multiples of h/2p The French physicist Louis\nde Broglie explained this puzzle in 1923, ten years after Bohr\nproposed his model We studied, in Chapter 11, about the de Broglie\u2019s\nhypothesis that material particles, such as electrons, also\nhave a wave nature" + }, + { + "Chapter": "9", + "sentence_range": "2436-2439", + "Text": "Why should the angular momentum have only those values\nthat are integral multiples of h/2p The French physicist Louis\nde Broglie explained this puzzle in 1923, ten years after Bohr\nproposed his model We studied, in Chapter 11, about the de Broglie\u2019s\nhypothesis that material particles, such as electrons, also\nhave a wave nature C" + }, + { + "Chapter": "9", + "sentence_range": "2437-2440", + "Text": "The French physicist Louis\nde Broglie explained this puzzle in 1923, ten years after Bohr\nproposed his model We studied, in Chapter 11, about the de Broglie\u2019s\nhypothesis that material particles, such as electrons, also\nhave a wave nature C J" + }, + { + "Chapter": "9", + "sentence_range": "2438-2441", + "Text": "We studied, in Chapter 11, about the de Broglie\u2019s\nhypothesis that material particles, such as electrons, also\nhave a wave nature C J Davisson and L" + }, + { + "Chapter": "9", + "sentence_range": "2439-2442", + "Text": "C J Davisson and L H" + }, + { + "Chapter": "9", + "sentence_range": "2440-2443", + "Text": "J Davisson and L H Germer later\nexperimentally verified the wave nature of electrons in 1927" + }, + { + "Chapter": "9", + "sentence_range": "2441-2444", + "Text": "Davisson and L H Germer later\nexperimentally verified the wave nature of electrons in 1927 Louis de Broglie argued that the electron in its circular orbit,\nas proposed by Bohr, must be seen as a particle wave" + }, + { + "Chapter": "9", + "sentence_range": "2442-2445", + "Text": "H Germer later\nexperimentally verified the wave nature of electrons in 1927 Louis de Broglie argued that the electron in its circular orbit,\nas proposed by Bohr, must be seen as a particle wave In\nanalogy to waves travelling on a string, particle waves too\ncan lead to standing waves under resonant conditions" + }, + { + "Chapter": "9", + "sentence_range": "2443-2446", + "Text": "Germer later\nexperimentally verified the wave nature of electrons in 1927 Louis de Broglie argued that the electron in its circular orbit,\nas proposed by Bohr, must be seen as a particle wave In\nanalogy to waves travelling on a string, particle waves too\ncan lead to standing waves under resonant conditions From\nChapter 14 of Class XI Physics textbook, we know that when\na string is plucked, a vast number of wavelengths are excited" + }, + { + "Chapter": "9", + "sentence_range": "2444-2447", + "Text": "Louis de Broglie argued that the electron in its circular orbit,\nas proposed by Bohr, must be seen as a particle wave In\nanalogy to waves travelling on a string, particle waves too\ncan lead to standing waves under resonant conditions From\nChapter 14 of Class XI Physics textbook, we know that when\na string is plucked, a vast number of wavelengths are excited However only those wavelengths survive which have nodes\nat the ends and form the standing wave in the string" + }, + { + "Chapter": "9", + "sentence_range": "2445-2448", + "Text": "In\nanalogy to waves travelling on a string, particle waves too\ncan lead to standing waves under resonant conditions From\nChapter 14 of Class XI Physics textbook, we know that when\na string is plucked, a vast number of wavelengths are excited However only those wavelengths survive which have nodes\nat the ends and form the standing wave in the string It means\nthat in a string, standing waves are formed when the total distance\ntravelled by a wave down the string and back is one wavelength, two\nwavelengths, or any integral number of wavelengths" + }, + { + "Chapter": "9", + "sentence_range": "2446-2449", + "Text": "From\nChapter 14 of Class XI Physics textbook, we know that when\na string is plucked, a vast number of wavelengths are excited However only those wavelengths survive which have nodes\nat the ends and form the standing wave in the string It means\nthat in a string, standing waves are formed when the total distance\ntravelled by a wave down the string and back is one wavelength, two\nwavelengths, or any integral number of wavelengths Waves with other\nwavelengths interfere with themselves upon reflection and their\namplitudes quickly drop to zero" + }, + { + "Chapter": "9", + "sentence_range": "2447-2450", + "Text": "However only those wavelengths survive which have nodes\nat the ends and form the standing wave in the string It means\nthat in a string, standing waves are formed when the total distance\ntravelled by a wave down the string and back is one wavelength, two\nwavelengths, or any integral number of wavelengths Waves with other\nwavelengths interfere with themselves upon reflection and their\namplitudes quickly drop to zero For an electron moving in nth circular\norbit of radius rn, the total distance is the circumference of the orbit,\n2prn" + }, + { + "Chapter": "9", + "sentence_range": "2448-2451", + "Text": "It means\nthat in a string, standing waves are formed when the total distance\ntravelled by a wave down the string and back is one wavelength, two\nwavelengths, or any integral number of wavelengths Waves with other\nwavelengths interfere with themselves upon reflection and their\namplitudes quickly drop to zero For an electron moving in nth circular\norbit of radius rn, the total distance is the circumference of the orbit,\n2prn Thus\nFIGURE 12" + }, + { + "Chapter": "9", + "sentence_range": "2449-2452", + "Text": "Waves with other\nwavelengths interfere with themselves upon reflection and their\namplitudes quickly drop to zero For an electron moving in nth circular\norbit of radius rn, the total distance is the circumference of the orbit,\n2prn Thus\nFIGURE 12 8 A standing wave\nis shown on a circular orbit\nwhere four de Broglie\nwavelengths fit into the\ncircumference of the orbit" + }, + { + "Chapter": "9", + "sentence_range": "2450-2453", + "Text": "For an electron moving in nth circular\norbit of radius rn, the total distance is the circumference of the orbit,\n2prn Thus\nFIGURE 12 8 A standing wave\nis shown on a circular orbit\nwhere four de Broglie\nwavelengths fit into the\ncircumference of the orbit Rationalised 2023-24\nPhysics\n302\n2p rn = nl, n = 1, 2, 3" + }, + { + "Chapter": "9", + "sentence_range": "2451-2454", + "Text": "Thus\nFIGURE 12 8 A standing wave\nis shown on a circular orbit\nwhere four de Broglie\nwavelengths fit into the\ncircumference of the orbit Rationalised 2023-24\nPhysics\n302\n2p rn = nl, n = 1, 2, 3 (12" + }, + { + "Chapter": "9", + "sentence_range": "2452-2455", + "Text": "8 A standing wave\nis shown on a circular orbit\nwhere four de Broglie\nwavelengths fit into the\ncircumference of the orbit Rationalised 2023-24\nPhysics\n302\n2p rn = nl, n = 1, 2, 3 (12 12)\nFigure 12" + }, + { + "Chapter": "9", + "sentence_range": "2453-2456", + "Text": "Rationalised 2023-24\nPhysics\n302\n2p rn = nl, n = 1, 2, 3 (12 12)\nFigure 12 8 illustrates a standing particle wave on a circular orbit\nfor n = 4, i" + }, + { + "Chapter": "9", + "sentence_range": "2454-2457", + "Text": "(12 12)\nFigure 12 8 illustrates a standing particle wave on a circular orbit\nfor n = 4, i e" + }, + { + "Chapter": "9", + "sentence_range": "2455-2458", + "Text": "12)\nFigure 12 8 illustrates a standing particle wave on a circular orbit\nfor n = 4, i e , 2prn = 4l, where l is the de Broglie wavelength of the electron\nmoving in nth orbit" + }, + { + "Chapter": "9", + "sentence_range": "2456-2459", + "Text": "8 illustrates a standing particle wave on a circular orbit\nfor n = 4, i e , 2prn = 4l, where l is the de Broglie wavelength of the electron\nmoving in nth orbit From Chapter 11, we have l = h/p, where p is the\nmagnitude of the electron\u2019s momentum" + }, + { + "Chapter": "9", + "sentence_range": "2457-2460", + "Text": "e , 2prn = 4l, where l is the de Broglie wavelength of the electron\nmoving in nth orbit From Chapter 11, we have l = h/p, where p is the\nmagnitude of the electron\u2019s momentum If the speed of the electron is\nmuch less than the speed of light, the momentum is mvn" + }, + { + "Chapter": "9", + "sentence_range": "2458-2461", + "Text": ", 2prn = 4l, where l is the de Broglie wavelength of the electron\nmoving in nth orbit From Chapter 11, we have l = h/p, where p is the\nmagnitude of the electron\u2019s momentum If the speed of the electron is\nmuch less than the speed of light, the momentum is mvn Thus, l = h/\nmvn" + }, + { + "Chapter": "9", + "sentence_range": "2459-2462", + "Text": "From Chapter 11, we have l = h/p, where p is the\nmagnitude of the electron\u2019s momentum If the speed of the electron is\nmuch less than the speed of light, the momentum is mvn Thus, l = h/\nmvn From Eq" + }, + { + "Chapter": "9", + "sentence_range": "2460-2463", + "Text": "If the speed of the electron is\nmuch less than the speed of light, the momentum is mvn Thus, l = h/\nmvn From Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2461-2464", + "Text": "Thus, l = h/\nmvn From Eq (12 12), we have\n2p rn = n h/mvn or m vn rn = nh/2p\nThis is the quantum condition proposed by Bohr for the angular\nmomentum of the electron [Eq" + }, + { + "Chapter": "9", + "sentence_range": "2462-2465", + "Text": "From Eq (12 12), we have\n2p rn = n h/mvn or m vn rn = nh/2p\nThis is the quantum condition proposed by Bohr for the angular\nmomentum of the electron [Eq (12" + }, + { + "Chapter": "9", + "sentence_range": "2463-2466", + "Text": "(12 12), we have\n2p rn = n h/mvn or m vn rn = nh/2p\nThis is the quantum condition proposed by Bohr for the angular\nmomentum of the electron [Eq (12 15)]" + }, + { + "Chapter": "9", + "sentence_range": "2464-2467", + "Text": "12), we have\n2p rn = n h/mvn or m vn rn = nh/2p\nThis is the quantum condition proposed by Bohr for the angular\nmomentum of the electron [Eq (12 15)] In Section 12" + }, + { + "Chapter": "9", + "sentence_range": "2465-2468", + "Text": "(12 15)] In Section 12 5, we saw that\nthis equation is the basis of explaining the discrete orbits and energy\nlevels in hydrogen atom" + }, + { + "Chapter": "9", + "sentence_range": "2466-2469", + "Text": "15)] In Section 12 5, we saw that\nthis equation is the basis of explaining the discrete orbits and energy\nlevels in hydrogen atom Thus de Broglie hypothesis provided an\nexplanation for Bohr\u2019s second postulate for the quantisation of angular\nmomentum of the orbiting electron" + }, + { + "Chapter": "9", + "sentence_range": "2467-2470", + "Text": "In Section 12 5, we saw that\nthis equation is the basis of explaining the discrete orbits and energy\nlevels in hydrogen atom Thus de Broglie hypothesis provided an\nexplanation for Bohr\u2019s second postulate for the quantisation of angular\nmomentum of the orbiting electron The quantised electron orbits and\nenergy states are due to the wave nature of the electron and only resonant\nstanding waves can persist" + }, + { + "Chapter": "9", + "sentence_range": "2468-2471", + "Text": "5, we saw that\nthis equation is the basis of explaining the discrete orbits and energy\nlevels in hydrogen atom Thus de Broglie hypothesis provided an\nexplanation for Bohr\u2019s second postulate for the quantisation of angular\nmomentum of the orbiting electron The quantised electron orbits and\nenergy states are due to the wave nature of the electron and only resonant\nstanding waves can persist Bohr\u2019s model, involving classical trajectory picture (planet-like electron\norbiting the nucleus), correctly predicts the gross features of the\nhydrogenic atoms*, in particular, the frequencies of the radiation emitted\nor selectively absorbed" + }, + { + "Chapter": "9", + "sentence_range": "2469-2472", + "Text": "Thus de Broglie hypothesis provided an\nexplanation for Bohr\u2019s second postulate for the quantisation of angular\nmomentum of the orbiting electron The quantised electron orbits and\nenergy states are due to the wave nature of the electron and only resonant\nstanding waves can persist Bohr\u2019s model, involving classical trajectory picture (planet-like electron\norbiting the nucleus), correctly predicts the gross features of the\nhydrogenic atoms*, in particular, the frequencies of the radiation emitted\nor selectively absorbed This model however has many limitations" + }, + { + "Chapter": "9", + "sentence_range": "2470-2473", + "Text": "The quantised electron orbits and\nenergy states are due to the wave nature of the electron and only resonant\nstanding waves can persist Bohr\u2019s model, involving classical trajectory picture (planet-like electron\norbiting the nucleus), correctly predicts the gross features of the\nhydrogenic atoms*, in particular, the frequencies of the radiation emitted\nor selectively absorbed This model however has many limitations Some are:\n(i)\nThe Bohr model is applicable to hydrogenic atoms" + }, + { + "Chapter": "9", + "sentence_range": "2471-2474", + "Text": "Bohr\u2019s model, involving classical trajectory picture (planet-like electron\norbiting the nucleus), correctly predicts the gross features of the\nhydrogenic atoms*, in particular, the frequencies of the radiation emitted\nor selectively absorbed This model however has many limitations Some are:\n(i)\nThe Bohr model is applicable to hydrogenic atoms It cannot be\nextended even to mere two electron atoms such as helium" + }, + { + "Chapter": "9", + "sentence_range": "2472-2475", + "Text": "This model however has many limitations Some are:\n(i)\nThe Bohr model is applicable to hydrogenic atoms It cannot be\nextended even to mere two electron atoms such as helium The analysis\nof atoms with more than one electron was attempted on the lines of\nBohr\u2019s model for hydrogenic atoms but did not meet with any success" + }, + { + "Chapter": "9", + "sentence_range": "2473-2476", + "Text": "Some are:\n(i)\nThe Bohr model is applicable to hydrogenic atoms It cannot be\nextended even to mere two electron atoms such as helium The analysis\nof atoms with more than one electron was attempted on the lines of\nBohr\u2019s model for hydrogenic atoms but did not meet with any success Difficulty lies in the fact that each electron interacts not only with the\npositively charged nucleus but also with all other electrons" + }, + { + "Chapter": "9", + "sentence_range": "2474-2477", + "Text": "It cannot be\nextended even to mere two electron atoms such as helium The analysis\nof atoms with more than one electron was attempted on the lines of\nBohr\u2019s model for hydrogenic atoms but did not meet with any success Difficulty lies in the fact that each electron interacts not only with the\npositively charged nucleus but also with all other electrons The formulation of Bohr model involves electrical force between\npositively charged nucleus and electron" + }, + { + "Chapter": "9", + "sentence_range": "2475-2478", + "Text": "The analysis\nof atoms with more than one electron was attempted on the lines of\nBohr\u2019s model for hydrogenic atoms but did not meet with any success Difficulty lies in the fact that each electron interacts not only with the\npositively charged nucleus but also with all other electrons The formulation of Bohr model involves electrical force between\npositively charged nucleus and electron It does not include the\nelectrical forces between electrons which necessarily appear in\nmulti-electron atoms" + }, + { + "Chapter": "9", + "sentence_range": "2476-2479", + "Text": "Difficulty lies in the fact that each electron interacts not only with the\npositively charged nucleus but also with all other electrons The formulation of Bohr model involves electrical force between\npositively charged nucleus and electron It does not include the\nelectrical forces between electrons which necessarily appear in\nmulti-electron atoms (ii) While the Bohr\u2019s model correctly predicts the frequencies of the light\nemitted by hydrogenic atoms, the model is unable to explain the\nrelative intensities of the frequencies in the spectrum" + }, + { + "Chapter": "9", + "sentence_range": "2477-2480", + "Text": "The formulation of Bohr model involves electrical force between\npositively charged nucleus and electron It does not include the\nelectrical forces between electrons which necessarily appear in\nmulti-electron atoms (ii) While the Bohr\u2019s model correctly predicts the frequencies of the light\nemitted by hydrogenic atoms, the model is unable to explain the\nrelative intensities of the frequencies in the spectrum In emission\nspectrum of hydrogen, some of the visible frequencies have weak\nintensity, others strong" + }, + { + "Chapter": "9", + "sentence_range": "2478-2481", + "Text": "It does not include the\nelectrical forces between electrons which necessarily appear in\nmulti-electron atoms (ii) While the Bohr\u2019s model correctly predicts the frequencies of the light\nemitted by hydrogenic atoms, the model is unable to explain the\nrelative intensities of the frequencies in the spectrum In emission\nspectrum of hydrogen, some of the visible frequencies have weak\nintensity, others strong Why" + }, + { + "Chapter": "9", + "sentence_range": "2479-2482", + "Text": "(ii) While the Bohr\u2019s model correctly predicts the frequencies of the light\nemitted by hydrogenic atoms, the model is unable to explain the\nrelative intensities of the frequencies in the spectrum In emission\nspectrum of hydrogen, some of the visible frequencies have weak\nintensity, others strong Why Experimental observations depict that\nsome transitions are more favoured than others" + }, + { + "Chapter": "9", + "sentence_range": "2480-2483", + "Text": "In emission\nspectrum of hydrogen, some of the visible frequencies have weak\nintensity, others strong Why Experimental observations depict that\nsome transitions are more favoured than others Bohr\u2019s model is\nunable to account for the intensity variations" + }, + { + "Chapter": "9", + "sentence_range": "2481-2484", + "Text": "Why Experimental observations depict that\nsome transitions are more favoured than others Bohr\u2019s model is\nunable to account for the intensity variations Bohr\u2019s model presents an elegant picture of an atom and cannot be\ngeneralised to complex atoms" + }, + { + "Chapter": "9", + "sentence_range": "2482-2485", + "Text": "Experimental observations depict that\nsome transitions are more favoured than others Bohr\u2019s model is\nunable to account for the intensity variations Bohr\u2019s model presents an elegant picture of an atom and cannot be\ngeneralised to complex atoms For complex atoms we have to use a new\nand radical theory based on Quantum Mechanics, which provides a more\ncomplete picture of the atomic structure" + }, + { + "Chapter": "9", + "sentence_range": "2483-2486", + "Text": "Bohr\u2019s model is\nunable to account for the intensity variations Bohr\u2019s model presents an elegant picture of an atom and cannot be\ngeneralised to complex atoms For complex atoms we have to use a new\nand radical theory based on Quantum Mechanics, which provides a more\ncomplete picture of the atomic structure *\nHydrogenic atoms are the atoms consisting of a nucleus with positive charge\n+Ze and a single electron, where Z is the proton number" + }, + { + "Chapter": "9", + "sentence_range": "2484-2487", + "Text": "Bohr\u2019s model presents an elegant picture of an atom and cannot be\ngeneralised to complex atoms For complex atoms we have to use a new\nand radical theory based on Quantum Mechanics, which provides a more\ncomplete picture of the atomic structure *\nHydrogenic atoms are the atoms consisting of a nucleus with positive charge\n+Ze and a single electron, where Z is the proton number Examples are hydrogen\natom, singly ionised helium, doubly ionised lithium, and so forth" + }, + { + "Chapter": "9", + "sentence_range": "2485-2488", + "Text": "For complex atoms we have to use a new\nand radical theory based on Quantum Mechanics, which provides a more\ncomplete picture of the atomic structure *\nHydrogenic atoms are the atoms consisting of a nucleus with positive charge\n+Ze and a single electron, where Z is the proton number Examples are hydrogen\natom, singly ionised helium, doubly ionised lithium, and so forth In these\natoms more complex electron-electron interactions are nonexistent" + }, + { + "Chapter": "9", + "sentence_range": "2486-2489", + "Text": "*\nHydrogenic atoms are the atoms consisting of a nucleus with positive charge\n+Ze and a single electron, where Z is the proton number Examples are hydrogen\natom, singly ionised helium, doubly ionised lithium, and so forth In these\natoms more complex electron-electron interactions are nonexistent Rationalised 2023-24\n303\nAtoms\nSUMMARY\n1" + }, + { + "Chapter": "9", + "sentence_range": "2487-2490", + "Text": "Examples are hydrogen\natom, singly ionised helium, doubly ionised lithium, and so forth In these\natoms more complex electron-electron interactions are nonexistent Rationalised 2023-24\n303\nAtoms\nSUMMARY\n1 Atom, as a whole, is electrically neutral and therefore contains equal\namount of positive and negative charges" + }, + { + "Chapter": "9", + "sentence_range": "2488-2491", + "Text": "In these\natoms more complex electron-electron interactions are nonexistent Rationalised 2023-24\n303\nAtoms\nSUMMARY\n1 Atom, as a whole, is electrically neutral and therefore contains equal\namount of positive and negative charges 2" + }, + { + "Chapter": "9", + "sentence_range": "2489-2492", + "Text": "Rationalised 2023-24\n303\nAtoms\nSUMMARY\n1 Atom, as a whole, is electrically neutral and therefore contains equal\namount of positive and negative charges 2 In Thomson\u2019s model, an atom is a spherical cloud of positive charges\nwith electrons embedded in it" + }, + { + "Chapter": "9", + "sentence_range": "2490-2493", + "Text": "Atom, as a whole, is electrically neutral and therefore contains equal\namount of positive and negative charges 2 In Thomson\u2019s model, an atom is a spherical cloud of positive charges\nwith electrons embedded in it 3" + }, + { + "Chapter": "9", + "sentence_range": "2491-2494", + "Text": "2 In Thomson\u2019s model, an atom is a spherical cloud of positive charges\nwith electrons embedded in it 3 In Rutherford\u2019s model, most of the mass of the atom and all its positive\ncharge are concentrated in a tiny nucleus (typically one by ten thousand\nthe size of an atom), and the electrons revolve around it" + }, + { + "Chapter": "9", + "sentence_range": "2492-2495", + "Text": "In Thomson\u2019s model, an atom is a spherical cloud of positive charges\nwith electrons embedded in it 3 In Rutherford\u2019s model, most of the mass of the atom and all its positive\ncharge are concentrated in a tiny nucleus (typically one by ten thousand\nthe size of an atom), and the electrons revolve around it 4" + }, + { + "Chapter": "9", + "sentence_range": "2493-2496", + "Text": "3 In Rutherford\u2019s model, most of the mass of the atom and all its positive\ncharge are concentrated in a tiny nucleus (typically one by ten thousand\nthe size of an atom), and the electrons revolve around it 4 Rutherford nuclear model has two main difficulties in explaining the\nstructure of atom: (a) It predicts that atoms are unstable because the\naccelerated electrons revolving around the nucleus must spiral into\nthe nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2494-2497", + "Text": "In Rutherford\u2019s model, most of the mass of the atom and all its positive\ncharge are concentrated in a tiny nucleus (typically one by ten thousand\nthe size of an atom), and the electrons revolve around it 4 Rutherford nuclear model has two main difficulties in explaining the\nstructure of atom: (a) It predicts that atoms are unstable because the\naccelerated electrons revolving around the nucleus must spiral into\nthe nucleus This contradicts the stability of matter" + }, + { + "Chapter": "9", + "sentence_range": "2495-2498", + "Text": "4 Rutherford nuclear model has two main difficulties in explaining the\nstructure of atom: (a) It predicts that atoms are unstable because the\naccelerated electrons revolving around the nucleus must spiral into\nthe nucleus This contradicts the stability of matter (b) It cannot\nexplain the characteristic line spectra of atoms of different elements" + }, + { + "Chapter": "9", + "sentence_range": "2496-2499", + "Text": "Rutherford nuclear model has two main difficulties in explaining the\nstructure of atom: (a) It predicts that atoms are unstable because the\naccelerated electrons revolving around the nucleus must spiral into\nthe nucleus This contradicts the stability of matter (b) It cannot\nexplain the characteristic line spectra of atoms of different elements 5" + }, + { + "Chapter": "9", + "sentence_range": "2497-2500", + "Text": "This contradicts the stability of matter (b) It cannot\nexplain the characteristic line spectra of atoms of different elements 5 Atoms of most of the elements are stable and emit characteristic\nspectrum" + }, + { + "Chapter": "9", + "sentence_range": "2498-2501", + "Text": "(b) It cannot\nexplain the characteristic line spectra of atoms of different elements 5 Atoms of most of the elements are stable and emit characteristic\nspectrum The spectrum consists of a set of isolated parallel lines\ntermed as line spectrum" + }, + { + "Chapter": "9", + "sentence_range": "2499-2502", + "Text": "5 Atoms of most of the elements are stable and emit characteristic\nspectrum The spectrum consists of a set of isolated parallel lines\ntermed as line spectrum It provides useful information about the\natomic structure" + }, + { + "Chapter": "9", + "sentence_range": "2500-2503", + "Text": "Atoms of most of the elements are stable and emit characteristic\nspectrum The spectrum consists of a set of isolated parallel lines\ntermed as line spectrum It provides useful information about the\natomic structure 6" + }, + { + "Chapter": "9", + "sentence_range": "2501-2504", + "Text": "The spectrum consists of a set of isolated parallel lines\ntermed as line spectrum It provides useful information about the\natomic structure 6 To explain the line spectra emitted by atoms, as well as the stability\nof atoms, Niel\u2019s Bohr proposed a model for hydrogenic (single elctron)\natoms" + }, + { + "Chapter": "9", + "sentence_range": "2502-2505", + "Text": "It provides useful information about the\natomic structure 6 To explain the line spectra emitted by atoms, as well as the stability\nof atoms, Niel\u2019s Bohr proposed a model for hydrogenic (single elctron)\natoms He introduced three postulates and laid the foundations of\nquantum mechanics:\n(a) In a hydrogen atom, an electron revolves in certain stable orbits\n(called stationary orbits) without the emission of radiant energy" + }, + { + "Chapter": "9", + "sentence_range": "2503-2506", + "Text": "6 To explain the line spectra emitted by atoms, as well as the stability\nof atoms, Niel\u2019s Bohr proposed a model for hydrogenic (single elctron)\natoms He introduced three postulates and laid the foundations of\nquantum mechanics:\n(a) In a hydrogen atom, an electron revolves in certain stable orbits\n(called stationary orbits) without the emission of radiant energy (b) The stationary orbits are those for which the angular momentum\nis some integral multiple of h/2p" + }, + { + "Chapter": "9", + "sentence_range": "2504-2507", + "Text": "To explain the line spectra emitted by atoms, as well as the stability\nof atoms, Niel\u2019s Bohr proposed a model for hydrogenic (single elctron)\natoms He introduced three postulates and laid the foundations of\nquantum mechanics:\n(a) In a hydrogen atom, an electron revolves in certain stable orbits\n(called stationary orbits) without the emission of radiant energy (b) The stationary orbits are those for which the angular momentum\nis some integral multiple of h/2p (Bohr\u2019s quantisation condition" + }, + { + "Chapter": "9", + "sentence_range": "2505-2508", + "Text": "He introduced three postulates and laid the foundations of\nquantum mechanics:\n(a) In a hydrogen atom, an electron revolves in certain stable orbits\n(called stationary orbits) without the emission of radiant energy (b) The stationary orbits are those for which the angular momentum\nis some integral multiple of h/2p (Bohr\u2019s quantisation condition )\nThat is L = nh/2p, where n is an integer called the principal\nquantum number" + }, + { + "Chapter": "9", + "sentence_range": "2506-2509", + "Text": "(b) The stationary orbits are those for which the angular momentum\nis some integral multiple of h/2p (Bohr\u2019s quantisation condition )\nThat is L = nh/2p, where n is an integer called the principal\nquantum number (c)\nThe third postulate states that an electron might make a transition\nfrom one of its specified non-radiating orbits to another of lower\nenergy" + }, + { + "Chapter": "9", + "sentence_range": "2507-2510", + "Text": "(Bohr\u2019s quantisation condition )\nThat is L = nh/2p, where n is an integer called the principal\nquantum number (c)\nThe third postulate states that an electron might make a transition\nfrom one of its specified non-radiating orbits to another of lower\nenergy When it does so, a photon is emitted having energy equal\nto the energy difference between the initial and final states" + }, + { + "Chapter": "9", + "sentence_range": "2508-2511", + "Text": ")\nThat is L = nh/2p, where n is an integer called the principal\nquantum number (c)\nThe third postulate states that an electron might make a transition\nfrom one of its specified non-radiating orbits to another of lower\nenergy When it does so, a photon is emitted having energy equal\nto the energy difference between the initial and final states The\nfrequency (n) of the emitted photon is then given by\nhn = Ei \u2013 Ef\nAn atom absorbs radiation of the same frequency the atom emits,\nin which case the electron is transferred to an orbit with a higher\nvalue of n" + }, + { + "Chapter": "9", + "sentence_range": "2509-2512", + "Text": "(c)\nThe third postulate states that an electron might make a transition\nfrom one of its specified non-radiating orbits to another of lower\nenergy When it does so, a photon is emitted having energy equal\nto the energy difference between the initial and final states The\nfrequency (n) of the emitted photon is then given by\nhn = Ei \u2013 Ef\nAn atom absorbs radiation of the same frequency the atom emits,\nin which case the electron is transferred to an orbit with a higher\nvalue of n Ei + hn = Ef\n7" + }, + { + "Chapter": "9", + "sentence_range": "2510-2513", + "Text": "When it does so, a photon is emitted having energy equal\nto the energy difference between the initial and final states The\nfrequency (n) of the emitted photon is then given by\nhn = Ei \u2013 Ef\nAn atom absorbs radiation of the same frequency the atom emits,\nin which case the electron is transferred to an orbit with a higher\nvalue of n Ei + hn = Ef\n7 As a result of the quantisation condition of angular momentum, the\nelectron orbits the nucleus at only specific radii" + }, + { + "Chapter": "9", + "sentence_range": "2511-2514", + "Text": "The\nfrequency (n) of the emitted photon is then given by\nhn = Ei \u2013 Ef\nAn atom absorbs radiation of the same frequency the atom emits,\nin which case the electron is transferred to an orbit with a higher\nvalue of n Ei + hn = Ef\n7 As a result of the quantisation condition of angular momentum, the\nelectron orbits the nucleus at only specific radii For a hydrogen atom\nit is given by\nr\nn\nm\nh\ne\nn = \uf8eb\n\uf8ed\uf8ec\n\uf8f8\uf8f7\uf8f6\n\uf8ed\uf8ec\uf8eb\n\uf8f6\n\uf8f8\uf8f7\n2\n2\n20\n2\n4\n\u03c0\n\u03c0\u03b5\nThe total energy is also quantised:\n4\n2\n2\n2\n0\n8\nn\nme\nE\nn\n\u03b5h\n= \u2212\n = \u201313" + }, + { + "Chapter": "9", + "sentence_range": "2512-2515", + "Text": "Ei + hn = Ef\n7 As a result of the quantisation condition of angular momentum, the\nelectron orbits the nucleus at only specific radii For a hydrogen atom\nit is given by\nr\nn\nm\nh\ne\nn = \uf8eb\n\uf8ed\uf8ec\n\uf8f8\uf8f7\uf8f6\n\uf8ed\uf8ec\uf8eb\n\uf8f6\n\uf8f8\uf8f7\n2\n2\n20\n2\n4\n\u03c0\n\u03c0\u03b5\nThe total energy is also quantised:\n4\n2\n2\n2\n0\n8\nn\nme\nE\nn\n\u03b5h\n= \u2212\n = \u201313 6 eV/n2\nThe n = 1 state is called ground state" + }, + { + "Chapter": "9", + "sentence_range": "2513-2516", + "Text": "As a result of the quantisation condition of angular momentum, the\nelectron orbits the nucleus at only specific radii For a hydrogen atom\nit is given by\nr\nn\nm\nh\ne\nn = \uf8eb\n\uf8ed\uf8ec\n\uf8f8\uf8f7\uf8f6\n\uf8ed\uf8ec\uf8eb\n\uf8f6\n\uf8f8\uf8f7\n2\n2\n20\n2\n4\n\u03c0\n\u03c0\u03b5\nThe total energy is also quantised:\n4\n2\n2\n2\n0\n8\nn\nme\nE\nn\n\u03b5h\n= \u2212\n = \u201313 6 eV/n2\nThe n = 1 state is called ground state In hydrogen atom the ground\nstate energy is \u201313" + }, + { + "Chapter": "9", + "sentence_range": "2514-2517", + "Text": "For a hydrogen atom\nit is given by\nr\nn\nm\nh\ne\nn = \uf8eb\n\uf8ed\uf8ec\n\uf8f8\uf8f7\uf8f6\n\uf8ed\uf8ec\uf8eb\n\uf8f6\n\uf8f8\uf8f7\n2\n2\n20\n2\n4\n\u03c0\n\u03c0\u03b5\nThe total energy is also quantised:\n4\n2\n2\n2\n0\n8\nn\nme\nE\nn\n\u03b5h\n= \u2212\n = \u201313 6 eV/n2\nThe n = 1 state is called ground state In hydrogen atom the ground\nstate energy is \u201313 6 eV" + }, + { + "Chapter": "9", + "sentence_range": "2515-2518", + "Text": "6 eV/n2\nThe n = 1 state is called ground state In hydrogen atom the ground\nstate energy is \u201313 6 eV Higher values of n correspond to excited\nstates (n > 1)" + }, + { + "Chapter": "9", + "sentence_range": "2516-2519", + "Text": "In hydrogen atom the ground\nstate energy is \u201313 6 eV Higher values of n correspond to excited\nstates (n > 1) Atoms are excited to these higher states by collisions\nwith other atoms or electrons or by absorption of a photon of right\nfrequency" + }, + { + "Chapter": "9", + "sentence_range": "2517-2520", + "Text": "6 eV Higher values of n correspond to excited\nstates (n > 1) Atoms are excited to these higher states by collisions\nwith other atoms or electrons or by absorption of a photon of right\nfrequency Rationalised 2023-24\nPhysics\n304\n8" + }, + { + "Chapter": "9", + "sentence_range": "2518-2521", + "Text": "Higher values of n correspond to excited\nstates (n > 1) Atoms are excited to these higher states by collisions\nwith other atoms or electrons or by absorption of a photon of right\nfrequency Rationalised 2023-24\nPhysics\n304\n8 de Broglie\u2019s hypothesis that electrons have a wavelength l = h/mv gave\nan explanation for Bohr\u2019s quantised orbits by bringing in the wave-\nparticle duality" + }, + { + "Chapter": "9", + "sentence_range": "2519-2522", + "Text": "Atoms are excited to these higher states by collisions\nwith other atoms or electrons or by absorption of a photon of right\nfrequency Rationalised 2023-24\nPhysics\n304\n8 de Broglie\u2019s hypothesis that electrons have a wavelength l = h/mv gave\nan explanation for Bohr\u2019s quantised orbits by bringing in the wave-\nparticle duality The orbits correspond to circular standing waves in\nwhich the circumference of the orbit equals a whole number of\nwavelengths" + }, + { + "Chapter": "9", + "sentence_range": "2520-2523", + "Text": "Rationalised 2023-24\nPhysics\n304\n8 de Broglie\u2019s hypothesis that electrons have a wavelength l = h/mv gave\nan explanation for Bohr\u2019s quantised orbits by bringing in the wave-\nparticle duality The orbits correspond to circular standing waves in\nwhich the circumference of the orbit equals a whole number of\nwavelengths 9" + }, + { + "Chapter": "9", + "sentence_range": "2521-2524", + "Text": "de Broglie\u2019s hypothesis that electrons have a wavelength l = h/mv gave\nan explanation for Bohr\u2019s quantised orbits by bringing in the wave-\nparticle duality The orbits correspond to circular standing waves in\nwhich the circumference of the orbit equals a whole number of\nwavelengths 9 Bohr\u2019s model is applicable only to hydrogenic (single electron) atoms" + }, + { + "Chapter": "9", + "sentence_range": "2522-2525", + "Text": "The orbits correspond to circular standing waves in\nwhich the circumference of the orbit equals a whole number of\nwavelengths 9 Bohr\u2019s model is applicable only to hydrogenic (single electron) atoms It cannot be extended to even two electron atoms such as helium" + }, + { + "Chapter": "9", + "sentence_range": "2523-2526", + "Text": "9 Bohr\u2019s model is applicable only to hydrogenic (single electron) atoms It cannot be extended to even two electron atoms such as helium This model is also unable to explain for the relative intensities of the\nfrequencies emitted even by hydrogenic atoms" + }, + { + "Chapter": "9", + "sentence_range": "2524-2527", + "Text": "Bohr\u2019s model is applicable only to hydrogenic (single electron) atoms It cannot be extended to even two electron atoms such as helium This model is also unable to explain for the relative intensities of the\nfrequencies emitted even by hydrogenic atoms POINTS TO PONDER\n1" + }, + { + "Chapter": "9", + "sentence_range": "2525-2528", + "Text": "It cannot be extended to even two electron atoms such as helium This model is also unable to explain for the relative intensities of the\nfrequencies emitted even by hydrogenic atoms POINTS TO PONDER\n1 Both the Thomson\u2019s as well as the Rutherford\u2019s models constitute an\nunstable system" + }, + { + "Chapter": "9", + "sentence_range": "2526-2529", + "Text": "This model is also unable to explain for the relative intensities of the\nfrequencies emitted even by hydrogenic atoms POINTS TO PONDER\n1 Both the Thomson\u2019s as well as the Rutherford\u2019s models constitute an\nunstable system Thomson\u2019s model is unstable electrostatically, while\nRutherford\u2019s model is unstable because of electromagnetic radiation\nof orbiting electrons" + }, + { + "Chapter": "9", + "sentence_range": "2527-2530", + "Text": "POINTS TO PONDER\n1 Both the Thomson\u2019s as well as the Rutherford\u2019s models constitute an\nunstable system Thomson\u2019s model is unstable electrostatically, while\nRutherford\u2019s model is unstable because of electromagnetic radiation\nof orbiting electrons 2" + }, + { + "Chapter": "9", + "sentence_range": "2528-2531", + "Text": "Both the Thomson\u2019s as well as the Rutherford\u2019s models constitute an\nunstable system Thomson\u2019s model is unstable electrostatically, while\nRutherford\u2019s model is unstable because of electromagnetic radiation\nof orbiting electrons 2 What made Bohr quantise angular momentum (second postulate) and\nnot some other quantity" + }, + { + "Chapter": "9", + "sentence_range": "2529-2532", + "Text": "Thomson\u2019s model is unstable electrostatically, while\nRutherford\u2019s model is unstable because of electromagnetic radiation\nof orbiting electrons 2 What made Bohr quantise angular momentum (second postulate) and\nnot some other quantity Note, h has dimensions of angular\nmomentum, and for circular orbits, angular momentum is a very\nrelevant quantity" + }, + { + "Chapter": "9", + "sentence_range": "2530-2533", + "Text": "2 What made Bohr quantise angular momentum (second postulate) and\nnot some other quantity Note, h has dimensions of angular\nmomentum, and for circular orbits, angular momentum is a very\nrelevant quantity The second postulate is then so natural" + }, + { + "Chapter": "9", + "sentence_range": "2531-2534", + "Text": "What made Bohr quantise angular momentum (second postulate) and\nnot some other quantity Note, h has dimensions of angular\nmomentum, and for circular orbits, angular momentum is a very\nrelevant quantity The second postulate is then so natural 3" + }, + { + "Chapter": "9", + "sentence_range": "2532-2535", + "Text": "Note, h has dimensions of angular\nmomentum, and for circular orbits, angular momentum is a very\nrelevant quantity The second postulate is then so natural 3 The orbital picture in Bohr\u2019s model of the hydrogen atom was\ninconsistent with the uncertainty principle" + }, + { + "Chapter": "9", + "sentence_range": "2533-2536", + "Text": "The second postulate is then so natural 3 The orbital picture in Bohr\u2019s model of the hydrogen atom was\ninconsistent with the uncertainty principle It was replaced by modern\nquantum mechanics in which Bohr\u2019s orbits are regions where the\nelectron may be found with large probability" + }, + { + "Chapter": "9", + "sentence_range": "2534-2537", + "Text": "3 The orbital picture in Bohr\u2019s model of the hydrogen atom was\ninconsistent with the uncertainty principle It was replaced by modern\nquantum mechanics in which Bohr\u2019s orbits are regions where the\nelectron may be found with large probability 4" + }, + { + "Chapter": "9", + "sentence_range": "2535-2538", + "Text": "The orbital picture in Bohr\u2019s model of the hydrogen atom was\ninconsistent with the uncertainty principle It was replaced by modern\nquantum mechanics in which Bohr\u2019s orbits are regions where the\nelectron may be found with large probability 4 Unlike the situation in the solar system, where planet-planet\ngravitational forces are very small as compared to the gravitational\nforce of the sun on each planet (because the mass of the sun is so\nmuch greater than the mass of any of the planets), the electron-electron\nelectric force interaction is comparable in magnitude to the electron-\nnucleus electrical force, because the charges and distances are of the\nsame order of magnitude" + }, + { + "Chapter": "9", + "sentence_range": "2536-2539", + "Text": "It was replaced by modern\nquantum mechanics in which Bohr\u2019s orbits are regions where the\nelectron may be found with large probability 4 Unlike the situation in the solar system, where planet-planet\ngravitational forces are very small as compared to the gravitational\nforce of the sun on each planet (because the mass of the sun is so\nmuch greater than the mass of any of the planets), the electron-electron\nelectric force interaction is comparable in magnitude to the electron-\nnucleus electrical force, because the charges and distances are of the\nsame order of magnitude This is the reason why the Bohr\u2019s model\nwith its planet-like electron is not applicable to many electron atoms" + }, + { + "Chapter": "9", + "sentence_range": "2537-2540", + "Text": "4 Unlike the situation in the solar system, where planet-planet\ngravitational forces are very small as compared to the gravitational\nforce of the sun on each planet (because the mass of the sun is so\nmuch greater than the mass of any of the planets), the electron-electron\nelectric force interaction is comparable in magnitude to the electron-\nnucleus electrical force, because the charges and distances are of the\nsame order of magnitude This is the reason why the Bohr\u2019s model\nwith its planet-like electron is not applicable to many electron atoms 5" + }, + { + "Chapter": "9", + "sentence_range": "2538-2541", + "Text": "Unlike the situation in the solar system, where planet-planet\ngravitational forces are very small as compared to the gravitational\nforce of the sun on each planet (because the mass of the sun is so\nmuch greater than the mass of any of the planets), the electron-electron\nelectric force interaction is comparable in magnitude to the electron-\nnucleus electrical force, because the charges and distances are of the\nsame order of magnitude This is the reason why the Bohr\u2019s model\nwith its planet-like electron is not applicable to many electron atoms 5 Bohr laid the foundation of the quantum theory by postulating specific\norbits in which electrons do not radiate" + }, + { + "Chapter": "9", + "sentence_range": "2539-2542", + "Text": "This is the reason why the Bohr\u2019s model\nwith its planet-like electron is not applicable to many electron atoms 5 Bohr laid the foundation of the quantum theory by postulating specific\norbits in which electrons do not radiate Bohr\u2019s model include only\none quantum number n" + }, + { + "Chapter": "9", + "sentence_range": "2540-2543", + "Text": "5 Bohr laid the foundation of the quantum theory by postulating specific\norbits in which electrons do not radiate Bohr\u2019s model include only\none quantum number n The new theory called quantum mechanics\nsupportes Bohr\u2019s postulate" + }, + { + "Chapter": "9", + "sentence_range": "2541-2544", + "Text": "Bohr laid the foundation of the quantum theory by postulating specific\norbits in which electrons do not radiate Bohr\u2019s model include only\none quantum number n The new theory called quantum mechanics\nsupportes Bohr\u2019s postulate However in quantum mechanics (more\ngenerally accepted), a given energy level may not correspond to just\none quantum state" + }, + { + "Chapter": "9", + "sentence_range": "2542-2545", + "Text": "Bohr\u2019s model include only\none quantum number n The new theory called quantum mechanics\nsupportes Bohr\u2019s postulate However in quantum mechanics (more\ngenerally accepted), a given energy level may not correspond to just\none quantum state For example, a state is characterised by four\nquantum numbers (n, l, m, and s), but for a pure Coulomb potential\n(as in hydrogen atom) the energy depends only on n" + }, + { + "Chapter": "9", + "sentence_range": "2543-2546", + "Text": "The new theory called quantum mechanics\nsupportes Bohr\u2019s postulate However in quantum mechanics (more\ngenerally accepted), a given energy level may not correspond to just\none quantum state For example, a state is characterised by four\nquantum numbers (n, l, m, and s), but for a pure Coulomb potential\n(as in hydrogen atom) the energy depends only on n 6" + }, + { + "Chapter": "9", + "sentence_range": "2544-2547", + "Text": "However in quantum mechanics (more\ngenerally accepted), a given energy level may not correspond to just\none quantum state For example, a state is characterised by four\nquantum numbers (n, l, m, and s), but for a pure Coulomb potential\n(as in hydrogen atom) the energy depends only on n 6 In Bohr model, contrary to ordinary classical expectation, the frequency\nof revolution of an electron in its orbit is not connected to the frequency\nof spectral line" + }, + { + "Chapter": "9", + "sentence_range": "2545-2548", + "Text": "For example, a state is characterised by four\nquantum numbers (n, l, m, and s), but for a pure Coulomb potential\n(as in hydrogen atom) the energy depends only on n 6 In Bohr model, contrary to ordinary classical expectation, the frequency\nof revolution of an electron in its orbit is not connected to the frequency\nof spectral line The later is the difference between two orbital energies\ndivided by h" + }, + { + "Chapter": "9", + "sentence_range": "2546-2549", + "Text": "6 In Bohr model, contrary to ordinary classical expectation, the frequency\nof revolution of an electron in its orbit is not connected to the frequency\nof spectral line The later is the difference between two orbital energies\ndivided by h For transitions between large quantum numbers (n to n\n\u2013 1, n very large), however, the two coincide as expected" + }, + { + "Chapter": "9", + "sentence_range": "2547-2550", + "Text": "In Bohr model, contrary to ordinary classical expectation, the frequency\nof revolution of an electron in its orbit is not connected to the frequency\nof spectral line The later is the difference between two orbital energies\ndivided by h For transitions between large quantum numbers (n to n\n\u2013 1, n very large), however, the two coincide as expected 7" + }, + { + "Chapter": "9", + "sentence_range": "2548-2551", + "Text": "The later is the difference between two orbital energies\ndivided by h For transitions between large quantum numbers (n to n\n\u2013 1, n very large), however, the two coincide as expected 7 Bohr\u2019s semiclassical model based on some aspects of classical physics\nand some aspects of modern physics also does not provide a true picture\nof the simplest hydrogenic atoms" + }, + { + "Chapter": "9", + "sentence_range": "2549-2552", + "Text": "For transitions between large quantum numbers (n to n\n\u2013 1, n very large), however, the two coincide as expected 7 Bohr\u2019s semiclassical model based on some aspects of classical physics\nand some aspects of modern physics also does not provide a true picture\nof the simplest hydrogenic atoms The true picture is quantum\nmechanical affair which differs from Bohr model in a number of\nfundamental ways" + }, + { + "Chapter": "9", + "sentence_range": "2550-2553", + "Text": "7 Bohr\u2019s semiclassical model based on some aspects of classical physics\nand some aspects of modern physics also does not provide a true picture\nof the simplest hydrogenic atoms The true picture is quantum\nmechanical affair which differs from Bohr model in a number of\nfundamental ways But then if the Bohr model is not strictly correct,\nwhy do we bother about it" + }, + { + "Chapter": "9", + "sentence_range": "2551-2554", + "Text": "Bohr\u2019s semiclassical model based on some aspects of classical physics\nand some aspects of modern physics also does not provide a true picture\nof the simplest hydrogenic atoms The true picture is quantum\nmechanical affair which differs from Bohr model in a number of\nfundamental ways But then if the Bohr model is not strictly correct,\nwhy do we bother about it The reasons which make Bohr\u2019s model\nstill useful are:\nRationalised 2023-24\n305\nAtoms\n(i)\nThe model is based on just three postulates but accounts for almost\nall the general features of the hydrogen spectrum" + }, + { + "Chapter": "9", + "sentence_range": "2552-2555", + "Text": "The true picture is quantum\nmechanical affair which differs from Bohr model in a number of\nfundamental ways But then if the Bohr model is not strictly correct,\nwhy do we bother about it The reasons which make Bohr\u2019s model\nstill useful are:\nRationalised 2023-24\n305\nAtoms\n(i)\nThe model is based on just three postulates but accounts for almost\nall the general features of the hydrogen spectrum (ii) The model incorporates many of the concepts we have learnt in\nclassical physics" + }, + { + "Chapter": "9", + "sentence_range": "2553-2556", + "Text": "But then if the Bohr model is not strictly correct,\nwhy do we bother about it The reasons which make Bohr\u2019s model\nstill useful are:\nRationalised 2023-24\n305\nAtoms\n(i)\nThe model is based on just three postulates but accounts for almost\nall the general features of the hydrogen spectrum (ii) The model incorporates many of the concepts we have learnt in\nclassical physics (iii) The model demonstrates how a theoretical physicist occasionally\nmust quite literally ignore certain problems of approach in hopes\nof being able to make some predictions" + }, + { + "Chapter": "9", + "sentence_range": "2554-2557", + "Text": "The reasons which make Bohr\u2019s model\nstill useful are:\nRationalised 2023-24\n305\nAtoms\n(i)\nThe model is based on just three postulates but accounts for almost\nall the general features of the hydrogen spectrum (ii) The model incorporates many of the concepts we have learnt in\nclassical physics (iii) The model demonstrates how a theoretical physicist occasionally\nmust quite literally ignore certain problems of approach in hopes\nof being able to make some predictions If the predictions of the\ntheory or model agree with experiment, a theoretician then must\nsomehow hope to explain away or rationalise the problems that\nwere ignored along the way" + }, + { + "Chapter": "9", + "sentence_range": "2555-2558", + "Text": "(ii) The model incorporates many of the concepts we have learnt in\nclassical physics (iii) The model demonstrates how a theoretical physicist occasionally\nmust quite literally ignore certain problems of approach in hopes\nof being able to make some predictions If the predictions of the\ntheory or model agree with experiment, a theoretician then must\nsomehow hope to explain away or rationalise the problems that\nwere ignored along the way EXERCISES\n12" + }, + { + "Chapter": "9", + "sentence_range": "2556-2559", + "Text": "(iii) The model demonstrates how a theoretical physicist occasionally\nmust quite literally ignore certain problems of approach in hopes\nof being able to make some predictions If the predictions of the\ntheory or model agree with experiment, a theoretician then must\nsomehow hope to explain away or rationalise the problems that\nwere ignored along the way EXERCISES\n12 1\nChoose the correct alternative from the clues given at the end of\nthe each statement:\n(a) The size of the atom in Thomson\u2019s model is" + }, + { + "Chapter": "9", + "sentence_range": "2557-2560", + "Text": "If the predictions of the\ntheory or model agree with experiment, a theoretician then must\nsomehow hope to explain away or rationalise the problems that\nwere ignored along the way EXERCISES\n12 1\nChoose the correct alternative from the clues given at the end of\nthe each statement:\n(a) The size of the atom in Thomson\u2019s model is the atomic\nsize in Rutherford\u2019s model" + }, + { + "Chapter": "9", + "sentence_range": "2558-2561", + "Text": "EXERCISES\n12 1\nChoose the correct alternative from the clues given at the end of\nthe each statement:\n(a) The size of the atom in Thomson\u2019s model is the atomic\nsize in Rutherford\u2019s model (much greater than/no different\nfrom/much less than" + }, + { + "Chapter": "9", + "sentence_range": "2559-2562", + "Text": "1\nChoose the correct alternative from the clues given at the end of\nthe each statement:\n(a) The size of the atom in Thomson\u2019s model is the atomic\nsize in Rutherford\u2019s model (much greater than/no different\nfrom/much less than )\n(b) In the ground state of" + }, + { + "Chapter": "9", + "sentence_range": "2560-2563", + "Text": "the atomic\nsize in Rutherford\u2019s model (much greater than/no different\nfrom/much less than )\n(b) In the ground state of electrons are in stable equilibrium,\nwhile in" + }, + { + "Chapter": "9", + "sentence_range": "2561-2564", + "Text": "(much greater than/no different\nfrom/much less than )\n(b) In the ground state of electrons are in stable equilibrium,\nwhile in electrons always experience a net force" + }, + { + "Chapter": "9", + "sentence_range": "2562-2565", + "Text": ")\n(b) In the ground state of electrons are in stable equilibrium,\nwhile in electrons always experience a net force (Thomson\u2019s model/ Rutherford\u2019s model" + }, + { + "Chapter": "9", + "sentence_range": "2563-2566", + "Text": "electrons are in stable equilibrium,\nwhile in electrons always experience a net force (Thomson\u2019s model/ Rutherford\u2019s model )\n(c) A classical atom based on" + }, + { + "Chapter": "9", + "sentence_range": "2564-2567", + "Text": "electrons always experience a net force (Thomson\u2019s model/ Rutherford\u2019s model )\n(c) A classical atom based on is doomed to collapse" + }, + { + "Chapter": "9", + "sentence_range": "2565-2568", + "Text": "(Thomson\u2019s model/ Rutherford\u2019s model )\n(c) A classical atom based on is doomed to collapse (Thomson\u2019s model/ Rutherford\u2019s model" + }, + { + "Chapter": "9", + "sentence_range": "2566-2569", + "Text": ")\n(c) A classical atom based on is doomed to collapse (Thomson\u2019s model/ Rutherford\u2019s model )\n(d) An atom has a nearly continuous mass distribution in a" + }, + { + "Chapter": "9", + "sentence_range": "2567-2570", + "Text": "is doomed to collapse (Thomson\u2019s model/ Rutherford\u2019s model )\n(d) An atom has a nearly continuous mass distribution in a but has a highly non-uniform mass distribution in" + }, + { + "Chapter": "9", + "sentence_range": "2568-2571", + "Text": "(Thomson\u2019s model/ Rutherford\u2019s model )\n(d) An atom has a nearly continuous mass distribution in a but has a highly non-uniform mass distribution in (Thomson\u2019s model/ Rutherford\u2019s model" + }, + { + "Chapter": "9", + "sentence_range": "2569-2572", + "Text": ")\n(d) An atom has a nearly continuous mass distribution in a but has a highly non-uniform mass distribution in (Thomson\u2019s model/ Rutherford\u2019s model )\n(e) The positively charged part of the atom possesses most of the\nmass in" + }, + { + "Chapter": "9", + "sentence_range": "2570-2573", + "Text": "but has a highly non-uniform mass distribution in (Thomson\u2019s model/ Rutherford\u2019s model )\n(e) The positively charged part of the atom possesses most of the\nmass in (Rutherford\u2019s model/both the models" + }, + { + "Chapter": "9", + "sentence_range": "2571-2574", + "Text": "(Thomson\u2019s model/ Rutherford\u2019s model )\n(e) The positively charged part of the atom possesses most of the\nmass in (Rutherford\u2019s model/both the models )\n12" + }, + { + "Chapter": "9", + "sentence_range": "2572-2575", + "Text": ")\n(e) The positively charged part of the atom possesses most of the\nmass in (Rutherford\u2019s model/both the models )\n12 2\nSuppose you are given a chance to repeat the alpha-particle\nscattering experiment using a thin sheet of solid hydrogen in place\nof the gold foil" + }, + { + "Chapter": "9", + "sentence_range": "2573-2576", + "Text": "(Rutherford\u2019s model/both the models )\n12 2\nSuppose you are given a chance to repeat the alpha-particle\nscattering experiment using a thin sheet of solid hydrogen in place\nof the gold foil (Hydrogen is a solid at temperatures below 14 K" + }, + { + "Chapter": "9", + "sentence_range": "2574-2577", + "Text": ")\n12 2\nSuppose you are given a chance to repeat the alpha-particle\nscattering experiment using a thin sheet of solid hydrogen in place\nof the gold foil (Hydrogen is a solid at temperatures below 14 K )\nWhat results do you expect" + }, + { + "Chapter": "9", + "sentence_range": "2575-2578", + "Text": "2\nSuppose you are given a chance to repeat the alpha-particle\nscattering experiment using a thin sheet of solid hydrogen in place\nof the gold foil (Hydrogen is a solid at temperatures below 14 K )\nWhat results do you expect 12" + }, + { + "Chapter": "9", + "sentence_range": "2576-2579", + "Text": "(Hydrogen is a solid at temperatures below 14 K )\nWhat results do you expect 12 3\nA difference of 2" + }, + { + "Chapter": "9", + "sentence_range": "2577-2580", + "Text": ")\nWhat results do you expect 12 3\nA difference of 2 3 eV separates two energy levels in an atom" + }, + { + "Chapter": "9", + "sentence_range": "2578-2581", + "Text": "12 3\nA difference of 2 3 eV separates two energy levels in an atom What\nis the frequency of radiation emitted when the atom make a\ntransition from the upper level to the lower level" + }, + { + "Chapter": "9", + "sentence_range": "2579-2582", + "Text": "3\nA difference of 2 3 eV separates two energy levels in an atom What\nis the frequency of radiation emitted when the atom make a\ntransition from the upper level to the lower level 12" + }, + { + "Chapter": "9", + "sentence_range": "2580-2583", + "Text": "3 eV separates two energy levels in an atom What\nis the frequency of radiation emitted when the atom make a\ntransition from the upper level to the lower level 12 4\nThe ground state energy of hydrogen atom is \u201313" + }, + { + "Chapter": "9", + "sentence_range": "2581-2584", + "Text": "What\nis the frequency of radiation emitted when the atom make a\ntransition from the upper level to the lower level 12 4\nThe ground state energy of hydrogen atom is \u201313 6 eV" + }, + { + "Chapter": "9", + "sentence_range": "2582-2585", + "Text": "12 4\nThe ground state energy of hydrogen atom is \u201313 6 eV What are the\nkinetic and potential energies of the electron in this state" + }, + { + "Chapter": "9", + "sentence_range": "2583-2586", + "Text": "4\nThe ground state energy of hydrogen atom is \u201313 6 eV What are the\nkinetic and potential energies of the electron in this state 12" + }, + { + "Chapter": "9", + "sentence_range": "2584-2587", + "Text": "6 eV What are the\nkinetic and potential energies of the electron in this state 12 5\nA hydrogen atom initially in the ground level absorbs a photon,\nwhich excites it to the n = 4 level" + }, + { + "Chapter": "9", + "sentence_range": "2585-2588", + "Text": "What are the\nkinetic and potential energies of the electron in this state 12 5\nA hydrogen atom initially in the ground level absorbs a photon,\nwhich excites it to the n = 4 level Determine the wavelength and\nfrequency of photon" + }, + { + "Chapter": "9", + "sentence_range": "2586-2589", + "Text": "12 5\nA hydrogen atom initially in the ground level absorbs a photon,\nwhich excites it to the n = 4 level Determine the wavelength and\nfrequency of photon 12" + }, + { + "Chapter": "9", + "sentence_range": "2587-2590", + "Text": "5\nA hydrogen atom initially in the ground level absorbs a photon,\nwhich excites it to the n = 4 level Determine the wavelength and\nfrequency of photon 12 6\n(a) Using the Bohr\u2019s model calculate the speed of the electron in a\nhydrogen atom in the n = 1, 2, and 3 levels" + }, + { + "Chapter": "9", + "sentence_range": "2588-2591", + "Text": "Determine the wavelength and\nfrequency of photon 12 6\n(a) Using the Bohr\u2019s model calculate the speed of the electron in a\nhydrogen atom in the n = 1, 2, and 3 levels (b) Calculate the orbital\nperiod in each of these levels" + }, + { + "Chapter": "9", + "sentence_range": "2589-2592", + "Text": "12 6\n(a) Using the Bohr\u2019s model calculate the speed of the electron in a\nhydrogen atom in the n = 1, 2, and 3 levels (b) Calculate the orbital\nperiod in each of these levels 12" + }, + { + "Chapter": "9", + "sentence_range": "2590-2593", + "Text": "6\n(a) Using the Bohr\u2019s model calculate the speed of the electron in a\nhydrogen atom in the n = 1, 2, and 3 levels (b) Calculate the orbital\nperiod in each of these levels 12 7\nThe radius of the innermost electron orbit of a hydrogen atom is\n5" + }, + { + "Chapter": "9", + "sentence_range": "2591-2594", + "Text": "(b) Calculate the orbital\nperiod in each of these levels 12 7\nThe radius of the innermost electron orbit of a hydrogen atom is\n5 3\u00d710\u201311 m" + }, + { + "Chapter": "9", + "sentence_range": "2592-2595", + "Text": "12 7\nThe radius of the innermost electron orbit of a hydrogen atom is\n5 3\u00d710\u201311 m What are the radii of the n = 2 and n =3 orbits" + }, + { + "Chapter": "9", + "sentence_range": "2593-2596", + "Text": "7\nThe radius of the innermost electron orbit of a hydrogen atom is\n5 3\u00d710\u201311 m What are the radii of the n = 2 and n =3 orbits 12" + }, + { + "Chapter": "9", + "sentence_range": "2594-2597", + "Text": "3\u00d710\u201311 m What are the radii of the n = 2 and n =3 orbits 12 8\nA 12" + }, + { + "Chapter": "9", + "sentence_range": "2595-2598", + "Text": "What are the radii of the n = 2 and n =3 orbits 12 8\nA 12 5 eV electron beam is used to bombard gaseous hydrogen at\nroom temperature" + }, + { + "Chapter": "9", + "sentence_range": "2596-2599", + "Text": "12 8\nA 12 5 eV electron beam is used to bombard gaseous hydrogen at\nroom temperature What series of wavelengths will be emitted" + }, + { + "Chapter": "9", + "sentence_range": "2597-2600", + "Text": "8\nA 12 5 eV electron beam is used to bombard gaseous hydrogen at\nroom temperature What series of wavelengths will be emitted 12" + }, + { + "Chapter": "9", + "sentence_range": "2598-2601", + "Text": "5 eV electron beam is used to bombard gaseous hydrogen at\nroom temperature What series of wavelengths will be emitted 12 9\nIn accordance with the Bohr\u2019s model, find the quantum number\nthat characterises the earth\u2019s revolution around the sun in an orbit\nof radius 1" + }, + { + "Chapter": "9", + "sentence_range": "2599-2602", + "Text": "What series of wavelengths will be emitted 12 9\nIn accordance with the Bohr\u2019s model, find the quantum number\nthat characterises the earth\u2019s revolution around the sun in an orbit\nof radius 1 5 \u00d7 1011 m with orbital speed 3 \u00d7 104 m/s" + }, + { + "Chapter": "9", + "sentence_range": "2600-2603", + "Text": "12 9\nIn accordance with the Bohr\u2019s model, find the quantum number\nthat characterises the earth\u2019s revolution around the sun in an orbit\nof radius 1 5 \u00d7 1011 m with orbital speed 3 \u00d7 104 m/s (Mass of earth\n= 6" + }, + { + "Chapter": "9", + "sentence_range": "2601-2604", + "Text": "9\nIn accordance with the Bohr\u2019s model, find the quantum number\nthat characterises the earth\u2019s revolution around the sun in an orbit\nof radius 1 5 \u00d7 1011 m with orbital speed 3 \u00d7 104 m/s (Mass of earth\n= 6 0 \u00d7 1024 kg" + }, + { + "Chapter": "9", + "sentence_range": "2602-2605", + "Text": "5 \u00d7 1011 m with orbital speed 3 \u00d7 104 m/s (Mass of earth\n= 6 0 \u00d7 1024 kg )\nRationalised 2023-24\nPhysics\n306\n13" + }, + { + "Chapter": "9", + "sentence_range": "2603-2606", + "Text": "(Mass of earth\n= 6 0 \u00d7 1024 kg )\nRationalised 2023-24\nPhysics\n306\n13 1 INTRODUCTION\nIn the previous chapter, we have learnt that in every atom, the positive\ncharge and mass are densely concentrated at the centre of the atom\nforming its nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2604-2607", + "Text": "0 \u00d7 1024 kg )\nRationalised 2023-24\nPhysics\n306\n13 1 INTRODUCTION\nIn the previous chapter, we have learnt that in every atom, the positive\ncharge and mass are densely concentrated at the centre of the atom\nforming its nucleus The overall dimensions of a nucleus are much smaller\nthan those of an atom" + }, + { + "Chapter": "9", + "sentence_range": "2605-2608", + "Text": ")\nRationalised 2023-24\nPhysics\n306\n13 1 INTRODUCTION\nIn the previous chapter, we have learnt that in every atom, the positive\ncharge and mass are densely concentrated at the centre of the atom\nforming its nucleus The overall dimensions of a nucleus are much smaller\nthan those of an atom Experiments on scattering of a-particles\ndemonstrated that the radius of a nucleus was smaller than the radius\nof an atom by a factor of about 104" + }, + { + "Chapter": "9", + "sentence_range": "2606-2609", + "Text": "1 INTRODUCTION\nIn the previous chapter, we have learnt that in every atom, the positive\ncharge and mass are densely concentrated at the centre of the atom\nforming its nucleus The overall dimensions of a nucleus are much smaller\nthan those of an atom Experiments on scattering of a-particles\ndemonstrated that the radius of a nucleus was smaller than the radius\nof an atom by a factor of about 104 This means the volume of a nucleus\nis about 10\u201312 times the volume of the atom" + }, + { + "Chapter": "9", + "sentence_range": "2607-2610", + "Text": "The overall dimensions of a nucleus are much smaller\nthan those of an atom Experiments on scattering of a-particles\ndemonstrated that the radius of a nucleus was smaller than the radius\nof an atom by a factor of about 104 This means the volume of a nucleus\nis about 10\u201312 times the volume of the atom In other words, an atom is\nalmost empty" + }, + { + "Chapter": "9", + "sentence_range": "2608-2611", + "Text": "Experiments on scattering of a-particles\ndemonstrated that the radius of a nucleus was smaller than the radius\nof an atom by a factor of about 104 This means the volume of a nucleus\nis about 10\u201312 times the volume of the atom In other words, an atom is\nalmost empty If an atom is enlarged to the size of a classroom, the nucleus\nwould be of the size of pinhead" + }, + { + "Chapter": "9", + "sentence_range": "2609-2612", + "Text": "This means the volume of a nucleus\nis about 10\u201312 times the volume of the atom In other words, an atom is\nalmost empty If an atom is enlarged to the size of a classroom, the nucleus\nwould be of the size of pinhead Nevertheless, the nucleus contains most\n(more than 99" + }, + { + "Chapter": "9", + "sentence_range": "2610-2613", + "Text": "In other words, an atom is\nalmost empty If an atom is enlarged to the size of a classroom, the nucleus\nwould be of the size of pinhead Nevertheless, the nucleus contains most\n(more than 99 9%) of the mass of an atom" + }, + { + "Chapter": "9", + "sentence_range": "2611-2614", + "Text": "If an atom is enlarged to the size of a classroom, the nucleus\nwould be of the size of pinhead Nevertheless, the nucleus contains most\n(more than 99 9%) of the mass of an atom Does the nucleus have a structure, just as the atom does" + }, + { + "Chapter": "9", + "sentence_range": "2612-2615", + "Text": "Nevertheless, the nucleus contains most\n(more than 99 9%) of the mass of an atom Does the nucleus have a structure, just as the atom does If so, what\nare the constituents of the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2613-2616", + "Text": "9%) of the mass of an atom Does the nucleus have a structure, just as the atom does If so, what\nare the constituents of the nucleus How are these held together" + }, + { + "Chapter": "9", + "sentence_range": "2614-2617", + "Text": "Does the nucleus have a structure, just as the atom does If so, what\nare the constituents of the nucleus How are these held together In this\nchapter, we shall look for answers to such questions" + }, + { + "Chapter": "9", + "sentence_range": "2615-2618", + "Text": "If so, what\nare the constituents of the nucleus How are these held together In this\nchapter, we shall look for answers to such questions We shall discuss\nvarious properties of nuclei such as their size, mass and stability, and\nalso associated nuclear phenomena such as radioactivity, fission and fusion" + }, + { + "Chapter": "9", + "sentence_range": "2616-2619", + "Text": "How are these held together In this\nchapter, we shall look for answers to such questions We shall discuss\nvarious properties of nuclei such as their size, mass and stability, and\nalso associated nuclear phenomena such as radioactivity, fission and fusion 13" + }, + { + "Chapter": "9", + "sentence_range": "2617-2620", + "Text": "In this\nchapter, we shall look for answers to such questions We shall discuss\nvarious properties of nuclei such as their size, mass and stability, and\nalso associated nuclear phenomena such as radioactivity, fission and fusion 13 2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS\nThe mass of an atom is very small, compared to a kilogram; for example,\nthe mass of a carbon atom, 12C, is 1" + }, + { + "Chapter": "9", + "sentence_range": "2618-2621", + "Text": "We shall discuss\nvarious properties of nuclei such as their size, mass and stability, and\nalso associated nuclear phenomena such as radioactivity, fission and fusion 13 2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS\nThe mass of an atom is very small, compared to a kilogram; for example,\nthe mass of a carbon atom, 12C, is 1 992647 \u00d7 10\u201326 kg" + }, + { + "Chapter": "9", + "sentence_range": "2619-2622", + "Text": "13 2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS\nThe mass of an atom is very small, compared to a kilogram; for example,\nthe mass of a carbon atom, 12C, is 1 992647 \u00d7 10\u201326 kg Kilogram is not\na very convenient unit to measure such small quantities" + }, + { + "Chapter": "9", + "sentence_range": "2620-2623", + "Text": "2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS\nThe mass of an atom is very small, compared to a kilogram; for example,\nthe mass of a carbon atom, 12C, is 1 992647 \u00d7 10\u201326 kg Kilogram is not\na very convenient unit to measure such small quantities Therefore, a\nChapter Thirteen\nNUCLEI\nRationalised 2023-24\n307\nNuclei\ndifferent mass unit is used for expressing atomic masses" + }, + { + "Chapter": "9", + "sentence_range": "2621-2624", + "Text": "992647 \u00d7 10\u201326 kg Kilogram is not\na very convenient unit to measure such small quantities Therefore, a\nChapter Thirteen\nNUCLEI\nRationalised 2023-24\n307\nNuclei\ndifferent mass unit is used for expressing atomic masses This unit is the\natomic mass unit (u), defined as 1/12th of the mass of the carbon (12C)\natom" + }, + { + "Chapter": "9", + "sentence_range": "2622-2625", + "Text": "Kilogram is not\na very convenient unit to measure such small quantities Therefore, a\nChapter Thirteen\nNUCLEI\nRationalised 2023-24\n307\nNuclei\ndifferent mass unit is used for expressing atomic masses This unit is the\natomic mass unit (u), defined as 1/12th of the mass of the carbon (12C)\natom According to this definition\n mass of one 12\nC atom\n1u = \n12\n \n26\n1" + }, + { + "Chapter": "9", + "sentence_range": "2623-2626", + "Text": "Therefore, a\nChapter Thirteen\nNUCLEI\nRationalised 2023-24\n307\nNuclei\ndifferent mass unit is used for expressing atomic masses This unit is the\natomic mass unit (u), defined as 1/12th of the mass of the carbon (12C)\natom According to this definition\n mass of one 12\nC atom\n1u = \n12\n \n26\n1 992647\n10\nkg\n12\n\u2212\n\u00d7\n=\n \n27\n1" + }, + { + "Chapter": "9", + "sentence_range": "2624-2627", + "Text": "This unit is the\natomic mass unit (u), defined as 1/12th of the mass of the carbon (12C)\natom According to this definition\n mass of one 12\nC atom\n1u = \n12\n \n26\n1 992647\n10\nkg\n12\n\u2212\n\u00d7\n=\n \n27\n1 660539\n10\nkg\n\u2212\n=\n\u00d7\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2625-2628", + "Text": "According to this definition\n mass of one 12\nC atom\n1u = \n12\n \n26\n1 992647\n10\nkg\n12\n\u2212\n\u00d7\n=\n \n27\n1 660539\n10\nkg\n\u2212\n=\n\u00d7\n(13 1)\nThe atomic masses of various elements expressed in atomic mass\nunit (u) are close to being integral multiples of the mass of a hydrogen\natom" + }, + { + "Chapter": "9", + "sentence_range": "2626-2629", + "Text": "992647\n10\nkg\n12\n\u2212\n\u00d7\n=\n \n27\n1 660539\n10\nkg\n\u2212\n=\n\u00d7\n(13 1)\nThe atomic masses of various elements expressed in atomic mass\nunit (u) are close to being integral multiples of the mass of a hydrogen\natom There are, however, many striking exceptions to this rule" + }, + { + "Chapter": "9", + "sentence_range": "2627-2630", + "Text": "660539\n10\nkg\n\u2212\n=\n\u00d7\n(13 1)\nThe atomic masses of various elements expressed in atomic mass\nunit (u) are close to being integral multiples of the mass of a hydrogen\natom There are, however, many striking exceptions to this rule For\nexample, the atomic mass of chlorine atom is 35" + }, + { + "Chapter": "9", + "sentence_range": "2628-2631", + "Text": "1)\nThe atomic masses of various elements expressed in atomic mass\nunit (u) are close to being integral multiples of the mass of a hydrogen\natom There are, however, many striking exceptions to this rule For\nexample, the atomic mass of chlorine atom is 35 46 u" + }, + { + "Chapter": "9", + "sentence_range": "2629-2632", + "Text": "There are, however, many striking exceptions to this rule For\nexample, the atomic mass of chlorine atom is 35 46 u Accurate measurement of atomic masses is carried out with a mass\nspectrometer, The measurement of atomic masses reveals the existence\nof different types of atoms of the same element, which exhibit the same\nchemical properties, but differ in mass" + }, + { + "Chapter": "9", + "sentence_range": "2630-2633", + "Text": "For\nexample, the atomic mass of chlorine atom is 35 46 u Accurate measurement of atomic masses is carried out with a mass\nspectrometer, The measurement of atomic masses reveals the existence\nof different types of atoms of the same element, which exhibit the same\nchemical properties, but differ in mass Such atomic species of the same\nelement differing in mass are called isotopes" + }, + { + "Chapter": "9", + "sentence_range": "2631-2634", + "Text": "46 u Accurate measurement of atomic masses is carried out with a mass\nspectrometer, The measurement of atomic masses reveals the existence\nof different types of atoms of the same element, which exhibit the same\nchemical properties, but differ in mass Such atomic species of the same\nelement differing in mass are called isotopes (In Greek, isotope means\nthe same place, i" + }, + { + "Chapter": "9", + "sentence_range": "2632-2635", + "Text": "Accurate measurement of atomic masses is carried out with a mass\nspectrometer, The measurement of atomic masses reveals the existence\nof different types of atoms of the same element, which exhibit the same\nchemical properties, but differ in mass Such atomic species of the same\nelement differing in mass are called isotopes (In Greek, isotope means\nthe same place, i e" + }, + { + "Chapter": "9", + "sentence_range": "2633-2636", + "Text": "Such atomic species of the same\nelement differing in mass are called isotopes (In Greek, isotope means\nthe same place, i e they occur in the same place in the periodic table of\nelements" + }, + { + "Chapter": "9", + "sentence_range": "2634-2637", + "Text": "(In Greek, isotope means\nthe same place, i e they occur in the same place in the periodic table of\nelements ) It was found that practically every element consists of a mixture\nof several isotopes" + }, + { + "Chapter": "9", + "sentence_range": "2635-2638", + "Text": "e they occur in the same place in the periodic table of\nelements ) It was found that practically every element consists of a mixture\nof several isotopes The relative abundance of different isotopes differs\nfrom element to element" + }, + { + "Chapter": "9", + "sentence_range": "2636-2639", + "Text": "they occur in the same place in the periodic table of\nelements ) It was found that practically every element consists of a mixture\nof several isotopes The relative abundance of different isotopes differs\nfrom element to element Chlorine, for example, has two isotopes having\nmasses 34" + }, + { + "Chapter": "9", + "sentence_range": "2637-2640", + "Text": ") It was found that practically every element consists of a mixture\nof several isotopes The relative abundance of different isotopes differs\nfrom element to element Chlorine, for example, has two isotopes having\nmasses 34 98 u and 36" + }, + { + "Chapter": "9", + "sentence_range": "2638-2641", + "Text": "The relative abundance of different isotopes differs\nfrom element to element Chlorine, for example, has two isotopes having\nmasses 34 98 u and 36 98 u, which are nearly integral multiples of the\nmass of a hydrogen atom" + }, + { + "Chapter": "9", + "sentence_range": "2639-2642", + "Text": "Chlorine, for example, has two isotopes having\nmasses 34 98 u and 36 98 u, which are nearly integral multiples of the\nmass of a hydrogen atom The relative abundances of these isotopes are\n75" + }, + { + "Chapter": "9", + "sentence_range": "2640-2643", + "Text": "98 u and 36 98 u, which are nearly integral multiples of the\nmass of a hydrogen atom The relative abundances of these isotopes are\n75 4 and 24" + }, + { + "Chapter": "9", + "sentence_range": "2641-2644", + "Text": "98 u, which are nearly integral multiples of the\nmass of a hydrogen atom The relative abundances of these isotopes are\n75 4 and 24 6 per cent, respectively" + }, + { + "Chapter": "9", + "sentence_range": "2642-2645", + "Text": "The relative abundances of these isotopes are\n75 4 and 24 6 per cent, respectively Thus, the average mass of a chlorine\natom is obtained by the weighted average of the masses of the two\nisotopes, which works out to be\n= 75" + }, + { + "Chapter": "9", + "sentence_range": "2643-2646", + "Text": "4 and 24 6 per cent, respectively Thus, the average mass of a chlorine\natom is obtained by the weighted average of the masses of the two\nisotopes, which works out to be\n= 75 4\n34" + }, + { + "Chapter": "9", + "sentence_range": "2644-2647", + "Text": "6 per cent, respectively Thus, the average mass of a chlorine\natom is obtained by the weighted average of the masses of the two\nisotopes, which works out to be\n= 75 4\n34 98\n24" + }, + { + "Chapter": "9", + "sentence_range": "2645-2648", + "Text": "Thus, the average mass of a chlorine\natom is obtained by the weighted average of the masses of the two\nisotopes, which works out to be\n= 75 4\n34 98\n24 6\n36" + }, + { + "Chapter": "9", + "sentence_range": "2646-2649", + "Text": "4\n34 98\n24 6\n36 98\n100\n\u00d7\n+\n\u00d7\n= 35" + }, + { + "Chapter": "9", + "sentence_range": "2647-2650", + "Text": "98\n24 6\n36 98\n100\n\u00d7\n+\n\u00d7\n= 35 47 u\nwhich agrees with the atomic mass of chlorine" + }, + { + "Chapter": "9", + "sentence_range": "2648-2651", + "Text": "6\n36 98\n100\n\u00d7\n+\n\u00d7\n= 35 47 u\nwhich agrees with the atomic mass of chlorine Even the lightest element, hydrogen has three isotopes having masses\n1" + }, + { + "Chapter": "9", + "sentence_range": "2649-2652", + "Text": "98\n100\n\u00d7\n+\n\u00d7\n= 35 47 u\nwhich agrees with the atomic mass of chlorine Even the lightest element, hydrogen has three isotopes having masses\n1 0078 u, 2" + }, + { + "Chapter": "9", + "sentence_range": "2650-2653", + "Text": "47 u\nwhich agrees with the atomic mass of chlorine Even the lightest element, hydrogen has three isotopes having masses\n1 0078 u, 2 0141 u, and 3" + }, + { + "Chapter": "9", + "sentence_range": "2651-2654", + "Text": "Even the lightest element, hydrogen has three isotopes having masses\n1 0078 u, 2 0141 u, and 3 0160 u" + }, + { + "Chapter": "9", + "sentence_range": "2652-2655", + "Text": "0078 u, 2 0141 u, and 3 0160 u The nucleus of the lightest atom of\nhydrogen, which has a relative abundance of 99" + }, + { + "Chapter": "9", + "sentence_range": "2653-2656", + "Text": "0141 u, and 3 0160 u The nucleus of the lightest atom of\nhydrogen, which has a relative abundance of 99 985%, is called the\nproton" + }, + { + "Chapter": "9", + "sentence_range": "2654-2657", + "Text": "0160 u The nucleus of the lightest atom of\nhydrogen, which has a relative abundance of 99 985%, is called the\nproton The mass of a proton is\n27\n1" + }, + { + "Chapter": "9", + "sentence_range": "2655-2658", + "Text": "The nucleus of the lightest atom of\nhydrogen, which has a relative abundance of 99 985%, is called the\nproton The mass of a proton is\n27\n1 00727 u\n1" + }, + { + "Chapter": "9", + "sentence_range": "2656-2659", + "Text": "985%, is called the\nproton The mass of a proton is\n27\n1 00727 u\n1 67262\n10\nkg\nmp\n\u2212\n=\n=\n\u00d7\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2657-2660", + "Text": "The mass of a proton is\n27\n1 00727 u\n1 67262\n10\nkg\nmp\n\u2212\n=\n=\n\u00d7\n(13 2)\nThis is equal to the mass of the hydrogen atom (= 1" + }, + { + "Chapter": "9", + "sentence_range": "2658-2661", + "Text": "00727 u\n1 67262\n10\nkg\nmp\n\u2212\n=\n=\n\u00d7\n(13 2)\nThis is equal to the mass of the hydrogen atom (= 1 00783u), minus\nthe mass of a single electron (me = 0" + }, + { + "Chapter": "9", + "sentence_range": "2659-2662", + "Text": "67262\n10\nkg\nmp\n\u2212\n=\n=\n\u00d7\n(13 2)\nThis is equal to the mass of the hydrogen atom (= 1 00783u), minus\nthe mass of a single electron (me = 0 00055 u)" + }, + { + "Chapter": "9", + "sentence_range": "2660-2663", + "Text": "2)\nThis is equal to the mass of the hydrogen atom (= 1 00783u), minus\nthe mass of a single electron (me = 0 00055 u) The other two isotopes of\nhydrogen are called deuterium and tritium" + }, + { + "Chapter": "9", + "sentence_range": "2661-2664", + "Text": "00783u), minus\nthe mass of a single electron (me = 0 00055 u) The other two isotopes of\nhydrogen are called deuterium and tritium Tritium nuclei, being\nunstable, do not occur naturally and are produced artificially in\nlaboratories" + }, + { + "Chapter": "9", + "sentence_range": "2662-2665", + "Text": "00055 u) The other two isotopes of\nhydrogen are called deuterium and tritium Tritium nuclei, being\nunstable, do not occur naturally and are produced artificially in\nlaboratories The positive charge in the nucleus is that of the protons" + }, + { + "Chapter": "9", + "sentence_range": "2663-2666", + "Text": "The other two isotopes of\nhydrogen are called deuterium and tritium Tritium nuclei, being\nunstable, do not occur naturally and are produced artificially in\nlaboratories The positive charge in the nucleus is that of the protons A proton\ncarries one unit of fundamental charge and is stable" + }, + { + "Chapter": "9", + "sentence_range": "2664-2667", + "Text": "Tritium nuclei, being\nunstable, do not occur naturally and are produced artificially in\nlaboratories The positive charge in the nucleus is that of the protons A proton\ncarries one unit of fundamental charge and is stable It was earlier thought\nthat the nucleus may contain electrons, but this was ruled out later using\narguments based on quantum theory" + }, + { + "Chapter": "9", + "sentence_range": "2665-2668", + "Text": "The positive charge in the nucleus is that of the protons A proton\ncarries one unit of fundamental charge and is stable It was earlier thought\nthat the nucleus may contain electrons, but this was ruled out later using\narguments based on quantum theory All the electrons of an atom are\noutside the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2666-2669", + "Text": "A proton\ncarries one unit of fundamental charge and is stable It was earlier thought\nthat the nucleus may contain electrons, but this was ruled out later using\narguments based on quantum theory All the electrons of an atom are\noutside the nucleus We know that the number of these electrons outside\nthe nucleus of the atom is Z, the atomic number" + }, + { + "Chapter": "9", + "sentence_range": "2667-2670", + "Text": "It was earlier thought\nthat the nucleus may contain electrons, but this was ruled out later using\narguments based on quantum theory All the electrons of an atom are\noutside the nucleus We know that the number of these electrons outside\nthe nucleus of the atom is Z, the atomic number The total charge of the\nRationalised 2023-24\nPhysics\n308\natomic electrons is thus (\u2013Ze), and since the atom is neutral, the charge\nof the nucleus is (+Ze)" + }, + { + "Chapter": "9", + "sentence_range": "2668-2671", + "Text": "All the electrons of an atom are\noutside the nucleus We know that the number of these electrons outside\nthe nucleus of the atom is Z, the atomic number The total charge of the\nRationalised 2023-24\nPhysics\n308\natomic electrons is thus (\u2013Ze), and since the atom is neutral, the charge\nof the nucleus is (+Ze) The number of protons in the nucleus of the atom\nis, therefore, exactly Z, the atomic number" + }, + { + "Chapter": "9", + "sentence_range": "2669-2672", + "Text": "We know that the number of these electrons outside\nthe nucleus of the atom is Z, the atomic number The total charge of the\nRationalised 2023-24\nPhysics\n308\natomic electrons is thus (\u2013Ze), and since the atom is neutral, the charge\nof the nucleus is (+Ze) The number of protons in the nucleus of the atom\nis, therefore, exactly Z, the atomic number Discovery of Neutron\nSince the nuclei of deuterium and tritium are isotopes of hydrogen, they\nmust contain only one proton each" + }, + { + "Chapter": "9", + "sentence_range": "2670-2673", + "Text": "The total charge of the\nRationalised 2023-24\nPhysics\n308\natomic electrons is thus (\u2013Ze), and since the atom is neutral, the charge\nof the nucleus is (+Ze) The number of protons in the nucleus of the atom\nis, therefore, exactly Z, the atomic number Discovery of Neutron\nSince the nuclei of deuterium and tritium are isotopes of hydrogen, they\nmust contain only one proton each But the masses of the nuclei of\nhydrogen, deuterium and tritium are in the ratio of 1:2:3" + }, + { + "Chapter": "9", + "sentence_range": "2671-2674", + "Text": "The number of protons in the nucleus of the atom\nis, therefore, exactly Z, the atomic number Discovery of Neutron\nSince the nuclei of deuterium and tritium are isotopes of hydrogen, they\nmust contain only one proton each But the masses of the nuclei of\nhydrogen, deuterium and tritium are in the ratio of 1:2:3 Therefore, the\nnuclei of deuterium and tritium must contain, in addition to a proton,\nsome neutral matter" + }, + { + "Chapter": "9", + "sentence_range": "2672-2675", + "Text": "Discovery of Neutron\nSince the nuclei of deuterium and tritium are isotopes of hydrogen, they\nmust contain only one proton each But the masses of the nuclei of\nhydrogen, deuterium and tritium are in the ratio of 1:2:3 Therefore, the\nnuclei of deuterium and tritium must contain, in addition to a proton,\nsome neutral matter The amount of neutral matter present in the nuclei\nof these isotopes, expressed in units of mass of a proton, is approximately\nequal to one and two, respectively" + }, + { + "Chapter": "9", + "sentence_range": "2673-2676", + "Text": "But the masses of the nuclei of\nhydrogen, deuterium and tritium are in the ratio of 1:2:3 Therefore, the\nnuclei of deuterium and tritium must contain, in addition to a proton,\nsome neutral matter The amount of neutral matter present in the nuclei\nof these isotopes, expressed in units of mass of a proton, is approximately\nequal to one and two, respectively This fact indicates that the nuclei of\natoms contain, in addition to protons, neutral matter in multiples of a\nbasic unit" + }, + { + "Chapter": "9", + "sentence_range": "2674-2677", + "Text": "Therefore, the\nnuclei of deuterium and tritium must contain, in addition to a proton,\nsome neutral matter The amount of neutral matter present in the nuclei\nof these isotopes, expressed in units of mass of a proton, is approximately\nequal to one and two, respectively This fact indicates that the nuclei of\natoms contain, in addition to protons, neutral matter in multiples of a\nbasic unit This hypothesis was verified in 1932 by James Chadwick\nwho observed emission of neutral radiation when beryllium nuclei were\nbombarded with alpha-particles (a-particles are helium nuclei, to be\ndiscussed in a later section)" + }, + { + "Chapter": "9", + "sentence_range": "2675-2678", + "Text": "The amount of neutral matter present in the nuclei\nof these isotopes, expressed in units of mass of a proton, is approximately\nequal to one and two, respectively This fact indicates that the nuclei of\natoms contain, in addition to protons, neutral matter in multiples of a\nbasic unit This hypothesis was verified in 1932 by James Chadwick\nwho observed emission of neutral radiation when beryllium nuclei were\nbombarded with alpha-particles (a-particles are helium nuclei, to be\ndiscussed in a later section) It was found that this neutral radiation\ncould knock out protons from light nuclei such as those of helium, carbon\nand nitrogen" + }, + { + "Chapter": "9", + "sentence_range": "2676-2679", + "Text": "This fact indicates that the nuclei of\natoms contain, in addition to protons, neutral matter in multiples of a\nbasic unit This hypothesis was verified in 1932 by James Chadwick\nwho observed emission of neutral radiation when beryllium nuclei were\nbombarded with alpha-particles (a-particles are helium nuclei, to be\ndiscussed in a later section) It was found that this neutral radiation\ncould knock out protons from light nuclei such as those of helium, carbon\nand nitrogen The only neutral radiation known at that time was photons\n(electromagnetic radiation)" + }, + { + "Chapter": "9", + "sentence_range": "2677-2680", + "Text": "This hypothesis was verified in 1932 by James Chadwick\nwho observed emission of neutral radiation when beryllium nuclei were\nbombarded with alpha-particles (a-particles are helium nuclei, to be\ndiscussed in a later section) It was found that this neutral radiation\ncould knock out protons from light nuclei such as those of helium, carbon\nand nitrogen The only neutral radiation known at that time was photons\n(electromagnetic radiation) Application of the principles of conservation\nof energy and momentum showed that if the neutral radiation consisted\nof photons, the energy of photons would have to be much higher than is\navailable from the bombardment of beryllium nuclei with a-particles" + }, + { + "Chapter": "9", + "sentence_range": "2678-2681", + "Text": "It was found that this neutral radiation\ncould knock out protons from light nuclei such as those of helium, carbon\nand nitrogen The only neutral radiation known at that time was photons\n(electromagnetic radiation) Application of the principles of conservation\nof energy and momentum showed that if the neutral radiation consisted\nof photons, the energy of photons would have to be much higher than is\navailable from the bombardment of beryllium nuclei with a-particles The clue to this puzzle, which Chadwick satisfactorily solved, was to\nassume that the neutral radiation consists of a new type of neutral\nparticles called neutrons" + }, + { + "Chapter": "9", + "sentence_range": "2679-2682", + "Text": "The only neutral radiation known at that time was photons\n(electromagnetic radiation) Application of the principles of conservation\nof energy and momentum showed that if the neutral radiation consisted\nof photons, the energy of photons would have to be much higher than is\navailable from the bombardment of beryllium nuclei with a-particles The clue to this puzzle, which Chadwick satisfactorily solved, was to\nassume that the neutral radiation consists of a new type of neutral\nparticles called neutrons From conservation of energy and momentum,\nhe was able to determine the mass of new particle \u2018as very nearly the\nsame as mass of proton\u2019" + }, + { + "Chapter": "9", + "sentence_range": "2680-2683", + "Text": "Application of the principles of conservation\nof energy and momentum showed that if the neutral radiation consisted\nof photons, the energy of photons would have to be much higher than is\navailable from the bombardment of beryllium nuclei with a-particles The clue to this puzzle, which Chadwick satisfactorily solved, was to\nassume that the neutral radiation consists of a new type of neutral\nparticles called neutrons From conservation of energy and momentum,\nhe was able to determine the mass of new particle \u2018as very nearly the\nsame as mass of proton\u2019 The mass of a neutron is now known to a high degree of accuracy" + }, + { + "Chapter": "9", + "sentence_range": "2681-2684", + "Text": "The clue to this puzzle, which Chadwick satisfactorily solved, was to\nassume that the neutral radiation consists of a new type of neutral\nparticles called neutrons From conservation of energy and momentum,\nhe was able to determine the mass of new particle \u2018as very nearly the\nsame as mass of proton\u2019 The mass of a neutron is now known to a high degree of accuracy It is\nm n = 1" + }, + { + "Chapter": "9", + "sentence_range": "2682-2685", + "Text": "From conservation of energy and momentum,\nhe was able to determine the mass of new particle \u2018as very nearly the\nsame as mass of proton\u2019 The mass of a neutron is now known to a high degree of accuracy It is\nm n = 1 00866 u = 1" + }, + { + "Chapter": "9", + "sentence_range": "2683-2686", + "Text": "The mass of a neutron is now known to a high degree of accuracy It is\nm n = 1 00866 u = 1 6749\u00d710\u201327 kg\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2684-2687", + "Text": "It is\nm n = 1 00866 u = 1 6749\u00d710\u201327 kg\n(13 3)\nChadwick was awarded the 1935 Nobel Prize in Physics for his\ndiscovery of the neutron" + }, + { + "Chapter": "9", + "sentence_range": "2685-2688", + "Text": "00866 u = 1 6749\u00d710\u201327 kg\n(13 3)\nChadwick was awarded the 1935 Nobel Prize in Physics for his\ndiscovery of the neutron A free neutron, unlike a free proton, is unstable" + }, + { + "Chapter": "9", + "sentence_range": "2686-2689", + "Text": "6749\u00d710\u201327 kg\n(13 3)\nChadwick was awarded the 1935 Nobel Prize in Physics for his\ndiscovery of the neutron A free neutron, unlike a free proton, is unstable It decays into a\nproton, an electron and a antineutrino (another elementary particle), and\nhas a mean life of about 1000s" + }, + { + "Chapter": "9", + "sentence_range": "2687-2690", + "Text": "3)\nChadwick was awarded the 1935 Nobel Prize in Physics for his\ndiscovery of the neutron A free neutron, unlike a free proton, is unstable It decays into a\nproton, an electron and a antineutrino (another elementary particle), and\nhas a mean life of about 1000s It is, however, stable inside the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2688-2691", + "Text": "A free neutron, unlike a free proton, is unstable It decays into a\nproton, an electron and a antineutrino (another elementary particle), and\nhas a mean life of about 1000s It is, however, stable inside the nucleus The composition of a nucleus can now be described using the following\nterms and symbols:\nZ - atomic number = number of protons\n[13" + }, + { + "Chapter": "9", + "sentence_range": "2689-2692", + "Text": "It decays into a\nproton, an electron and a antineutrino (another elementary particle), and\nhas a mean life of about 1000s It is, however, stable inside the nucleus The composition of a nucleus can now be described using the following\nterms and symbols:\nZ - atomic number = number of protons\n[13 4(a)]\nN - neutron number = number of neutrons\n[13" + }, + { + "Chapter": "9", + "sentence_range": "2690-2693", + "Text": "It is, however, stable inside the nucleus The composition of a nucleus can now be described using the following\nterms and symbols:\nZ - atomic number = number of protons\n[13 4(a)]\nN - neutron number = number of neutrons\n[13 4(b)]\nA - mass number = Z + N\n = total number of protons and neutrons [13" + }, + { + "Chapter": "9", + "sentence_range": "2691-2694", + "Text": "The composition of a nucleus can now be described using the following\nterms and symbols:\nZ - atomic number = number of protons\n[13 4(a)]\nN - neutron number = number of neutrons\n[13 4(b)]\nA - mass number = Z + N\n = total number of protons and neutrons [13 4(c)]\nOne also uses the term nucleon for a proton or a neutron" + }, + { + "Chapter": "9", + "sentence_range": "2692-2695", + "Text": "4(a)]\nN - neutron number = number of neutrons\n[13 4(b)]\nA - mass number = Z + N\n = total number of protons and neutrons [13 4(c)]\nOne also uses the term nucleon for a proton or a neutron Thus the\nnumber of nucleons in an atom is its mass number A" + }, + { + "Chapter": "9", + "sentence_range": "2693-2696", + "Text": "4(b)]\nA - mass number = Z + N\n = total number of protons and neutrons [13 4(c)]\nOne also uses the term nucleon for a proton or a neutron Thus the\nnumber of nucleons in an atom is its mass number A Nuclear species or nuclides are shown by the notation X\nZA\n where X is\nthe chemical symbol of the species" + }, + { + "Chapter": "9", + "sentence_range": "2694-2697", + "Text": "4(c)]\nOne also uses the term nucleon for a proton or a neutron Thus the\nnumber of nucleons in an atom is its mass number A Nuclear species or nuclides are shown by the notation X\nZA\n where X is\nthe chemical symbol of the species For example, the nucleus of gold is\ndenoted by 197\n79 Au" + }, + { + "Chapter": "9", + "sentence_range": "2695-2698", + "Text": "Thus the\nnumber of nucleons in an atom is its mass number A Nuclear species or nuclides are shown by the notation X\nZA\n where X is\nthe chemical symbol of the species For example, the nucleus of gold is\ndenoted by 197\n79 Au It contains 197 nucleons, of which 79 are protons\nand the rest118 are neutrons" + }, + { + "Chapter": "9", + "sentence_range": "2696-2699", + "Text": "Nuclear species or nuclides are shown by the notation X\nZA\n where X is\nthe chemical symbol of the species For example, the nucleus of gold is\ndenoted by 197\n79 Au It contains 197 nucleons, of which 79 are protons\nand the rest118 are neutrons Rationalised 2023-24\n309\nNuclei\nThe composition of isotopes of an element can now be readily\nexplained" + }, + { + "Chapter": "9", + "sentence_range": "2697-2700", + "Text": "For example, the nucleus of gold is\ndenoted by 197\n79 Au It contains 197 nucleons, of which 79 are protons\nand the rest118 are neutrons Rationalised 2023-24\n309\nNuclei\nThe composition of isotopes of an element can now be readily\nexplained The nuclei of isotopes of a given element contain the same\nnumber of protons, but differ from each other in their number of neutrons" + }, + { + "Chapter": "9", + "sentence_range": "2698-2701", + "Text": "It contains 197 nucleons, of which 79 are protons\nand the rest118 are neutrons Rationalised 2023-24\n309\nNuclei\nThe composition of isotopes of an element can now be readily\nexplained The nuclei of isotopes of a given element contain the same\nnumber of protons, but differ from each other in their number of neutrons Deuterium, 2\n1 H, which is an isotope of hydrogen, contains one proton\nand one neutron" + }, + { + "Chapter": "9", + "sentence_range": "2699-2702", + "Text": "Rationalised 2023-24\n309\nNuclei\nThe composition of isotopes of an element can now be readily\nexplained The nuclei of isotopes of a given element contain the same\nnumber of protons, but differ from each other in their number of neutrons Deuterium, 2\n1 H, which is an isotope of hydrogen, contains one proton\nand one neutron Its other isotope tritium, 3\n1 H, contains one proton and\ntwo neutrons" + }, + { + "Chapter": "9", + "sentence_range": "2700-2703", + "Text": "The nuclei of isotopes of a given element contain the same\nnumber of protons, but differ from each other in their number of neutrons Deuterium, 2\n1 H, which is an isotope of hydrogen, contains one proton\nand one neutron Its other isotope tritium, 3\n1 H, contains one proton and\ntwo neutrons The element gold has 32 isotopes, ranging from A =173 to\nA = 204" + }, + { + "Chapter": "9", + "sentence_range": "2701-2704", + "Text": "Deuterium, 2\n1 H, which is an isotope of hydrogen, contains one proton\nand one neutron Its other isotope tritium, 3\n1 H, contains one proton and\ntwo neutrons The element gold has 32 isotopes, ranging from A =173 to\nA = 204 We have already mentioned that chemical properties of elements\ndepend on their electronic structure" + }, + { + "Chapter": "9", + "sentence_range": "2702-2705", + "Text": "Its other isotope tritium, 3\n1 H, contains one proton and\ntwo neutrons The element gold has 32 isotopes, ranging from A =173 to\nA = 204 We have already mentioned that chemical properties of elements\ndepend on their electronic structure As the atoms of isotopes have\nidentical electronic structure they have identical chemical behaviour and\nare placed in the same location in the periodic table" + }, + { + "Chapter": "9", + "sentence_range": "2703-2706", + "Text": "The element gold has 32 isotopes, ranging from A =173 to\nA = 204 We have already mentioned that chemical properties of elements\ndepend on their electronic structure As the atoms of isotopes have\nidentical electronic structure they have identical chemical behaviour and\nare placed in the same location in the periodic table All nuclides with same mass number A are called isobars" + }, + { + "Chapter": "9", + "sentence_range": "2704-2707", + "Text": "We have already mentioned that chemical properties of elements\ndepend on their electronic structure As the atoms of isotopes have\nidentical electronic structure they have identical chemical behaviour and\nare placed in the same location in the periodic table All nuclides with same mass number A are called isobars For\nexample, the nuclides 3\n1 H and 3\n2He are isobars" + }, + { + "Chapter": "9", + "sentence_range": "2705-2708", + "Text": "As the atoms of isotopes have\nidentical electronic structure they have identical chemical behaviour and\nare placed in the same location in the periodic table All nuclides with same mass number A are called isobars For\nexample, the nuclides 3\n1 H and 3\n2He are isobars Nuclides with same\nneutron number N but different atomic number Z, for example 198\n80 Hg\nand 197\n79 Au , are called isotones" + }, + { + "Chapter": "9", + "sentence_range": "2706-2709", + "Text": "All nuclides with same mass number A are called isobars For\nexample, the nuclides 3\n1 H and 3\n2He are isobars Nuclides with same\nneutron number N but different atomic number Z, for example 198\n80 Hg\nand 197\n79 Au , are called isotones 13" + }, + { + "Chapter": "9", + "sentence_range": "2707-2710", + "Text": "For\nexample, the nuclides 3\n1 H and 3\n2He are isobars Nuclides with same\nneutron number N but different atomic number Z, for example 198\n80 Hg\nand 197\n79 Au , are called isotones 13 3 SIZE OF THE NUCLEUS\nAs we have seen in Chapter 12, Rutherford was the pioneer who\npostulated and established the existence of the atomic nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2708-2711", + "Text": "Nuclides with same\nneutron number N but different atomic number Z, for example 198\n80 Hg\nand 197\n79 Au , are called isotones 13 3 SIZE OF THE NUCLEUS\nAs we have seen in Chapter 12, Rutherford was the pioneer who\npostulated and established the existence of the atomic nucleus At\nRutherford\u2019s suggestion, Geiger and Marsden performed their classic\nexperiment: on the scattering of a-particles from thin gold foils" + }, + { + "Chapter": "9", + "sentence_range": "2709-2712", + "Text": "13 3 SIZE OF THE NUCLEUS\nAs we have seen in Chapter 12, Rutherford was the pioneer who\npostulated and established the existence of the atomic nucleus At\nRutherford\u2019s suggestion, Geiger and Marsden performed their classic\nexperiment: on the scattering of a-particles from thin gold foils Their\nexperiments revealed that the distance of closest approach to a gold\nnucleus of an a-particle of kinetic energy 5" + }, + { + "Chapter": "9", + "sentence_range": "2710-2713", + "Text": "3 SIZE OF THE NUCLEUS\nAs we have seen in Chapter 12, Rutherford was the pioneer who\npostulated and established the existence of the atomic nucleus At\nRutherford\u2019s suggestion, Geiger and Marsden performed their classic\nexperiment: on the scattering of a-particles from thin gold foils Their\nexperiments revealed that the distance of closest approach to a gold\nnucleus of an a-particle of kinetic energy 5 5 MeV is about 4" + }, + { + "Chapter": "9", + "sentence_range": "2711-2714", + "Text": "At\nRutherford\u2019s suggestion, Geiger and Marsden performed their classic\nexperiment: on the scattering of a-particles from thin gold foils Their\nexperiments revealed that the distance of closest approach to a gold\nnucleus of an a-particle of kinetic energy 5 5 MeV is about 4 0 \u00d7 10\u201314 m" + }, + { + "Chapter": "9", + "sentence_range": "2712-2715", + "Text": "Their\nexperiments revealed that the distance of closest approach to a gold\nnucleus of an a-particle of kinetic energy 5 5 MeV is about 4 0 \u00d7 10\u201314 m The scattering of a-particle by the gold sheet could be understood by\nRutherford by assuming that the coulomb repulsive force was solely\nresponsible for scattering" + }, + { + "Chapter": "9", + "sentence_range": "2713-2716", + "Text": "5 MeV is about 4 0 \u00d7 10\u201314 m The scattering of a-particle by the gold sheet could be understood by\nRutherford by assuming that the coulomb repulsive force was solely\nresponsible for scattering Since the positive charge is confined to the\nnucleus, the actual size of the nucleus has to be less than 4" + }, + { + "Chapter": "9", + "sentence_range": "2714-2717", + "Text": "0 \u00d7 10\u201314 m The scattering of a-particle by the gold sheet could be understood by\nRutherford by assuming that the coulomb repulsive force was solely\nresponsible for scattering Since the positive charge is confined to the\nnucleus, the actual size of the nucleus has to be less than 4 0 \u00d7 10\u201314 m" + }, + { + "Chapter": "9", + "sentence_range": "2715-2718", + "Text": "The scattering of a-particle by the gold sheet could be understood by\nRutherford by assuming that the coulomb repulsive force was solely\nresponsible for scattering Since the positive charge is confined to the\nnucleus, the actual size of the nucleus has to be less than 4 0 \u00d7 10\u201314 m If we use a-particles of higher energies than 5" + }, + { + "Chapter": "9", + "sentence_range": "2716-2719", + "Text": "Since the positive charge is confined to the\nnucleus, the actual size of the nucleus has to be less than 4 0 \u00d7 10\u201314 m If we use a-particles of higher energies than 5 5 MeV, the distance of\nclosest approach to the gold nucleus will be smaller and at some point\nthe scattering will begin to be affected by the short range nuclear forces,\nand differ from Rutherford\u2019s calculations" + }, + { + "Chapter": "9", + "sentence_range": "2717-2720", + "Text": "0 \u00d7 10\u201314 m If we use a-particles of higher energies than 5 5 MeV, the distance of\nclosest approach to the gold nucleus will be smaller and at some point\nthe scattering will begin to be affected by the short range nuclear forces,\nand differ from Rutherford\u2019s calculations Rutherford\u2019s calculations are\nbased on pure coulomb repulsion between the positive charges of the a-\nparticle and the gold nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2718-2721", + "Text": "If we use a-particles of higher energies than 5 5 MeV, the distance of\nclosest approach to the gold nucleus will be smaller and at some point\nthe scattering will begin to be affected by the short range nuclear forces,\nand differ from Rutherford\u2019s calculations Rutherford\u2019s calculations are\nbased on pure coulomb repulsion between the positive charges of the a-\nparticle and the gold nucleus From the distance at which deviations set\nin, nuclear sizes can be inferred" + }, + { + "Chapter": "9", + "sentence_range": "2719-2722", + "Text": "5 MeV, the distance of\nclosest approach to the gold nucleus will be smaller and at some point\nthe scattering will begin to be affected by the short range nuclear forces,\nand differ from Rutherford\u2019s calculations Rutherford\u2019s calculations are\nbased on pure coulomb repulsion between the positive charges of the a-\nparticle and the gold nucleus From the distance at which deviations set\nin, nuclear sizes can be inferred By performing scattering experiments in which fast electrons, instead\nof a-particles, are projectiles that bombard targets made up of various\nelements, the sizes of nuclei of various elements have been accurately\nmeasured" + }, + { + "Chapter": "9", + "sentence_range": "2720-2723", + "Text": "Rutherford\u2019s calculations are\nbased on pure coulomb repulsion between the positive charges of the a-\nparticle and the gold nucleus From the distance at which deviations set\nin, nuclear sizes can be inferred By performing scattering experiments in which fast electrons, instead\nof a-particles, are projectiles that bombard targets made up of various\nelements, the sizes of nuclei of various elements have been accurately\nmeasured It has been found that a nucleus of mass number A has a radius\nR = R 0 A1/3\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2721-2724", + "Text": "From the distance at which deviations set\nin, nuclear sizes can be inferred By performing scattering experiments in which fast electrons, instead\nof a-particles, are projectiles that bombard targets made up of various\nelements, the sizes of nuclei of various elements have been accurately\nmeasured It has been found that a nucleus of mass number A has a radius\nR = R 0 A1/3\n(13 5)\nwhere R0 = 1" + }, + { + "Chapter": "9", + "sentence_range": "2722-2725", + "Text": "By performing scattering experiments in which fast electrons, instead\nof a-particles, are projectiles that bombard targets made up of various\nelements, the sizes of nuclei of various elements have been accurately\nmeasured It has been found that a nucleus of mass number A has a radius\nR = R 0 A1/3\n(13 5)\nwhere R0 = 1 2 \u00d7 10\u201315 m (=1" + }, + { + "Chapter": "9", + "sentence_range": "2723-2726", + "Text": "It has been found that a nucleus of mass number A has a radius\nR = R 0 A1/3\n(13 5)\nwhere R0 = 1 2 \u00d7 10\u201315 m (=1 2 fm; 1 fm = 10\u201315 m)" + }, + { + "Chapter": "9", + "sentence_range": "2724-2727", + "Text": "5)\nwhere R0 = 1 2 \u00d7 10\u201315 m (=1 2 fm; 1 fm = 10\u201315 m) This means the volume\nof the nucleus, which is proportional to R 3 is proportional to A" + }, + { + "Chapter": "9", + "sentence_range": "2725-2728", + "Text": "2 \u00d7 10\u201315 m (=1 2 fm; 1 fm = 10\u201315 m) This means the volume\nof the nucleus, which is proportional to R 3 is proportional to A Thus the\ndensity of nucleus is a constant, independent of A, for all nuclei" + }, + { + "Chapter": "9", + "sentence_range": "2726-2729", + "Text": "2 fm; 1 fm = 10\u201315 m) This means the volume\nof the nucleus, which is proportional to R 3 is proportional to A Thus the\ndensity of nucleus is a constant, independent of A, for all nuclei Different\nnuclei are like a drop of liquid of constant density" + }, + { + "Chapter": "9", + "sentence_range": "2727-2730", + "Text": "This means the volume\nof the nucleus, which is proportional to R 3 is proportional to A Thus the\ndensity of nucleus is a constant, independent of A, for all nuclei Different\nnuclei are like a drop of liquid of constant density The density of nuclear\nmatter is approximately 2" + }, + { + "Chapter": "9", + "sentence_range": "2728-2731", + "Text": "Thus the\ndensity of nucleus is a constant, independent of A, for all nuclei Different\nnuclei are like a drop of liquid of constant density The density of nuclear\nmatter is approximately 2 3 \u00d7 1017 kg m\u20133" + }, + { + "Chapter": "9", + "sentence_range": "2729-2732", + "Text": "Different\nnuclei are like a drop of liquid of constant density The density of nuclear\nmatter is approximately 2 3 \u00d7 1017 kg m\u20133 This density is very large\ncompared to ordinary matter, say water, which is 103 kg m\u20133" + }, + { + "Chapter": "9", + "sentence_range": "2730-2733", + "Text": "The density of nuclear\nmatter is approximately 2 3 \u00d7 1017 kg m\u20133 This density is very large\ncompared to ordinary matter, say water, which is 103 kg m\u20133 This is\nunderstandable, as we have already seen that most of the atom is empty" + }, + { + "Chapter": "9", + "sentence_range": "2731-2734", + "Text": "3 \u00d7 1017 kg m\u20133 This density is very large\ncompared to ordinary matter, say water, which is 103 kg m\u20133 This is\nunderstandable, as we have already seen that most of the atom is empty Ordinary matter consisting of atoms has a large amount of empty space" + }, + { + "Chapter": "9", + "sentence_range": "2732-2735", + "Text": "This density is very large\ncompared to ordinary matter, say water, which is 103 kg m\u20133 This is\nunderstandable, as we have already seen that most of the atom is empty Ordinary matter consisting of atoms has a large amount of empty space Rationalised 2023-24\nPhysics\n310\n EXAMPLE 13" + }, + { + "Chapter": "9", + "sentence_range": "2733-2736", + "Text": "This is\nunderstandable, as we have already seen that most of the atom is empty Ordinary matter consisting of atoms has a large amount of empty space Rationalised 2023-24\nPhysics\n310\n EXAMPLE 13 2\nExample 13" + }, + { + "Chapter": "9", + "sentence_range": "2734-2737", + "Text": "Ordinary matter consisting of atoms has a large amount of empty space Rationalised 2023-24\nPhysics\n310\n EXAMPLE 13 2\nExample 13 1 Given the mass of iron nucleus as 55" + }, + { + "Chapter": "9", + "sentence_range": "2735-2738", + "Text": "Rationalised 2023-24\nPhysics\n310\n EXAMPLE 13 2\nExample 13 1 Given the mass of iron nucleus as 55 85u and A=56,\nfind the nuclear density" + }, + { + "Chapter": "9", + "sentence_range": "2736-2739", + "Text": "2\nExample 13 1 Given the mass of iron nucleus as 55 85u and A=56,\nfind the nuclear density Solution\nmFe = 55" + }, + { + "Chapter": "9", + "sentence_range": "2737-2740", + "Text": "1 Given the mass of iron nucleus as 55 85u and A=56,\nfind the nuclear density Solution\nmFe = 55 85, u = 9" + }, + { + "Chapter": "9", + "sentence_range": "2738-2741", + "Text": "85u and A=56,\nfind the nuclear density Solution\nmFe = 55 85, u = 9 27 \u00d7 10\u201326 kg\nNuclear density = \nmass\nvolume = \n26\n15 3\n9" + }, + { + "Chapter": "9", + "sentence_range": "2739-2742", + "Text": "Solution\nmFe = 55 85, u = 9 27 \u00d7 10\u201326 kg\nNuclear density = \nmass\nvolume = \n26\n15 3\n9 27 10\n1\n56\n(4 /3)(1" + }, + { + "Chapter": "9", + "sentence_range": "2740-2743", + "Text": "85, u = 9 27 \u00d7 10\u201326 kg\nNuclear density = \nmass\nvolume = \n26\n15 3\n9 27 10\n1\n56\n(4 /3)(1 2\n10\n)\n\u2212\n\u2212\n\u00d7\n\u00d7\n\u03c0\n\u00d7\n = 2" + }, + { + "Chapter": "9", + "sentence_range": "2741-2744", + "Text": "27 \u00d7 10\u201326 kg\nNuclear density = \nmass\nvolume = \n26\n15 3\n9 27 10\n1\n56\n(4 /3)(1 2\n10\n)\n\u2212\n\u2212\n\u00d7\n\u00d7\n\u03c0\n\u00d7\n = 2 29 \u00d7 1017 kg m\u20133\nThe density of matter in neutron stars (an astrophysical object) is\ncomparable to this density" + }, + { + "Chapter": "9", + "sentence_range": "2742-2745", + "Text": "27 10\n1\n56\n(4 /3)(1 2\n10\n)\n\u2212\n\u2212\n\u00d7\n\u00d7\n\u03c0\n\u00d7\n = 2 29 \u00d7 1017 kg m\u20133\nThe density of matter in neutron stars (an astrophysical object) is\ncomparable to this density This shows that matter in these objects\nhas been compressed to such an extent that they resemble a big nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2743-2746", + "Text": "2\n10\n)\n\u2212\n\u2212\n\u00d7\n\u00d7\n\u03c0\n\u00d7\n = 2 29 \u00d7 1017 kg m\u20133\nThe density of matter in neutron stars (an astrophysical object) is\ncomparable to this density This shows that matter in these objects\nhas been compressed to such an extent that they resemble a big nucleus 13" + }, + { + "Chapter": "9", + "sentence_range": "2744-2747", + "Text": "29 \u00d7 1017 kg m\u20133\nThe density of matter in neutron stars (an astrophysical object) is\ncomparable to this density This shows that matter in these objects\nhas been compressed to such an extent that they resemble a big nucleus 13 4 MASS-ENERGY AND NUCLEAR BINDING ENERGY\n13" + }, + { + "Chapter": "9", + "sentence_range": "2745-2748", + "Text": "This shows that matter in these objects\nhas been compressed to such an extent that they resemble a big nucleus 13 4 MASS-ENERGY AND NUCLEAR BINDING ENERGY\n13 4" + }, + { + "Chapter": "9", + "sentence_range": "2746-2749", + "Text": "13 4 MASS-ENERGY AND NUCLEAR BINDING ENERGY\n13 4 1 Mass \u2013 Energy\nEinstein showed from his theory of special relativity that it is necessary\nto treat mass as another form of energy" + }, + { + "Chapter": "9", + "sentence_range": "2747-2750", + "Text": "4 MASS-ENERGY AND NUCLEAR BINDING ENERGY\n13 4 1 Mass \u2013 Energy\nEinstein showed from his theory of special relativity that it is necessary\nto treat mass as another form of energy Before the advent of this theory\nof special relativity it was presumed that mass and energy were conserved\nseparately in a reaction" + }, + { + "Chapter": "9", + "sentence_range": "2748-2751", + "Text": "4 1 Mass \u2013 Energy\nEinstein showed from his theory of special relativity that it is necessary\nto treat mass as another form of energy Before the advent of this theory\nof special relativity it was presumed that mass and energy were conserved\nseparately in a reaction However, Einstein showed that mass is another\nform of energy and one can convert mass-energy into other forms of\nenergy, say kinetic energy and vice-versa" + }, + { + "Chapter": "9", + "sentence_range": "2749-2752", + "Text": "1 Mass \u2013 Energy\nEinstein showed from his theory of special relativity that it is necessary\nto treat mass as another form of energy Before the advent of this theory\nof special relativity it was presumed that mass and energy were conserved\nseparately in a reaction However, Einstein showed that mass is another\nform of energy and one can convert mass-energy into other forms of\nenergy, say kinetic energy and vice-versa Einstein gave the famous mass-energy equivalence relation\nE = mc 2\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2750-2753", + "Text": "Before the advent of this theory\nof special relativity it was presumed that mass and energy were conserved\nseparately in a reaction However, Einstein showed that mass is another\nform of energy and one can convert mass-energy into other forms of\nenergy, say kinetic energy and vice-versa Einstein gave the famous mass-energy equivalence relation\nE = mc 2\n(13 6)\nHere the energy equivalent of mass m is related by the above equation\nand c is the velocity of light in vacuum and is approximately equal to\n3\u00d7108 m s\u20131" + }, + { + "Chapter": "9", + "sentence_range": "2751-2754", + "Text": "However, Einstein showed that mass is another\nform of energy and one can convert mass-energy into other forms of\nenergy, say kinetic energy and vice-versa Einstein gave the famous mass-energy equivalence relation\nE = mc 2\n(13 6)\nHere the energy equivalent of mass m is related by the above equation\nand c is the velocity of light in vacuum and is approximately equal to\n3\u00d7108 m s\u20131 Example 13" + }, + { + "Chapter": "9", + "sentence_range": "2752-2755", + "Text": "Einstein gave the famous mass-energy equivalence relation\nE = mc 2\n(13 6)\nHere the energy equivalent of mass m is related by the above equation\nand c is the velocity of light in vacuum and is approximately equal to\n3\u00d7108 m s\u20131 Example 13 2 Calculate the energy equivalent of 1 g of substance" + }, + { + "Chapter": "9", + "sentence_range": "2753-2756", + "Text": "6)\nHere the energy equivalent of mass m is related by the above equation\nand c is the velocity of light in vacuum and is approximately equal to\n3\u00d7108 m s\u20131 Example 13 2 Calculate the energy equivalent of 1 g of substance Solution\nEnergy, E = 10\u20133 \u00d7 ( 3 \u00d7 108)2 J\n E = 10\u20133 \u00d7 9 \u00d7 1016 = 9 \u00d7 1013 J\nThus, if one gram of matter is converted to energy, there is a release\nof enormous amount of energy" + }, + { + "Chapter": "9", + "sentence_range": "2754-2757", + "Text": "Example 13 2 Calculate the energy equivalent of 1 g of substance Solution\nEnergy, E = 10\u20133 \u00d7 ( 3 \u00d7 108)2 J\n E = 10\u20133 \u00d7 9 \u00d7 1016 = 9 \u00d7 1013 J\nThus, if one gram of matter is converted to energy, there is a release\nof enormous amount of energy Experimental verification of the Einstein\u2019s mass-energy relation has\nbeen achieved in the study of nuclear reactions amongst nucleons, nuclei,\nelectrons and other more recently discovered particles" + }, + { + "Chapter": "9", + "sentence_range": "2755-2758", + "Text": "2 Calculate the energy equivalent of 1 g of substance Solution\nEnergy, E = 10\u20133 \u00d7 ( 3 \u00d7 108)2 J\n E = 10\u20133 \u00d7 9 \u00d7 1016 = 9 \u00d7 1013 J\nThus, if one gram of matter is converted to energy, there is a release\nof enormous amount of energy Experimental verification of the Einstein\u2019s mass-energy relation has\nbeen achieved in the study of nuclear reactions amongst nucleons, nuclei,\nelectrons and other more recently discovered particles In a reaction the\nconservation law of energy states that the initial energy and the final\nenergy are equal provided the energy associated with mass is also\nincluded" + }, + { + "Chapter": "9", + "sentence_range": "2756-2759", + "Text": "Solution\nEnergy, E = 10\u20133 \u00d7 ( 3 \u00d7 108)2 J\n E = 10\u20133 \u00d7 9 \u00d7 1016 = 9 \u00d7 1013 J\nThus, if one gram of matter is converted to energy, there is a release\nof enormous amount of energy Experimental verification of the Einstein\u2019s mass-energy relation has\nbeen achieved in the study of nuclear reactions amongst nucleons, nuclei,\nelectrons and other more recently discovered particles In a reaction the\nconservation law of energy states that the initial energy and the final\nenergy are equal provided the energy associated with mass is also\nincluded This concept is important in understanding nuclear masses\nand the interaction of nuclei with one another" + }, + { + "Chapter": "9", + "sentence_range": "2757-2760", + "Text": "Experimental verification of the Einstein\u2019s mass-energy relation has\nbeen achieved in the study of nuclear reactions amongst nucleons, nuclei,\nelectrons and other more recently discovered particles In a reaction the\nconservation law of energy states that the initial energy and the final\nenergy are equal provided the energy associated with mass is also\nincluded This concept is important in understanding nuclear masses\nand the interaction of nuclei with one another They form the subject\nmatter of the next few sections" + }, + { + "Chapter": "9", + "sentence_range": "2758-2761", + "Text": "In a reaction the\nconservation law of energy states that the initial energy and the final\nenergy are equal provided the energy associated with mass is also\nincluded This concept is important in understanding nuclear masses\nand the interaction of nuclei with one another They form the subject\nmatter of the next few sections 13" + }, + { + "Chapter": "9", + "sentence_range": "2759-2762", + "Text": "This concept is important in understanding nuclear masses\nand the interaction of nuclei with one another They form the subject\nmatter of the next few sections 13 4" + }, + { + "Chapter": "9", + "sentence_range": "2760-2763", + "Text": "They form the subject\nmatter of the next few sections 13 4 2 Nuclear binding energy\nIn Section 13" + }, + { + "Chapter": "9", + "sentence_range": "2761-2764", + "Text": "13 4 2 Nuclear binding energy\nIn Section 13 2 we have seen that the nucleus is made up of neutrons\nand protons" + }, + { + "Chapter": "9", + "sentence_range": "2762-2765", + "Text": "4 2 Nuclear binding energy\nIn Section 13 2 we have seen that the nucleus is made up of neutrons\nand protons Therefore it may be expected that the mass of the nucleus\nis equal to the total mass of its individual protons and neutrons" + }, + { + "Chapter": "9", + "sentence_range": "2763-2766", + "Text": "2 Nuclear binding energy\nIn Section 13 2 we have seen that the nucleus is made up of neutrons\nand protons Therefore it may be expected that the mass of the nucleus\nis equal to the total mass of its individual protons and neutrons However,\n EXAMPLE 13" + }, + { + "Chapter": "9", + "sentence_range": "2764-2767", + "Text": "2 we have seen that the nucleus is made up of neutrons\nand protons Therefore it may be expected that the mass of the nucleus\nis equal to the total mass of its individual protons and neutrons However,\n EXAMPLE 13 1\nRationalised 2023-24\n311\nNuclei\n EXAMPLE 13" + }, + { + "Chapter": "9", + "sentence_range": "2765-2768", + "Text": "Therefore it may be expected that the mass of the nucleus\nis equal to the total mass of its individual protons and neutrons However,\n EXAMPLE 13 1\nRationalised 2023-24\n311\nNuclei\n EXAMPLE 13 3\nthe nuclear mass M is found to be always less than this" + }, + { + "Chapter": "9", + "sentence_range": "2766-2769", + "Text": "However,\n EXAMPLE 13 1\nRationalised 2023-24\n311\nNuclei\n EXAMPLE 13 3\nthe nuclear mass M is found to be always less than this For example, let\nus consider 16\n8 O ; a nucleus which has 8 neutrons and 8 protons" + }, + { + "Chapter": "9", + "sentence_range": "2767-2770", + "Text": "1\nRationalised 2023-24\n311\nNuclei\n EXAMPLE 13 3\nthe nuclear mass M is found to be always less than this For example, let\nus consider 16\n8 O ; a nucleus which has 8 neutrons and 8 protons We\nhave\nMass of 8 neutrons = 8 \u00d7 1" + }, + { + "Chapter": "9", + "sentence_range": "2768-2771", + "Text": "3\nthe nuclear mass M is found to be always less than this For example, let\nus consider 16\n8 O ; a nucleus which has 8 neutrons and 8 protons We\nhave\nMass of 8 neutrons = 8 \u00d7 1 00866 u\nMass of 8 protons = 8 \u00d7 1" + }, + { + "Chapter": "9", + "sentence_range": "2769-2772", + "Text": "For example, let\nus consider 16\n8 O ; a nucleus which has 8 neutrons and 8 protons We\nhave\nMass of 8 neutrons = 8 \u00d7 1 00866 u\nMass of 8 protons = 8 \u00d7 1 00727 u\nMass of 8 electrons = 8 \u00d7 0" + }, + { + "Chapter": "9", + "sentence_range": "2770-2773", + "Text": "We\nhave\nMass of 8 neutrons = 8 \u00d7 1 00866 u\nMass of 8 protons = 8 \u00d7 1 00727 u\nMass of 8 electrons = 8 \u00d7 0 00055 u\nTherefore the expected mass of 16\n= 8 \u00d7 2" + }, + { + "Chapter": "9", + "sentence_range": "2771-2774", + "Text": "00866 u\nMass of 8 protons = 8 \u00d7 1 00727 u\nMass of 8 electrons = 8 \u00d7 0 00055 u\nTherefore the expected mass of 16\n= 8 \u00d7 2 01593 u = 16" + }, + { + "Chapter": "9", + "sentence_range": "2772-2775", + "Text": "00727 u\nMass of 8 electrons = 8 \u00d7 0 00055 u\nTherefore the expected mass of 16\n= 8 \u00d7 2 01593 u = 16 12744 u" + }, + { + "Chapter": "9", + "sentence_range": "2773-2776", + "Text": "00055 u\nTherefore the expected mass of 16\n= 8 \u00d7 2 01593 u = 16 12744 u 8 O nucleus\nThe atomic mass of 16\n8 O found from mass spectroscopy experiments\nis seen to be 15" + }, + { + "Chapter": "9", + "sentence_range": "2774-2777", + "Text": "01593 u = 16 12744 u 8 O nucleus\nThe atomic mass of 16\n8 O found from mass spectroscopy experiments\nis seen to be 15 99493 u" + }, + { + "Chapter": "9", + "sentence_range": "2775-2778", + "Text": "12744 u 8 O nucleus\nThe atomic mass of 16\n8 O found from mass spectroscopy experiments\nis seen to be 15 99493 u Substracting the mass of 8 electrons (8 \u00d7 0" + }, + { + "Chapter": "9", + "sentence_range": "2776-2779", + "Text": "8 O nucleus\nThe atomic mass of 16\n8 O found from mass spectroscopy experiments\nis seen to be 15 99493 u Substracting the mass of 8 electrons (8 \u00d7 0 00055 u)\nfrom this, we get the experimental mass of 16\n8 O nucleus to be 15" + }, + { + "Chapter": "9", + "sentence_range": "2777-2780", + "Text": "99493 u Substracting the mass of 8 electrons (8 \u00d7 0 00055 u)\nfrom this, we get the experimental mass of 16\n8 O nucleus to be 15 99053 u" + }, + { + "Chapter": "9", + "sentence_range": "2778-2781", + "Text": "Substracting the mass of 8 electrons (8 \u00d7 0 00055 u)\nfrom this, we get the experimental mass of 16\n8 O nucleus to be 15 99053 u Thus, we find that the mass of the 16\n8 O nucleus is less than the total\nmass of its constituents by 0" + }, + { + "Chapter": "9", + "sentence_range": "2779-2782", + "Text": "00055 u)\nfrom this, we get the experimental mass of 16\n8 O nucleus to be 15 99053 u Thus, we find that the mass of the 16\n8 O nucleus is less than the total\nmass of its constituents by 0 13691u" + }, + { + "Chapter": "9", + "sentence_range": "2780-2783", + "Text": "99053 u Thus, we find that the mass of the 16\n8 O nucleus is less than the total\nmass of its constituents by 0 13691u The difference in mass of a nucleus\nand its constituents, DM, is called the mass defect, and is given by\n[\n(\n)\n]\np\nn\nM\nZm\nA\nZ m\nM\n\u2206\n=\n+\n\u2212\n\u2212\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2781-2784", + "Text": "Thus, we find that the mass of the 16\n8 O nucleus is less than the total\nmass of its constituents by 0 13691u The difference in mass of a nucleus\nand its constituents, DM, is called the mass defect, and is given by\n[\n(\n)\n]\np\nn\nM\nZm\nA\nZ m\nM\n\u2206\n=\n+\n\u2212\n\u2212\n(13 7)\nWhat is the meaning of the mass defect" + }, + { + "Chapter": "9", + "sentence_range": "2782-2785", + "Text": "13691u The difference in mass of a nucleus\nand its constituents, DM, is called the mass defect, and is given by\n[\n(\n)\n]\np\nn\nM\nZm\nA\nZ m\nM\n\u2206\n=\n+\n\u2212\n\u2212\n(13 7)\nWhat is the meaning of the mass defect It is here that Einstein\u2019s\nequivalence of mass and energy plays a role" + }, + { + "Chapter": "9", + "sentence_range": "2783-2786", + "Text": "The difference in mass of a nucleus\nand its constituents, DM, is called the mass defect, and is given by\n[\n(\n)\n]\np\nn\nM\nZm\nA\nZ m\nM\n\u2206\n=\n+\n\u2212\n\u2212\n(13 7)\nWhat is the meaning of the mass defect It is here that Einstein\u2019s\nequivalence of mass and energy plays a role Since the mass of the oxygen\nnucleus is less that the sum of the masses of its constituents (8 protons\nand 8 neutrons, in the unbound state), the equivalent energy of the oxygen\nnucleus is less than that of the sum of the equivalent energies of its\nconstituents" + }, + { + "Chapter": "9", + "sentence_range": "2784-2787", + "Text": "7)\nWhat is the meaning of the mass defect It is here that Einstein\u2019s\nequivalence of mass and energy plays a role Since the mass of the oxygen\nnucleus is less that the sum of the masses of its constituents (8 protons\nand 8 neutrons, in the unbound state), the equivalent energy of the oxygen\nnucleus is less than that of the sum of the equivalent energies of its\nconstituents If one wants to break the oxygen nucleus into 8 protons\nand 8 neutrons, this extra energy DM c2, has to supplied" + }, + { + "Chapter": "9", + "sentence_range": "2785-2788", + "Text": "It is here that Einstein\u2019s\nequivalence of mass and energy plays a role Since the mass of the oxygen\nnucleus is less that the sum of the masses of its constituents (8 protons\nand 8 neutrons, in the unbound state), the equivalent energy of the oxygen\nnucleus is less than that of the sum of the equivalent energies of its\nconstituents If one wants to break the oxygen nucleus into 8 protons\nand 8 neutrons, this extra energy DM c2, has to supplied This energy\nrequired Eb is related to the mass defect by\nEb = D M c2\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2786-2789", + "Text": "Since the mass of the oxygen\nnucleus is less that the sum of the masses of its constituents (8 protons\nand 8 neutrons, in the unbound state), the equivalent energy of the oxygen\nnucleus is less than that of the sum of the equivalent energies of its\nconstituents If one wants to break the oxygen nucleus into 8 protons\nand 8 neutrons, this extra energy DM c2, has to supplied This energy\nrequired Eb is related to the mass defect by\nEb = D M c2\n(13 8)\nExample 13" + }, + { + "Chapter": "9", + "sentence_range": "2787-2790", + "Text": "If one wants to break the oxygen nucleus into 8 protons\nand 8 neutrons, this extra energy DM c2, has to supplied This energy\nrequired Eb is related to the mass defect by\nEb = D M c2\n(13 8)\nExample 13 3 Find the energy equivalent of one atomic mass unit,\nfirst in Joules and then in MeV" + }, + { + "Chapter": "9", + "sentence_range": "2788-2791", + "Text": "This energy\nrequired Eb is related to the mass defect by\nEb = D M c2\n(13 8)\nExample 13 3 Find the energy equivalent of one atomic mass unit,\nfirst in Joules and then in MeV Using this, express the mass defect\nof 16\n8 O in MeV/c2" + }, + { + "Chapter": "9", + "sentence_range": "2789-2792", + "Text": "8)\nExample 13 3 Find the energy equivalent of one atomic mass unit,\nfirst in Joules and then in MeV Using this, express the mass defect\nof 16\n8 O in MeV/c2 Solution\n1u = 1" + }, + { + "Chapter": "9", + "sentence_range": "2790-2793", + "Text": "3 Find the energy equivalent of one atomic mass unit,\nfirst in Joules and then in MeV Using this, express the mass defect\nof 16\n8 O in MeV/c2 Solution\n1u = 1 6605 \u00d7 10\u201327 kg\nTo convert it into energy units, we multiply it by c 2 and find that\nenergy equivalent = 1" + }, + { + "Chapter": "9", + "sentence_range": "2791-2794", + "Text": "Using this, express the mass defect\nof 16\n8 O in MeV/c2 Solution\n1u = 1 6605 \u00d7 10\u201327 kg\nTo convert it into energy units, we multiply it by c 2 and find that\nenergy equivalent = 1 6605 \u00d7 10\u201327 \u00d7 (2" + }, + { + "Chapter": "9", + "sentence_range": "2792-2795", + "Text": "Solution\n1u = 1 6605 \u00d7 10\u201327 kg\nTo convert it into energy units, we multiply it by c 2 and find that\nenergy equivalent = 1 6605 \u00d7 10\u201327 \u00d7 (2 9979 \u00d7 108)2 kg m2/s2\n = 1" + }, + { + "Chapter": "9", + "sentence_range": "2793-2796", + "Text": "6605 \u00d7 10\u201327 kg\nTo convert it into energy units, we multiply it by c 2 and find that\nenergy equivalent = 1 6605 \u00d7 10\u201327 \u00d7 (2 9979 \u00d7 108)2 kg m2/s2\n = 1 4924 \u00d7 10\u201310 J\n = \n10\n1" + }, + { + "Chapter": "9", + "sentence_range": "2794-2797", + "Text": "6605 \u00d7 10\u201327 \u00d7 (2 9979 \u00d7 108)2 kg m2/s2\n = 1 4924 \u00d7 10\u201310 J\n = \n10\n1 4924 1019\neV\n1" + }, + { + "Chapter": "9", + "sentence_range": "2795-2798", + "Text": "9979 \u00d7 108)2 kg m2/s2\n = 1 4924 \u00d7 10\u201310 J\n = \n10\n1 4924 1019\neV\n1 602 10\n\u2212\n\u2212\n\u00d7\n\u00d7\n = 0" + }, + { + "Chapter": "9", + "sentence_range": "2796-2799", + "Text": "4924 \u00d7 10\u201310 J\n = \n10\n1 4924 1019\neV\n1 602 10\n\u2212\n\u2212\n\u00d7\n\u00d7\n = 0 9315 \u00d7 109 eV\n = 931" + }, + { + "Chapter": "9", + "sentence_range": "2797-2800", + "Text": "4924 1019\neV\n1 602 10\n\u2212\n\u2212\n\u00d7\n\u00d7\n = 0 9315 \u00d7 109 eV\n = 931 5 MeV\nor, 1u = 931" + }, + { + "Chapter": "9", + "sentence_range": "2798-2801", + "Text": "602 10\n\u2212\n\u2212\n\u00d7\n\u00d7\n = 0 9315 \u00d7 109 eV\n = 931 5 MeV\nor, 1u = 931 5 MeV/c2\nFor 16\n8 O , DM = 0" + }, + { + "Chapter": "9", + "sentence_range": "2799-2802", + "Text": "9315 \u00d7 109 eV\n = 931 5 MeV\nor, 1u = 931 5 MeV/c2\nFor 16\n8 O , DM = 0 13691 u = 0" + }, + { + "Chapter": "9", + "sentence_range": "2800-2803", + "Text": "5 MeV\nor, 1u = 931 5 MeV/c2\nFor 16\n8 O , DM = 0 13691 u = 0 13691\u00d7931" + }, + { + "Chapter": "9", + "sentence_range": "2801-2804", + "Text": "5 MeV/c2\nFor 16\n8 O , DM = 0 13691 u = 0 13691\u00d7931 5 MeV/c2\n= 127" + }, + { + "Chapter": "9", + "sentence_range": "2802-2805", + "Text": "13691 u = 0 13691\u00d7931 5 MeV/c2\n= 127 5 MeV/c 2\nThe energy needed to separate 16\n8 O into its constituents is thus\n127" + }, + { + "Chapter": "9", + "sentence_range": "2803-2806", + "Text": "13691\u00d7931 5 MeV/c2\n= 127 5 MeV/c 2\nThe energy needed to separate 16\n8 O into its constituents is thus\n127 5 MeV/c2" + }, + { + "Chapter": "9", + "sentence_range": "2804-2807", + "Text": "5 MeV/c2\n= 127 5 MeV/c 2\nThe energy needed to separate 16\n8 O into its constituents is thus\n127 5 MeV/c2 If a certain number of neutrons and protons are brought together to\nform a nucleus of a certain charge and mass, an energy Eb will be released\nRationalised 2023-24\nPhysics\n312\nin the process" + }, + { + "Chapter": "9", + "sentence_range": "2805-2808", + "Text": "5 MeV/c 2\nThe energy needed to separate 16\n8 O into its constituents is thus\n127 5 MeV/c2 If a certain number of neutrons and protons are brought together to\nform a nucleus of a certain charge and mass, an energy Eb will be released\nRationalised 2023-24\nPhysics\n312\nin the process The energy Eb is called the binding energy of the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2806-2809", + "Text": "5 MeV/c2 If a certain number of neutrons and protons are brought together to\nform a nucleus of a certain charge and mass, an energy Eb will be released\nRationalised 2023-24\nPhysics\n312\nin the process The energy Eb is called the binding energy of the nucleus If we separate a nucleus into its nucleons, we would have to supply a\ntotal energy equal to Eb, to those particles" + }, + { + "Chapter": "9", + "sentence_range": "2807-2810", + "Text": "If a certain number of neutrons and protons are brought together to\nform a nucleus of a certain charge and mass, an energy Eb will be released\nRationalised 2023-24\nPhysics\n312\nin the process The energy Eb is called the binding energy of the nucleus If we separate a nucleus into its nucleons, we would have to supply a\ntotal energy equal to Eb, to those particles Although we cannot tear\napart a nucleus in this way, the nuclear binding energy is still a convenient\nmeasure of how well a nucleus is held together" + }, + { + "Chapter": "9", + "sentence_range": "2808-2811", + "Text": "The energy Eb is called the binding energy of the nucleus If we separate a nucleus into its nucleons, we would have to supply a\ntotal energy equal to Eb, to those particles Although we cannot tear\napart a nucleus in this way, the nuclear binding energy is still a convenient\nmeasure of how well a nucleus is held together A more useful measure\nof the binding between the constituents of the nucleus is the binding\nenergy per nucleon, Ebn, which is the ratio of the binding energy Eb of a\nnucleus to the number of the nucleons, A, in that nucleus:\nEbn = Eb / A\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2809-2812", + "Text": "If we separate a nucleus into its nucleons, we would have to supply a\ntotal energy equal to Eb, to those particles Although we cannot tear\napart a nucleus in this way, the nuclear binding energy is still a convenient\nmeasure of how well a nucleus is held together A more useful measure\nof the binding between the constituents of the nucleus is the binding\nenergy per nucleon, Ebn, which is the ratio of the binding energy Eb of a\nnucleus to the number of the nucleons, A, in that nucleus:\nEbn = Eb / A\n(13 9)\nWe can think of binding energy per nucleon as the average energy\nper nucleon needed to separate a nucleus into its individual nucleons" + }, + { + "Chapter": "9", + "sentence_range": "2810-2813", + "Text": "Although we cannot tear\napart a nucleus in this way, the nuclear binding energy is still a convenient\nmeasure of how well a nucleus is held together A more useful measure\nof the binding between the constituents of the nucleus is the binding\nenergy per nucleon, Ebn, which is the ratio of the binding energy Eb of a\nnucleus to the number of the nucleons, A, in that nucleus:\nEbn = Eb / A\n(13 9)\nWe can think of binding energy per nucleon as the average energy\nper nucleon needed to separate a nucleus into its individual nucleons Figure 13" + }, + { + "Chapter": "9", + "sentence_range": "2811-2814", + "Text": "A more useful measure\nof the binding between the constituents of the nucleus is the binding\nenergy per nucleon, Ebn, which is the ratio of the binding energy Eb of a\nnucleus to the number of the nucleons, A, in that nucleus:\nEbn = Eb / A\n(13 9)\nWe can think of binding energy per nucleon as the average energy\nper nucleon needed to separate a nucleus into its individual nucleons Figure 13 1 is a plot of the\nbinding energy per nucleon Ebn\nversus the mass number A for a\nlarge number of nuclei" + }, + { + "Chapter": "9", + "sentence_range": "2812-2815", + "Text": "9)\nWe can think of binding energy per nucleon as the average energy\nper nucleon needed to separate a nucleus into its individual nucleons Figure 13 1 is a plot of the\nbinding energy per nucleon Ebn\nversus the mass number A for a\nlarge number of nuclei We notice\nthe following main features of\nthe plot:\n(i)\nthe binding energy per\nnucleon, Ebn, is practically\nconstant, i" + }, + { + "Chapter": "9", + "sentence_range": "2813-2816", + "Text": "Figure 13 1 is a plot of the\nbinding energy per nucleon Ebn\nversus the mass number A for a\nlarge number of nuclei We notice\nthe following main features of\nthe plot:\n(i)\nthe binding energy per\nnucleon, Ebn, is practically\nconstant, i e" + }, + { + "Chapter": "9", + "sentence_range": "2814-2817", + "Text": "1 is a plot of the\nbinding energy per nucleon Ebn\nversus the mass number A for a\nlarge number of nuclei We notice\nthe following main features of\nthe plot:\n(i)\nthe binding energy per\nnucleon, Ebn, is practically\nconstant, i e practically\nindependent of the atomic\nnumber for nuclei of middle\nmass number ( 30 < A < 170)" + }, + { + "Chapter": "9", + "sentence_range": "2815-2818", + "Text": "We notice\nthe following main features of\nthe plot:\n(i)\nthe binding energy per\nnucleon, Ebn, is practically\nconstant, i e practically\nindependent of the atomic\nnumber for nuclei of middle\nmass number ( 30 < A < 170) The curve has a maximum of\nabout 8" + }, + { + "Chapter": "9", + "sentence_range": "2816-2819", + "Text": "e practically\nindependent of the atomic\nnumber for nuclei of middle\nmass number ( 30 < A < 170) The curve has a maximum of\nabout 8 75 MeV for A = 56\nand has a value of 7" + }, + { + "Chapter": "9", + "sentence_range": "2817-2820", + "Text": "practically\nindependent of the atomic\nnumber for nuclei of middle\nmass number ( 30 < A < 170) The curve has a maximum of\nabout 8 75 MeV for A = 56\nand has a value of 7 6 MeV\nfor A = 238" + }, + { + "Chapter": "9", + "sentence_range": "2818-2821", + "Text": "The curve has a maximum of\nabout 8 75 MeV for A = 56\nand has a value of 7 6 MeV\nfor A = 238 (ii) Ebn is lower for both light\nnuclei (A<30) and heavy\nnuclei (A>170)" + }, + { + "Chapter": "9", + "sentence_range": "2819-2822", + "Text": "75 MeV for A = 56\nand has a value of 7 6 MeV\nfor A = 238 (ii) Ebn is lower for both light\nnuclei (A<30) and heavy\nnuclei (A>170) We can draw some conclusions from these two observations:\n(i)\nThe force is attractive and sufficiently strong to produce a binding\nenergy of a few MeV per nucleon" + }, + { + "Chapter": "9", + "sentence_range": "2820-2823", + "Text": "6 MeV\nfor A = 238 (ii) Ebn is lower for both light\nnuclei (A<30) and heavy\nnuclei (A>170) We can draw some conclusions from these two observations:\n(i)\nThe force is attractive and sufficiently strong to produce a binding\nenergy of a few MeV per nucleon (ii) The constancy of the binding energy in the range 30 < A < 170 is a\nconsequence of the fact that the nuclear force is short-ranged" + }, + { + "Chapter": "9", + "sentence_range": "2821-2824", + "Text": "(ii) Ebn is lower for both light\nnuclei (A<30) and heavy\nnuclei (A>170) We can draw some conclusions from these two observations:\n(i)\nThe force is attractive and sufficiently strong to produce a binding\nenergy of a few MeV per nucleon (ii) The constancy of the binding energy in the range 30 < A < 170 is a\nconsequence of the fact that the nuclear force is short-ranged Consider\na particular nucleon inside a sufficiently large nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2822-2825", + "Text": "We can draw some conclusions from these two observations:\n(i)\nThe force is attractive and sufficiently strong to produce a binding\nenergy of a few MeV per nucleon (ii) The constancy of the binding energy in the range 30 < A < 170 is a\nconsequence of the fact that the nuclear force is short-ranged Consider\na particular nucleon inside a sufficiently large nucleus It will be under\nthe influence of only some of its neighbours, which come within the\nrange of the nuclear force" + }, + { + "Chapter": "9", + "sentence_range": "2823-2826", + "Text": "(ii) The constancy of the binding energy in the range 30 < A < 170 is a\nconsequence of the fact that the nuclear force is short-ranged Consider\na particular nucleon inside a sufficiently large nucleus It will be under\nthe influence of only some of its neighbours, which come within the\nrange of the nuclear force If any other nucleon is at a distance more\nthan the range of the nuclear force from the particular nucleon it will\nhave no influence on the binding energy of the nucleon under\nconsideration" + }, + { + "Chapter": "9", + "sentence_range": "2824-2827", + "Text": "Consider\na particular nucleon inside a sufficiently large nucleus It will be under\nthe influence of only some of its neighbours, which come within the\nrange of the nuclear force If any other nucleon is at a distance more\nthan the range of the nuclear force from the particular nucleon it will\nhave no influence on the binding energy of the nucleon under\nconsideration If a nucleon can have a maximum of p neighbours\nwithin the range of nuclear force, its binding energy would be\nproportional to p" + }, + { + "Chapter": "9", + "sentence_range": "2825-2828", + "Text": "It will be under\nthe influence of only some of its neighbours, which come within the\nrange of the nuclear force If any other nucleon is at a distance more\nthan the range of the nuclear force from the particular nucleon it will\nhave no influence on the binding energy of the nucleon under\nconsideration If a nucleon can have a maximum of p neighbours\nwithin the range of nuclear force, its binding energy would be\nproportional to p Let the binding energy of the nucleus be pk, where\nk is a constant having the dimensions of energy" + }, + { + "Chapter": "9", + "sentence_range": "2826-2829", + "Text": "If any other nucleon is at a distance more\nthan the range of the nuclear force from the particular nucleon it will\nhave no influence on the binding energy of the nucleon under\nconsideration If a nucleon can have a maximum of p neighbours\nwithin the range of nuclear force, its binding energy would be\nproportional to p Let the binding energy of the nucleus be pk, where\nk is a constant having the dimensions of energy If we increase A by\nadding nucleons they will not change the binding energy of a nucleon\ninside" + }, + { + "Chapter": "9", + "sentence_range": "2827-2830", + "Text": "If a nucleon can have a maximum of p neighbours\nwithin the range of nuclear force, its binding energy would be\nproportional to p Let the binding energy of the nucleus be pk, where\nk is a constant having the dimensions of energy If we increase A by\nadding nucleons they will not change the binding energy of a nucleon\ninside Since most of the nucleons in a large nucleus reside inside it\nand not on the surface, the change in binding energy per nucleon\nwould be small" + }, + { + "Chapter": "9", + "sentence_range": "2828-2831", + "Text": "Let the binding energy of the nucleus be pk, where\nk is a constant having the dimensions of energy If we increase A by\nadding nucleons they will not change the binding energy of a nucleon\ninside Since most of the nucleons in a large nucleus reside inside it\nand not on the surface, the change in binding energy per nucleon\nwould be small The binding energy per nucleon is a constant and is\napproximately equal to pk" + }, + { + "Chapter": "9", + "sentence_range": "2829-2832", + "Text": "If we increase A by\nadding nucleons they will not change the binding energy of a nucleon\ninside Since most of the nucleons in a large nucleus reside inside it\nand not on the surface, the change in binding energy per nucleon\nwould be small The binding energy per nucleon is a constant and is\napproximately equal to pk The property that a given nucleon\nFIGURE 13" + }, + { + "Chapter": "9", + "sentence_range": "2830-2833", + "Text": "Since most of the nucleons in a large nucleus reside inside it\nand not on the surface, the change in binding energy per nucleon\nwould be small The binding energy per nucleon is a constant and is\napproximately equal to pk The property that a given nucleon\nFIGURE 13 1 The binding energy per nucleon\nas a function of mass number" + }, + { + "Chapter": "9", + "sentence_range": "2831-2834", + "Text": "The binding energy per nucleon is a constant and is\napproximately equal to pk The property that a given nucleon\nFIGURE 13 1 The binding energy per nucleon\nas a function of mass number Rationalised 2023-24\n313\nNuclei\ninfluences only nucleons close to it is also referred to as saturation\nproperty of the nuclear force" + }, + { + "Chapter": "9", + "sentence_range": "2832-2835", + "Text": "The property that a given nucleon\nFIGURE 13 1 The binding energy per nucleon\nas a function of mass number Rationalised 2023-24\n313\nNuclei\ninfluences only nucleons close to it is also referred to as saturation\nproperty of the nuclear force (iii) A very heavy nucleus, say A = 240, has lower binding energy per\nnucleon compared to that of a nucleus with A = 120" + }, + { + "Chapter": "9", + "sentence_range": "2833-2836", + "Text": "1 The binding energy per nucleon\nas a function of mass number Rationalised 2023-24\n313\nNuclei\ninfluences only nucleons close to it is also referred to as saturation\nproperty of the nuclear force (iii) A very heavy nucleus, say A = 240, has lower binding energy per\nnucleon compared to that of a nucleus with A = 120 Thus if a\nnucleus A = 240 breaks into two A = 120 nuclei, nucleons get more\ntightly bound" + }, + { + "Chapter": "9", + "sentence_range": "2834-2837", + "Text": "Rationalised 2023-24\n313\nNuclei\ninfluences only nucleons close to it is also referred to as saturation\nproperty of the nuclear force (iii) A very heavy nucleus, say A = 240, has lower binding energy per\nnucleon compared to that of a nucleus with A = 120 Thus if a\nnucleus A = 240 breaks into two A = 120 nuclei, nucleons get more\ntightly bound This implies energy would be released in the process" + }, + { + "Chapter": "9", + "sentence_range": "2835-2838", + "Text": "(iii) A very heavy nucleus, say A = 240, has lower binding energy per\nnucleon compared to that of a nucleus with A = 120 Thus if a\nnucleus A = 240 breaks into two A = 120 nuclei, nucleons get more\ntightly bound This implies energy would be released in the process It has very important implications for energy production through\nfission, to be discussed later in Section 13" + }, + { + "Chapter": "9", + "sentence_range": "2836-2839", + "Text": "Thus if a\nnucleus A = 240 breaks into two A = 120 nuclei, nucleons get more\ntightly bound This implies energy would be released in the process It has very important implications for energy production through\nfission, to be discussed later in Section 13 7" + }, + { + "Chapter": "9", + "sentence_range": "2837-2840", + "Text": "This implies energy would be released in the process It has very important implications for energy production through\nfission, to be discussed later in Section 13 7 1" + }, + { + "Chapter": "9", + "sentence_range": "2838-2841", + "Text": "It has very important implications for energy production through\nfission, to be discussed later in Section 13 7 1 (iv) Consider two very light nuclei (A \u2264 10) joining to form a heavier\nnucleus" + }, + { + "Chapter": "9", + "sentence_range": "2839-2842", + "Text": "7 1 (iv) Consider two very light nuclei (A \u2264 10) joining to form a heavier\nnucleus The binding energy per nucleon of the fused heavier nuclei\nis more than the binding energy per nucleon of the lighter nuclei" + }, + { + "Chapter": "9", + "sentence_range": "2840-2843", + "Text": "1 (iv) Consider two very light nuclei (A \u2264 10) joining to form a heavier\nnucleus The binding energy per nucleon of the fused heavier nuclei\nis more than the binding energy per nucleon of the lighter nuclei This means that the final system is more tightly bound than the initial\nsystem" + }, + { + "Chapter": "9", + "sentence_range": "2841-2844", + "Text": "(iv) Consider two very light nuclei (A \u2264 10) joining to form a heavier\nnucleus The binding energy per nucleon of the fused heavier nuclei\nis more than the binding energy per nucleon of the lighter nuclei This means that the final system is more tightly bound than the initial\nsystem Again energy would be released in such a process of\nfusion" + }, + { + "Chapter": "9", + "sentence_range": "2842-2845", + "Text": "The binding energy per nucleon of the fused heavier nuclei\nis more than the binding energy per nucleon of the lighter nuclei This means that the final system is more tightly bound than the initial\nsystem Again energy would be released in such a process of\nfusion This is the energy source of sun, to be discussed later in\nSection 13" + }, + { + "Chapter": "9", + "sentence_range": "2843-2846", + "Text": "This means that the final system is more tightly bound than the initial\nsystem Again energy would be released in such a process of\nfusion This is the energy source of sun, to be discussed later in\nSection 13 7" + }, + { + "Chapter": "9", + "sentence_range": "2844-2847", + "Text": "Again energy would be released in such a process of\nfusion This is the energy source of sun, to be discussed later in\nSection 13 7 2" + }, + { + "Chapter": "9", + "sentence_range": "2845-2848", + "Text": "This is the energy source of sun, to be discussed later in\nSection 13 7 2 13" + }, + { + "Chapter": "9", + "sentence_range": "2846-2849", + "Text": "7 2 13 5 NUCLEAR FORCE\nThe force that determines the motion of atomic electrons is the familiar\nCoulomb force" + }, + { + "Chapter": "9", + "sentence_range": "2847-2850", + "Text": "2 13 5 NUCLEAR FORCE\nThe force that determines the motion of atomic electrons is the familiar\nCoulomb force In Section 13" + }, + { + "Chapter": "9", + "sentence_range": "2848-2851", + "Text": "13 5 NUCLEAR FORCE\nThe force that determines the motion of atomic electrons is the familiar\nCoulomb force In Section 13 4, we have seen that for average mass\nnuclei the binding energy per nucleon is approximately 8 MeV, which is\nmuch larger than the binding energy in atoms" + }, + { + "Chapter": "9", + "sentence_range": "2849-2852", + "Text": "5 NUCLEAR FORCE\nThe force that determines the motion of atomic electrons is the familiar\nCoulomb force In Section 13 4, we have seen that for average mass\nnuclei the binding energy per nucleon is approximately 8 MeV, which is\nmuch larger than the binding energy in atoms Therefore, to bind a\nnucleus together there must be a strong attractive force of a totally\ndifferent kind" + }, + { + "Chapter": "9", + "sentence_range": "2850-2853", + "Text": "In Section 13 4, we have seen that for average mass\nnuclei the binding energy per nucleon is approximately 8 MeV, which is\nmuch larger than the binding energy in atoms Therefore, to bind a\nnucleus together there must be a strong attractive force of a totally\ndifferent kind It must be strong enough to overcome the repulsion\nbetween the (positively charged) protons and to bind both protons and\nneutrons into the tiny nuclear volume" + }, + { + "Chapter": "9", + "sentence_range": "2851-2854", + "Text": "4, we have seen that for average mass\nnuclei the binding energy per nucleon is approximately 8 MeV, which is\nmuch larger than the binding energy in atoms Therefore, to bind a\nnucleus together there must be a strong attractive force of a totally\ndifferent kind It must be strong enough to overcome the repulsion\nbetween the (positively charged) protons and to bind both protons and\nneutrons into the tiny nuclear volume We have already seen\nthat the constancy of binding energy per nucleon can be\nunderstood in terms of its short-range" + }, + { + "Chapter": "9", + "sentence_range": "2852-2855", + "Text": "Therefore, to bind a\nnucleus together there must be a strong attractive force of a totally\ndifferent kind It must be strong enough to overcome the repulsion\nbetween the (positively charged) protons and to bind both protons and\nneutrons into the tiny nuclear volume We have already seen\nthat the constancy of binding energy per nucleon can be\nunderstood in terms of its short-range Many features of the\nnuclear binding force are summarised below" + }, + { + "Chapter": "9", + "sentence_range": "2853-2856", + "Text": "It must be strong enough to overcome the repulsion\nbetween the (positively charged) protons and to bind both protons and\nneutrons into the tiny nuclear volume We have already seen\nthat the constancy of binding energy per nucleon can be\nunderstood in terms of its short-range Many features of the\nnuclear binding force are summarised below These are\nobtained from a variety of experiments carried out during 1930\nto 1950" + }, + { + "Chapter": "9", + "sentence_range": "2854-2857", + "Text": "We have already seen\nthat the constancy of binding energy per nucleon can be\nunderstood in terms of its short-range Many features of the\nnuclear binding force are summarised below These are\nobtained from a variety of experiments carried out during 1930\nto 1950 (i)\nThe nuclear force is much stronger than the Coulomb force\nacting between charges or the gravitational forces between\nmasses" + }, + { + "Chapter": "9", + "sentence_range": "2855-2858", + "Text": "Many features of the\nnuclear binding force are summarised below These are\nobtained from a variety of experiments carried out during 1930\nto 1950 (i)\nThe nuclear force is much stronger than the Coulomb force\nacting between charges or the gravitational forces between\nmasses The nuclear binding force has to dominate over\nthe Coulomb repulsive force between protons inside the\nnucleus" + }, + { + "Chapter": "9", + "sentence_range": "2856-2859", + "Text": "These are\nobtained from a variety of experiments carried out during 1930\nto 1950 (i)\nThe nuclear force is much stronger than the Coulomb force\nacting between charges or the gravitational forces between\nmasses The nuclear binding force has to dominate over\nthe Coulomb repulsive force between protons inside the\nnucleus This happens only because the nuclear force is\nmuch stronger than the coulomb force" + }, + { + "Chapter": "9", + "sentence_range": "2857-2860", + "Text": "(i)\nThe nuclear force is much stronger than the Coulomb force\nacting between charges or the gravitational forces between\nmasses The nuclear binding force has to dominate over\nthe Coulomb repulsive force between protons inside the\nnucleus This happens only because the nuclear force is\nmuch stronger than the coulomb force The gravitational\nforce is much weaker than even Coulomb force" + }, + { + "Chapter": "9", + "sentence_range": "2858-2861", + "Text": "The nuclear binding force has to dominate over\nthe Coulomb repulsive force between protons inside the\nnucleus This happens only because the nuclear force is\nmuch stronger than the coulomb force The gravitational\nforce is much weaker than even Coulomb force (ii) The nuclear force between two nucleons falls rapidly to\nzero as their distance is more than a few femtometres" + }, + { + "Chapter": "9", + "sentence_range": "2859-2862", + "Text": "This happens only because the nuclear force is\nmuch stronger than the coulomb force The gravitational\nforce is much weaker than even Coulomb force (ii) The nuclear force between two nucleons falls rapidly to\nzero as their distance is more than a few femtometres This\nleads to saturation of forces in a medium or a large-sized\nnucleus, which is the reason for the constancy of the\nbinding energy per nucleon" + }, + { + "Chapter": "9", + "sentence_range": "2860-2863", + "Text": "The gravitational\nforce is much weaker than even Coulomb force (ii) The nuclear force between two nucleons falls rapidly to\nzero as their distance is more than a few femtometres This\nleads to saturation of forces in a medium or a large-sized\nnucleus, which is the reason for the constancy of the\nbinding energy per nucleon A rough plot of the potential energy between two nucleons\nas a function of distance is shown in the Fig" + }, + { + "Chapter": "9", + "sentence_range": "2861-2864", + "Text": "(ii) The nuclear force between two nucleons falls rapidly to\nzero as their distance is more than a few femtometres This\nleads to saturation of forces in a medium or a large-sized\nnucleus, which is the reason for the constancy of the\nbinding energy per nucleon A rough plot of the potential energy between two nucleons\nas a function of distance is shown in the Fig 13" + }, + { + "Chapter": "9", + "sentence_range": "2862-2865", + "Text": "This\nleads to saturation of forces in a medium or a large-sized\nnucleus, which is the reason for the constancy of the\nbinding energy per nucleon A rough plot of the potential energy between two nucleons\nas a function of distance is shown in the Fig 13 2" + }, + { + "Chapter": "9", + "sentence_range": "2863-2866", + "Text": "A rough plot of the potential energy between two nucleons\nas a function of distance is shown in the Fig 13 2 The\npotential energy is a minimum at a distance r0 of about\n0" + }, + { + "Chapter": "9", + "sentence_range": "2864-2867", + "Text": "13 2 The\npotential energy is a minimum at a distance r0 of about\n0 8 fm" + }, + { + "Chapter": "9", + "sentence_range": "2865-2868", + "Text": "2 The\npotential energy is a minimum at a distance r0 of about\n0 8 fm This means that the force is attractive for distances larger\nthan 0" + }, + { + "Chapter": "9", + "sentence_range": "2866-2869", + "Text": "The\npotential energy is a minimum at a distance r0 of about\n0 8 fm This means that the force is attractive for distances larger\nthan 0 8 fm and repulsive if they are separated by distances less\nthan 0" + }, + { + "Chapter": "9", + "sentence_range": "2867-2870", + "Text": "8 fm This means that the force is attractive for distances larger\nthan 0 8 fm and repulsive if they are separated by distances less\nthan 0 8 fm" + }, + { + "Chapter": "9", + "sentence_range": "2868-2871", + "Text": "This means that the force is attractive for distances larger\nthan 0 8 fm and repulsive if they are separated by distances less\nthan 0 8 fm FIGURE 13" + }, + { + "Chapter": "9", + "sentence_range": "2869-2872", + "Text": "8 fm and repulsive if they are separated by distances less\nthan 0 8 fm FIGURE 13 2 Potential energy\nof a pair of nucleons as a\nfunction of their separation" + }, + { + "Chapter": "9", + "sentence_range": "2870-2873", + "Text": "8 fm FIGURE 13 2 Potential energy\nof a pair of nucleons as a\nfunction of their separation For a separation greater\nthan r0, the force is attractive\nand for separations less\nthan r0, the force is\nstrongly repulsive" + }, + { + "Chapter": "9", + "sentence_range": "2871-2874", + "Text": "FIGURE 13 2 Potential energy\nof a pair of nucleons as a\nfunction of their separation For a separation greater\nthan r0, the force is attractive\nand for separations less\nthan r0, the force is\nstrongly repulsive Rationalised 2023-24\nPhysics\n314\n(iii) The nuclear force between neutron-neutron, proton-neutron and\nproton-proton is approximately the same" + }, + { + "Chapter": "9", + "sentence_range": "2872-2875", + "Text": "2 Potential energy\nof a pair of nucleons as a\nfunction of their separation For a separation greater\nthan r0, the force is attractive\nand for separations less\nthan r0, the force is\nstrongly repulsive Rationalised 2023-24\nPhysics\n314\n(iii) The nuclear force between neutron-neutron, proton-neutron and\nproton-proton is approximately the same The nuclear force does not\ndepend on the electric charge" + }, + { + "Chapter": "9", + "sentence_range": "2873-2876", + "Text": "For a separation greater\nthan r0, the force is attractive\nand for separations less\nthan r0, the force is\nstrongly repulsive Rationalised 2023-24\nPhysics\n314\n(iii) The nuclear force between neutron-neutron, proton-neutron and\nproton-proton is approximately the same The nuclear force does not\ndepend on the electric charge Unlike Coulomb\u2019s law or the Newton\u2019s law of gravitation there is no\nsimple mathematical form of the nuclear force" + }, + { + "Chapter": "9", + "sentence_range": "2874-2877", + "Text": "Rationalised 2023-24\nPhysics\n314\n(iii) The nuclear force between neutron-neutron, proton-neutron and\nproton-proton is approximately the same The nuclear force does not\ndepend on the electric charge Unlike Coulomb\u2019s law or the Newton\u2019s law of gravitation there is no\nsimple mathematical form of the nuclear force 13" + }, + { + "Chapter": "9", + "sentence_range": "2875-2878", + "Text": "The nuclear force does not\ndepend on the electric charge Unlike Coulomb\u2019s law or the Newton\u2019s law of gravitation there is no\nsimple mathematical form of the nuclear force 13 6 RADIOACTIVITY\nA" + }, + { + "Chapter": "9", + "sentence_range": "2876-2879", + "Text": "Unlike Coulomb\u2019s law or the Newton\u2019s law of gravitation there is no\nsimple mathematical form of the nuclear force 13 6 RADIOACTIVITY\nA H" + }, + { + "Chapter": "9", + "sentence_range": "2877-2880", + "Text": "13 6 RADIOACTIVITY\nA H Becquerel discovered radioactivity in 1896 purely by accident" + }, + { + "Chapter": "9", + "sentence_range": "2878-2881", + "Text": "6 RADIOACTIVITY\nA H Becquerel discovered radioactivity in 1896 purely by accident While\nstudying the fluorescence and phosphorescence of compounds irradiated\nwith visible light, Becquerel observed an interesting phenomenon" + }, + { + "Chapter": "9", + "sentence_range": "2879-2882", + "Text": "H Becquerel discovered radioactivity in 1896 purely by accident While\nstudying the fluorescence and phosphorescence of compounds irradiated\nwith visible light, Becquerel observed an interesting phenomenon After\nilluminating some pieces of uranium-potassium sulphate with visible\nlight, he wrapped them in black paper and separated the package from a\nphotographic plate by a piece of silver" + }, + { + "Chapter": "9", + "sentence_range": "2880-2883", + "Text": "Becquerel discovered radioactivity in 1896 purely by accident While\nstudying the fluorescence and phosphorescence of compounds irradiated\nwith visible light, Becquerel observed an interesting phenomenon After\nilluminating some pieces of uranium-potassium sulphate with visible\nlight, he wrapped them in black paper and separated the package from a\nphotographic plate by a piece of silver When, after several hours of\nexposure, the photographic plate was developed, it showed blackening\ndue to something that must have been emitted by the compound and\nwas able to penetrate both black paper and the silver" + }, + { + "Chapter": "9", + "sentence_range": "2881-2884", + "Text": "While\nstudying the fluorescence and phosphorescence of compounds irradiated\nwith visible light, Becquerel observed an interesting phenomenon After\nilluminating some pieces of uranium-potassium sulphate with visible\nlight, he wrapped them in black paper and separated the package from a\nphotographic plate by a piece of silver When, after several hours of\nexposure, the photographic plate was developed, it showed blackening\ndue to something that must have been emitted by the compound and\nwas able to penetrate both black paper and the silver Experiments performed subsequently showed that radioactivity was\na nuclear phenomenon in which an unstable nucleus undergoes a decay" + }, + { + "Chapter": "9", + "sentence_range": "2882-2885", + "Text": "After\nilluminating some pieces of uranium-potassium sulphate with visible\nlight, he wrapped them in black paper and separated the package from a\nphotographic plate by a piece of silver When, after several hours of\nexposure, the photographic plate was developed, it showed blackening\ndue to something that must have been emitted by the compound and\nwas able to penetrate both black paper and the silver Experiments performed subsequently showed that radioactivity was\na nuclear phenomenon in which an unstable nucleus undergoes a decay This is referred to as radioactive decay" + }, + { + "Chapter": "9", + "sentence_range": "2883-2886", + "Text": "When, after several hours of\nexposure, the photographic plate was developed, it showed blackening\ndue to something that must have been emitted by the compound and\nwas able to penetrate both black paper and the silver Experiments performed subsequently showed that radioactivity was\na nuclear phenomenon in which an unstable nucleus undergoes a decay This is referred to as radioactive decay Three types of radioactive decay\noccur in nature :\n(i) a-decay in which a helium nucleus \n4\n2He is emitted;\n(ii) b-decay in which electrons or positrons (particles with the same mass\nas electrons, but with a charge exactly opposite to that of electron)\nare emitted;\n(iii) g-decay in which high energy (hundreds of keV or more) photons are\nemitted" + }, + { + "Chapter": "9", + "sentence_range": "2884-2887", + "Text": "Experiments performed subsequently showed that radioactivity was\na nuclear phenomenon in which an unstable nucleus undergoes a decay This is referred to as radioactive decay Three types of radioactive decay\noccur in nature :\n(i) a-decay in which a helium nucleus \n4\n2He is emitted;\n(ii) b-decay in which electrons or positrons (particles with the same mass\nas electrons, but with a charge exactly opposite to that of electron)\nare emitted;\n(iii) g-decay in which high energy (hundreds of keV or more) photons are\nemitted Each of these decay will be considered in subsequent sub-sections" + }, + { + "Chapter": "9", + "sentence_range": "2885-2888", + "Text": "This is referred to as radioactive decay Three types of radioactive decay\noccur in nature :\n(i) a-decay in which a helium nucleus \n4\n2He is emitted;\n(ii) b-decay in which electrons or positrons (particles with the same mass\nas electrons, but with a charge exactly opposite to that of electron)\nare emitted;\n(iii) g-decay in which high energy (hundreds of keV or more) photons are\nemitted Each of these decay will be considered in subsequent sub-sections 13" + }, + { + "Chapter": "9", + "sentence_range": "2886-2889", + "Text": "Three types of radioactive decay\noccur in nature :\n(i) a-decay in which a helium nucleus \n4\n2He is emitted;\n(ii) b-decay in which electrons or positrons (particles with the same mass\nas electrons, but with a charge exactly opposite to that of electron)\nare emitted;\n(iii) g-decay in which high energy (hundreds of keV or more) photons are\nemitted Each of these decay will be considered in subsequent sub-sections 13 7 NUCLEAR ENERGY\nThe curve of binding energy per nucleon Ebn, given in Fig" + }, + { + "Chapter": "9", + "sentence_range": "2887-2890", + "Text": "Each of these decay will be considered in subsequent sub-sections 13 7 NUCLEAR ENERGY\nThe curve of binding energy per nucleon Ebn, given in Fig 13" + }, + { + "Chapter": "9", + "sentence_range": "2888-2891", + "Text": "13 7 NUCLEAR ENERGY\nThe curve of binding energy per nucleon Ebn, given in Fig 13 1, has\na long flat middle region between A = 30 and A = 170" + }, + { + "Chapter": "9", + "sentence_range": "2889-2892", + "Text": "7 NUCLEAR ENERGY\nThe curve of binding energy per nucleon Ebn, given in Fig 13 1, has\na long flat middle region between A = 30 and A = 170 In this region\nthe binding energy per nucleon is nearly constant (8" + }, + { + "Chapter": "9", + "sentence_range": "2890-2893", + "Text": "13 1, has\na long flat middle region between A = 30 and A = 170 In this region\nthe binding energy per nucleon is nearly constant (8 0 MeV)" + }, + { + "Chapter": "9", + "sentence_range": "2891-2894", + "Text": "1, has\na long flat middle region between A = 30 and A = 170 In this region\nthe binding energy per nucleon is nearly constant (8 0 MeV) For\nthe lighter nuclei region, A < 30, and for the heavier nuclei region,\nA > 170, the binding energy per nucleon is less than 8" + }, + { + "Chapter": "9", + "sentence_range": "2892-2895", + "Text": "In this region\nthe binding energy per nucleon is nearly constant (8 0 MeV) For\nthe lighter nuclei region, A < 30, and for the heavier nuclei region,\nA > 170, the binding energy per nucleon is less than 8 0 MeV, as we\nhave noted earlier" + }, + { + "Chapter": "9", + "sentence_range": "2893-2896", + "Text": "0 MeV) For\nthe lighter nuclei region, A < 30, and for the heavier nuclei region,\nA > 170, the binding energy per nucleon is less than 8 0 MeV, as we\nhave noted earlier Now, the greater the binding energy, the less is the\ntotal mass of a bound system, such as a nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2894-2897", + "Text": "For\nthe lighter nuclei region, A < 30, and for the heavier nuclei region,\nA > 170, the binding energy per nucleon is less than 8 0 MeV, as we\nhave noted earlier Now, the greater the binding energy, the less is the\ntotal mass of a bound system, such as a nucleus Consequently, if nuclei\nwith less total binding energy transform to nuclei with greater binding\nenergy, there will be a net energy release" + }, + { + "Chapter": "9", + "sentence_range": "2895-2898", + "Text": "0 MeV, as we\nhave noted earlier Now, the greater the binding energy, the less is the\ntotal mass of a bound system, such as a nucleus Consequently, if nuclei\nwith less total binding energy transform to nuclei with greater binding\nenergy, there will be a net energy release This is what happens when a\nheavy nucleus decays into two or more intermediate mass fragments\n(fission) or when light nuclei fuse into a havier nucleus (fusion" + }, + { + "Chapter": "9", + "sentence_range": "2896-2899", + "Text": "Now, the greater the binding energy, the less is the\ntotal mass of a bound system, such as a nucleus Consequently, if nuclei\nwith less total binding energy transform to nuclei with greater binding\nenergy, there will be a net energy release This is what happens when a\nheavy nucleus decays into two or more intermediate mass fragments\n(fission) or when light nuclei fuse into a havier nucleus (fusion )\nExothermic chemical reactions underlie conventional energy sources\nsuch as coal or petroleum" + }, + { + "Chapter": "9", + "sentence_range": "2897-2900", + "Text": "Consequently, if nuclei\nwith less total binding energy transform to nuclei with greater binding\nenergy, there will be a net energy release This is what happens when a\nheavy nucleus decays into two or more intermediate mass fragments\n(fission) or when light nuclei fuse into a havier nucleus (fusion )\nExothermic chemical reactions underlie conventional energy sources\nsuch as coal or petroleum Here the energies involved are in the range of\nelectron volts" + }, + { + "Chapter": "9", + "sentence_range": "2898-2901", + "Text": "This is what happens when a\nheavy nucleus decays into two or more intermediate mass fragments\n(fission) or when light nuclei fuse into a havier nucleus (fusion )\nExothermic chemical reactions underlie conventional energy sources\nsuch as coal or petroleum Here the energies involved are in the range of\nelectron volts On the other hand, in a nuclear reaction, the energy release\nis of the order of MeV" + }, + { + "Chapter": "9", + "sentence_range": "2899-2902", + "Text": ")\nExothermic chemical reactions underlie conventional energy sources\nsuch as coal or petroleum Here the energies involved are in the range of\nelectron volts On the other hand, in a nuclear reaction, the energy release\nis of the order of MeV Thus for the same quantity of matter, nuclear\nsources produce a million times more energy than a chemical source" + }, + { + "Chapter": "9", + "sentence_range": "2900-2903", + "Text": "Here the energies involved are in the range of\nelectron volts On the other hand, in a nuclear reaction, the energy release\nis of the order of MeV Thus for the same quantity of matter, nuclear\nsources produce a million times more energy than a chemical source Fission of 1 kg of uranium, for example, generates 1014 J of energy;\ncompare it with burning of 1 kg of coal that gives 107 J" + }, + { + "Chapter": "9", + "sentence_range": "2901-2904", + "Text": "On the other hand, in a nuclear reaction, the energy release\nis of the order of MeV Thus for the same quantity of matter, nuclear\nsources produce a million times more energy than a chemical source Fission of 1 kg of uranium, for example, generates 1014 J of energy;\ncompare it with burning of 1 kg of coal that gives 107 J Rationalised 2023-24\n315\nNuclei\n13" + }, + { + "Chapter": "9", + "sentence_range": "2902-2905", + "Text": "Thus for the same quantity of matter, nuclear\nsources produce a million times more energy than a chemical source Fission of 1 kg of uranium, for example, generates 1014 J of energy;\ncompare it with burning of 1 kg of coal that gives 107 J Rationalised 2023-24\n315\nNuclei\n13 7" + }, + { + "Chapter": "9", + "sentence_range": "2903-2906", + "Text": "Fission of 1 kg of uranium, for example, generates 1014 J of energy;\ncompare it with burning of 1 kg of coal that gives 107 J Rationalised 2023-24\n315\nNuclei\n13 7 1 Fission\nNew possibilities emerge when we go beyond natural radioactive decays\nand study nuclear reactions by bombarding nuclei with other nuclear\nparticles such as proton, neutron, a-particle, etc" + }, + { + "Chapter": "9", + "sentence_range": "2904-2907", + "Text": "Rationalised 2023-24\n315\nNuclei\n13 7 1 Fission\nNew possibilities emerge when we go beyond natural radioactive decays\nand study nuclear reactions by bombarding nuclei with other nuclear\nparticles such as proton, neutron, a-particle, etc A most important neutron-induced nuclear reaction is fission" + }, + { + "Chapter": "9", + "sentence_range": "2905-2908", + "Text": "7 1 Fission\nNew possibilities emerge when we go beyond natural radioactive decays\nand study nuclear reactions by bombarding nuclei with other nuclear\nparticles such as proton, neutron, a-particle, etc A most important neutron-induced nuclear reaction is fission An\nexample of fission is when a uranium isotope 235\n92 U bombarded with a\nneutron breaks into two intermediate mass nuclear fragments\n1\n235\n236\n144\n89\n1\n0\n92\n92\n56\n36\n0\nn\nU\nU\nBa\nKr\n3 n\n+\n\u2192\n\u2192\n+\n+\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2906-2909", + "Text": "1 Fission\nNew possibilities emerge when we go beyond natural radioactive decays\nand study nuclear reactions by bombarding nuclei with other nuclear\nparticles such as proton, neutron, a-particle, etc A most important neutron-induced nuclear reaction is fission An\nexample of fission is when a uranium isotope 235\n92 U bombarded with a\nneutron breaks into two intermediate mass nuclear fragments\n1\n235\n236\n144\n89\n1\n0\n92\n92\n56\n36\n0\nn\nU\nU\nBa\nKr\n3 n\n+\n\u2192\n\u2192\n+\n+\n(13 10)\nThe same reaction can produce other pairs of intermediate mass\nfragments\n1\n235\n236\n133\n99\n1\n0\n92\n92\n51\n41\n0\nn\nU\nU\nSb\nNb\n4 n\n+\n\u2192\n\u2192\n+\n+\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2907-2910", + "Text": "A most important neutron-induced nuclear reaction is fission An\nexample of fission is when a uranium isotope 235\n92 U bombarded with a\nneutron breaks into two intermediate mass nuclear fragments\n1\n235\n236\n144\n89\n1\n0\n92\n92\n56\n36\n0\nn\nU\nU\nBa\nKr\n3 n\n+\n\u2192\n\u2192\n+\n+\n(13 10)\nThe same reaction can produce other pairs of intermediate mass\nfragments\n1\n235\n236\n133\n99\n1\n0\n92\n92\n51\n41\n0\nn\nU\nU\nSb\nNb\n4 n\n+\n\u2192\n\u2192\n+\n+\n(13 11)\nOr, as another example,\n1\n235\n140\n94\n1\n0\n92\n54\n38\n0\nn\nU\nXe\nSr\n2 n\n+\n\u2192\n+\n+\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2908-2911", + "Text": "An\nexample of fission is when a uranium isotope 235\n92 U bombarded with a\nneutron breaks into two intermediate mass nuclear fragments\n1\n235\n236\n144\n89\n1\n0\n92\n92\n56\n36\n0\nn\nU\nU\nBa\nKr\n3 n\n+\n\u2192\n\u2192\n+\n+\n(13 10)\nThe same reaction can produce other pairs of intermediate mass\nfragments\n1\n235\n236\n133\n99\n1\n0\n92\n92\n51\n41\n0\nn\nU\nU\nSb\nNb\n4 n\n+\n\u2192\n\u2192\n+\n+\n(13 11)\nOr, as another example,\n1\n235\n140\n94\n1\n0\n92\n54\n38\n0\nn\nU\nXe\nSr\n2 n\n+\n\u2192\n+\n+\n(13 12)\nThe fragment products are radioactive nuclei; they emit b particles in\nsuccession to achieve stable end products" + }, + { + "Chapter": "9", + "sentence_range": "2909-2912", + "Text": "10)\nThe same reaction can produce other pairs of intermediate mass\nfragments\n1\n235\n236\n133\n99\n1\n0\n92\n92\n51\n41\n0\nn\nU\nU\nSb\nNb\n4 n\n+\n\u2192\n\u2192\n+\n+\n(13 11)\nOr, as another example,\n1\n235\n140\n94\n1\n0\n92\n54\n38\n0\nn\nU\nXe\nSr\n2 n\n+\n\u2192\n+\n+\n(13 12)\nThe fragment products are radioactive nuclei; they emit b particles in\nsuccession to achieve stable end products The energy released (the Q value ) in the fission reaction of nuclei like\nuranium is of the order of 200 MeV per fissioning nucleus" + }, + { + "Chapter": "9", + "sentence_range": "2910-2913", + "Text": "11)\nOr, as another example,\n1\n235\n140\n94\n1\n0\n92\n54\n38\n0\nn\nU\nXe\nSr\n2 n\n+\n\u2192\n+\n+\n(13 12)\nThe fragment products are radioactive nuclei; they emit b particles in\nsuccession to achieve stable end products The energy released (the Q value ) in the fission reaction of nuclei like\nuranium is of the order of 200 MeV per fissioning nucleus This is\nestimated as follows:\nLet us take a nucleus with A = 240 breaking into two fragments each\nof A = 120" + }, + { + "Chapter": "9", + "sentence_range": "2911-2914", + "Text": "12)\nThe fragment products are radioactive nuclei; they emit b particles in\nsuccession to achieve stable end products The energy released (the Q value ) in the fission reaction of nuclei like\nuranium is of the order of 200 MeV per fissioning nucleus This is\nestimated as follows:\nLet us take a nucleus with A = 240 breaking into two fragments each\nof A = 120 Then\nEbn for A = 240 nucleus is about 7" + }, + { + "Chapter": "9", + "sentence_range": "2912-2915", + "Text": "The energy released (the Q value ) in the fission reaction of nuclei like\nuranium is of the order of 200 MeV per fissioning nucleus This is\nestimated as follows:\nLet us take a nucleus with A = 240 breaking into two fragments each\nof A = 120 Then\nEbn for A = 240 nucleus is about 7 6 MeV,\nEbn for the two A = 120 fragment nuclei is about 8" + }, + { + "Chapter": "9", + "sentence_range": "2913-2916", + "Text": "This is\nestimated as follows:\nLet us take a nucleus with A = 240 breaking into two fragments each\nof A = 120 Then\nEbn for A = 240 nucleus is about 7 6 MeV,\nEbn for the two A = 120 fragment nuclei is about 8 5 MeV" + }, + { + "Chapter": "9", + "sentence_range": "2914-2917", + "Text": "Then\nEbn for A = 240 nucleus is about 7 6 MeV,\nEbn for the two A = 120 fragment nuclei is about 8 5 MeV \\\nGain in binding energy for nucleon is about 0" + }, + { + "Chapter": "9", + "sentence_range": "2915-2918", + "Text": "6 MeV,\nEbn for the two A = 120 fragment nuclei is about 8 5 MeV \\\nGain in binding energy for nucleon is about 0 9 MeV" + }, + { + "Chapter": "9", + "sentence_range": "2916-2919", + "Text": "5 MeV \\\nGain in binding energy for nucleon is about 0 9 MeV Hence the total gain in binding energy is 240\u00d70" + }, + { + "Chapter": "9", + "sentence_range": "2917-2920", + "Text": "\\\nGain in binding energy for nucleon is about 0 9 MeV Hence the total gain in binding energy is 240\u00d70 9 or 216 MeV" + }, + { + "Chapter": "9", + "sentence_range": "2918-2921", + "Text": "9 MeV Hence the total gain in binding energy is 240\u00d70 9 or 216 MeV The disintegration energy in fission events first appears as the kinetic\nenergy of the fragments and neutrons" + }, + { + "Chapter": "9", + "sentence_range": "2919-2922", + "Text": "Hence the total gain in binding energy is 240\u00d70 9 or 216 MeV The disintegration energy in fission events first appears as the kinetic\nenergy of the fragments and neutrons Eventually it is transferred to the\nsurrounding matter appearing as heat" + }, + { + "Chapter": "9", + "sentence_range": "2920-2923", + "Text": "9 or 216 MeV The disintegration energy in fission events first appears as the kinetic\nenergy of the fragments and neutrons Eventually it is transferred to the\nsurrounding matter appearing as heat The source of energy in nuclear\nreactors, which produce electricity, is nuclear fission" + }, + { + "Chapter": "9", + "sentence_range": "2921-2924", + "Text": "The disintegration energy in fission events first appears as the kinetic\nenergy of the fragments and neutrons Eventually it is transferred to the\nsurrounding matter appearing as heat The source of energy in nuclear\nreactors, which produce electricity, is nuclear fission The enormous\nenergy released in an atom bomb comes from uncontrolled nuclear\nfission" + }, + { + "Chapter": "9", + "sentence_range": "2922-2925", + "Text": "Eventually it is transferred to the\nsurrounding matter appearing as heat The source of energy in nuclear\nreactors, which produce electricity, is nuclear fission The enormous\nenergy released in an atom bomb comes from uncontrolled nuclear\nfission 13" + }, + { + "Chapter": "9", + "sentence_range": "2923-2926", + "Text": "The source of energy in nuclear\nreactors, which produce electricity, is nuclear fission The enormous\nenergy released in an atom bomb comes from uncontrolled nuclear\nfission 13 7" + }, + { + "Chapter": "9", + "sentence_range": "2924-2927", + "Text": "The enormous\nenergy released in an atom bomb comes from uncontrolled nuclear\nfission 13 7 2 Nuclear fusion \u2013 energy generation in stars\nWhen two light nuclei fuse to form a larger nucleus, energy is released,\nsince the larger nucleus is more tightly bound, as seen from the binding\nenergy curve in Fig" + }, + { + "Chapter": "9", + "sentence_range": "2925-2928", + "Text": "13 7 2 Nuclear fusion \u2013 energy generation in stars\nWhen two light nuclei fuse to form a larger nucleus, energy is released,\nsince the larger nucleus is more tightly bound, as seen from the binding\nenergy curve in Fig 13" + }, + { + "Chapter": "9", + "sentence_range": "2926-2929", + "Text": "7 2 Nuclear fusion \u2013 energy generation in stars\nWhen two light nuclei fuse to form a larger nucleus, energy is released,\nsince the larger nucleus is more tightly bound, as seen from the binding\nenergy curve in Fig 13 1" + }, + { + "Chapter": "9", + "sentence_range": "2927-2930", + "Text": "2 Nuclear fusion \u2013 energy generation in stars\nWhen two light nuclei fuse to form a larger nucleus, energy is released,\nsince the larger nucleus is more tightly bound, as seen from the binding\nenergy curve in Fig 13 1 Some examples of such energy liberating nuclear\nfusion reactions are :\n1\n1\n2\n1\n1\n1\nH\nH\nH\n+\n\u2192\n+ e+ + n + 0" + }, + { + "Chapter": "9", + "sentence_range": "2928-2931", + "Text": "13 1 Some examples of such energy liberating nuclear\nfusion reactions are :\n1\n1\n2\n1\n1\n1\nH\nH\nH\n+\n\u2192\n+ e+ + n + 0 42 MeV\n[13" + }, + { + "Chapter": "9", + "sentence_range": "2929-2932", + "Text": "1 Some examples of such energy liberating nuclear\nfusion reactions are :\n1\n1\n2\n1\n1\n1\nH\nH\nH\n+\n\u2192\n+ e+ + n + 0 42 MeV\n[13 13(a)]\n2\n2\n3\n1\n1\n2\nH\nH\nHe\n+\n\u2192\n+ n + 3" + }, + { + "Chapter": "9", + "sentence_range": "2930-2933", + "Text": "Some examples of such energy liberating nuclear\nfusion reactions are :\n1\n1\n2\n1\n1\n1\nH\nH\nH\n+\n\u2192\n+ e+ + n + 0 42 MeV\n[13 13(a)]\n2\n2\n3\n1\n1\n2\nH\nH\nHe\n+\n\u2192\n+ n + 3 27 MeV\n[13" + }, + { + "Chapter": "9", + "sentence_range": "2931-2934", + "Text": "42 MeV\n[13 13(a)]\n2\n2\n3\n1\n1\n2\nH\nH\nHe\n+\n\u2192\n+ n + 3 27 MeV\n[13 13(b)]\n2\n2\n3\n1\n1\n1\n1\n1\nH\nH\nH\nH\n+\n\u2192\n+\n+ 4" + }, + { + "Chapter": "9", + "sentence_range": "2932-2935", + "Text": "13(a)]\n2\n2\n3\n1\n1\n2\nH\nH\nHe\n+\n\u2192\n+ n + 3 27 MeV\n[13 13(b)]\n2\n2\n3\n1\n1\n1\n1\n1\nH\nH\nH\nH\n+\n\u2192\n+\n+ 4 03 MeV\n[13" + }, + { + "Chapter": "9", + "sentence_range": "2933-2936", + "Text": "27 MeV\n[13 13(b)]\n2\n2\n3\n1\n1\n1\n1\n1\nH\nH\nH\nH\n+\n\u2192\n+\n+ 4 03 MeV\n[13 13(c)]\nIn the first reaction, two protons combine to form a deuteron and\na positron with a release of 0" + }, + { + "Chapter": "9", + "sentence_range": "2934-2937", + "Text": "13(b)]\n2\n2\n3\n1\n1\n1\n1\n1\nH\nH\nH\nH\n+\n\u2192\n+\n+ 4 03 MeV\n[13 13(c)]\nIn the first reaction, two protons combine to form a deuteron and\na positron with a release of 0 42 MeV energy" + }, + { + "Chapter": "9", + "sentence_range": "2935-2938", + "Text": "03 MeV\n[13 13(c)]\nIn the first reaction, two protons combine to form a deuteron and\na positron with a release of 0 42 MeV energy In reaction [13" + }, + { + "Chapter": "9", + "sentence_range": "2936-2939", + "Text": "13(c)]\nIn the first reaction, two protons combine to form a deuteron and\na positron with a release of 0 42 MeV energy In reaction [13 13(b)], two\nRationalised 2023-24\nPhysics\n316\ndeuterons combine to form the light isotope of helium" + }, + { + "Chapter": "9", + "sentence_range": "2937-2940", + "Text": "42 MeV energy In reaction [13 13(b)], two\nRationalised 2023-24\nPhysics\n316\ndeuterons combine to form the light isotope of helium In reaction\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2938-2941", + "Text": "In reaction [13 13(b)], two\nRationalised 2023-24\nPhysics\n316\ndeuterons combine to form the light isotope of helium In reaction\n(13 13c), two deuterons combine to form a triton and a proton" + }, + { + "Chapter": "9", + "sentence_range": "2939-2942", + "Text": "13(b)], two\nRationalised 2023-24\nPhysics\n316\ndeuterons combine to form the light isotope of helium In reaction\n(13 13c), two deuterons combine to form a triton and a proton For\nfusion to take place, the two nuclei must come close enough so that\nattractive short-range nuclear force is able to affect them" + }, + { + "Chapter": "9", + "sentence_range": "2940-2943", + "Text": "In reaction\n(13 13c), two deuterons combine to form a triton and a proton For\nfusion to take place, the two nuclei must come close enough so that\nattractive short-range nuclear force is able to affect them However,\nsince they are both positively charged particles, they experience coulomb\nrepulsion" + }, + { + "Chapter": "9", + "sentence_range": "2941-2944", + "Text": "13c), two deuterons combine to form a triton and a proton For\nfusion to take place, the two nuclei must come close enough so that\nattractive short-range nuclear force is able to affect them However,\nsince they are both positively charged particles, they experience coulomb\nrepulsion They, therefore, must have enough energy to overcome this\ncoulomb barrier" + }, + { + "Chapter": "9", + "sentence_range": "2942-2945", + "Text": "For\nfusion to take place, the two nuclei must come close enough so that\nattractive short-range nuclear force is able to affect them However,\nsince they are both positively charged particles, they experience coulomb\nrepulsion They, therefore, must have enough energy to overcome this\ncoulomb barrier The height of the barrier depends on the charges and\nradii of the two interacting nuclei" + }, + { + "Chapter": "9", + "sentence_range": "2943-2946", + "Text": "However,\nsince they are both positively charged particles, they experience coulomb\nrepulsion They, therefore, must have enough energy to overcome this\ncoulomb barrier The height of the barrier depends on the charges and\nradii of the two interacting nuclei It can be shown, for example, that\nthe barrier height for two protons is ~ 400 keV, and is higher for nuclei\nwith higher charges" + }, + { + "Chapter": "9", + "sentence_range": "2944-2947", + "Text": "They, therefore, must have enough energy to overcome this\ncoulomb barrier The height of the barrier depends on the charges and\nradii of the two interacting nuclei It can be shown, for example, that\nthe barrier height for two protons is ~ 400 keV, and is higher for nuclei\nwith higher charges We can estimate the temperature at which two\nprotons in a proton gas would (averagely) have enough energy to\novercome the coulomb barrier:\n(3/2)k T = K \u2243 400 keV, which gives T ~ 3 \u00d7 109 K" + }, + { + "Chapter": "9", + "sentence_range": "2945-2948", + "Text": "The height of the barrier depends on the charges and\nradii of the two interacting nuclei It can be shown, for example, that\nthe barrier height for two protons is ~ 400 keV, and is higher for nuclei\nwith higher charges We can estimate the temperature at which two\nprotons in a proton gas would (averagely) have enough energy to\novercome the coulomb barrier:\n(3/2)k T = K \u2243 400 keV, which gives T ~ 3 \u00d7 109 K When fusion is achieved by raising the temperature of the system so\nthat particles have enough kinetic energy to overcome the coulomb\nrepulsive behaviour, it is called thermonuclear fusion" + }, + { + "Chapter": "9", + "sentence_range": "2946-2949", + "Text": "It can be shown, for example, that\nthe barrier height for two protons is ~ 400 keV, and is higher for nuclei\nwith higher charges We can estimate the temperature at which two\nprotons in a proton gas would (averagely) have enough energy to\novercome the coulomb barrier:\n(3/2)k T = K \u2243 400 keV, which gives T ~ 3 \u00d7 109 K When fusion is achieved by raising the temperature of the system so\nthat particles have enough kinetic energy to overcome the coulomb\nrepulsive behaviour, it is called thermonuclear fusion Thermonuclear fusion is the source of energy output in the interior\nof stars" + }, + { + "Chapter": "9", + "sentence_range": "2947-2950", + "Text": "We can estimate the temperature at which two\nprotons in a proton gas would (averagely) have enough energy to\novercome the coulomb barrier:\n(3/2)k T = K \u2243 400 keV, which gives T ~ 3 \u00d7 109 K When fusion is achieved by raising the temperature of the system so\nthat particles have enough kinetic energy to overcome the coulomb\nrepulsive behaviour, it is called thermonuclear fusion Thermonuclear fusion is the source of energy output in the interior\nof stars The interior of the sun has a temperature of 1" + }, + { + "Chapter": "9", + "sentence_range": "2948-2951", + "Text": "When fusion is achieved by raising the temperature of the system so\nthat particles have enough kinetic energy to overcome the coulomb\nrepulsive behaviour, it is called thermonuclear fusion Thermonuclear fusion is the source of energy output in the interior\nof stars The interior of the sun has a temperature of 1 5\u00d7107 K, which\nis considerably less than the estimated temperature required for fusion\nof particles of average energy" + }, + { + "Chapter": "9", + "sentence_range": "2949-2952", + "Text": "Thermonuclear fusion is the source of energy output in the interior\nof stars The interior of the sun has a temperature of 1 5\u00d7107 K, which\nis considerably less than the estimated temperature required for fusion\nof particles of average energy Clearly, fusion in the sun involves protons\nwhose energies are much above the average energy" + }, + { + "Chapter": "9", + "sentence_range": "2950-2953", + "Text": "The interior of the sun has a temperature of 1 5\u00d7107 K, which\nis considerably less than the estimated temperature required for fusion\nof particles of average energy Clearly, fusion in the sun involves protons\nwhose energies are much above the average energy The fusion reaction in the sun is a multi-step process in which the\nhydrogen is burned into helium" + }, + { + "Chapter": "9", + "sentence_range": "2951-2954", + "Text": "5\u00d7107 K, which\nis considerably less than the estimated temperature required for fusion\nof particles of average energy Clearly, fusion in the sun involves protons\nwhose energies are much above the average energy The fusion reaction in the sun is a multi-step process in which the\nhydrogen is burned into helium Thus, the fuel in the sun is the hydrogen\nin its core" + }, + { + "Chapter": "9", + "sentence_range": "2952-2955", + "Text": "Clearly, fusion in the sun involves protons\nwhose energies are much above the average energy The fusion reaction in the sun is a multi-step process in which the\nhydrogen is burned into helium Thus, the fuel in the sun is the hydrogen\nin its core The proton-proton (p, p) cycle by which this occurs is\nrepresented by the following sets of reactions:\n1\n1\n2\n1\n1\n1\nH\nH\nH\n+\n\u2192\n+ e+ + n + 0" + }, + { + "Chapter": "9", + "sentence_range": "2953-2956", + "Text": "The fusion reaction in the sun is a multi-step process in which the\nhydrogen is burned into helium Thus, the fuel in the sun is the hydrogen\nin its core The proton-proton (p, p) cycle by which this occurs is\nrepresented by the following sets of reactions:\n1\n1\n2\n1\n1\n1\nH\nH\nH\n+\n\u2192\n+ e+ + n + 0 42 MeV\n(i)\ne + + e \u2013 \u00ae g + g + 1" + }, + { + "Chapter": "9", + "sentence_range": "2954-2957", + "Text": "Thus, the fuel in the sun is the hydrogen\nin its core The proton-proton (p, p) cycle by which this occurs is\nrepresented by the following sets of reactions:\n1\n1\n2\n1\n1\n1\nH\nH\nH\n+\n\u2192\n+ e+ + n + 0 42 MeV\n(i)\ne + + e \u2013 \u00ae g + g + 1 02 MeV\n(ii)\n2\n1\n3\n1\n1\n2\nH\nH\nHe\n+\n\u2192\n+ g + 5" + }, + { + "Chapter": "9", + "sentence_range": "2955-2958", + "Text": "The proton-proton (p, p) cycle by which this occurs is\nrepresented by the following sets of reactions:\n1\n1\n2\n1\n1\n1\nH\nH\nH\n+\n\u2192\n+ e+ + n + 0 42 MeV\n(i)\ne + + e \u2013 \u00ae g + g + 1 02 MeV\n(ii)\n2\n1\n3\n1\n1\n2\nH\nH\nHe\n+\n\u2192\n+ g + 5 49 MeV\n(iii)\n+\n\u2192\n+\n+\n3\n3\n4\n1\n1\n2\n2\n2\n1\n1\nHe \nHe \nHe\nH\nH + 12" + }, + { + "Chapter": "9", + "sentence_range": "2956-2959", + "Text": "42 MeV\n(i)\ne + + e \u2013 \u00ae g + g + 1 02 MeV\n(ii)\n2\n1\n3\n1\n1\n2\nH\nH\nHe\n+\n\u2192\n+ g + 5 49 MeV\n(iii)\n+\n\u2192\n+\n+\n3\n3\n4\n1\n1\n2\n2\n2\n1\n1\nHe \nHe \nHe\nH\nH + 12 86 MeV (iv)\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2957-2960", + "Text": "02 MeV\n(ii)\n2\n1\n3\n1\n1\n2\nH\nH\nHe\n+\n\u2192\n+ g + 5 49 MeV\n(iii)\n+\n\u2192\n+\n+\n3\n3\n4\n1\n1\n2\n2\n2\n1\n1\nHe \nHe \nHe\nH\nH + 12 86 MeV (iv)\n(13 14)\nFor the fourth reaction to occur, the first three reactions must occur\ntwice, in which case two light helium nuclei unite to form ordinary helium\nnucleus" + }, + { + "Chapter": "9", + "sentence_range": "2958-2961", + "Text": "49 MeV\n(iii)\n+\n\u2192\n+\n+\n3\n3\n4\n1\n1\n2\n2\n2\n1\n1\nHe \nHe \nHe\nH\nH + 12 86 MeV (iv)\n(13 14)\nFor the fourth reaction to occur, the first three reactions must occur\ntwice, in which case two light helium nuclei unite to form ordinary helium\nnucleus If we consider the combination 2(i) + 2(ii) + 2(iii) +(iv), the net\neffect is\n1\n4\n1\n2\n4 H\n2\nHe\n2\n6\n26" + }, + { + "Chapter": "9", + "sentence_range": "2959-2962", + "Text": "86 MeV (iv)\n(13 14)\nFor the fourth reaction to occur, the first three reactions must occur\ntwice, in which case two light helium nuclei unite to form ordinary helium\nnucleus If we consider the combination 2(i) + 2(ii) + 2(iii) +(iv), the net\neffect is\n1\n4\n1\n2\n4 H\n2\nHe\n2\n6\n26 7 MeV\ne\n\u03bd\n\u03b3\n\u2212\n+\n\u2192\n+\n+\n+\nor \n1\n4\n1\n2\n(4 H\n4\n)\n( He\n2\n)\n2\n6\n26" + }, + { + "Chapter": "9", + "sentence_range": "2960-2963", + "Text": "14)\nFor the fourth reaction to occur, the first three reactions must occur\ntwice, in which case two light helium nuclei unite to form ordinary helium\nnucleus If we consider the combination 2(i) + 2(ii) + 2(iii) +(iv), the net\neffect is\n1\n4\n1\n2\n4 H\n2\nHe\n2\n6\n26 7 MeV\ne\n\u03bd\n\u03b3\n\u2212\n+\n\u2192\n+\n+\n+\nor \n1\n4\n1\n2\n(4 H\n4\n)\n( He\n2\n)\n2\n6\n26 7MeV\ne\ne\n\u03bd\n\u03b3\n\u2212\n\u2212\n+\n\u2192\n+\n+\n+\n+\n(13" + }, + { + "Chapter": "9", + "sentence_range": "2961-2964", + "Text": "If we consider the combination 2(i) + 2(ii) + 2(iii) +(iv), the net\neffect is\n1\n4\n1\n2\n4 H\n2\nHe\n2\n6\n26 7 MeV\ne\n\u03bd\n\u03b3\n\u2212\n+\n\u2192\n+\n+\n+\nor \n1\n4\n1\n2\n(4 H\n4\n)\n( He\n2\n)\n2\n6\n26 7MeV\ne\ne\n\u03bd\n\u03b3\n\u2212\n\u2212\n+\n\u2192\n+\n+\n+\n+\n(13 15)\nThus, four hydrogen atoms combine to form an 4\n2He atom with a\nrelease of 26" + }, + { + "Chapter": "9", + "sentence_range": "2962-2965", + "Text": "7 MeV\ne\n\u03bd\n\u03b3\n\u2212\n+\n\u2192\n+\n+\n+\nor \n1\n4\n1\n2\n(4 H\n4\n)\n( He\n2\n)\n2\n6\n26 7MeV\ne\ne\n\u03bd\n\u03b3\n\u2212\n\u2212\n+\n\u2192\n+\n+\n+\n+\n(13 15)\nThus, four hydrogen atoms combine to form an 4\n2He atom with a\nrelease of 26 7 MeV of energy" + }, + { + "Chapter": "9", + "sentence_range": "2963-2966", + "Text": "7MeV\ne\ne\n\u03bd\n\u03b3\n\u2212\n\u2212\n+\n\u2192\n+\n+\n+\n+\n(13 15)\nThus, four hydrogen atoms combine to form an 4\n2He atom with a\nrelease of 26 7 MeV of energy Helium is not the only element that can be synthesized in the interior of\na star" + }, + { + "Chapter": "9", + "sentence_range": "2964-2967", + "Text": "15)\nThus, four hydrogen atoms combine to form an 4\n2He atom with a\nrelease of 26 7 MeV of energy Helium is not the only element that can be synthesized in the interior of\na star As the hydrogen in the core gets depleted and becomes helium, the\ncore starts to cool" + }, + { + "Chapter": "9", + "sentence_range": "2965-2968", + "Text": "7 MeV of energy Helium is not the only element that can be synthesized in the interior of\na star As the hydrogen in the core gets depleted and becomes helium, the\ncore starts to cool The star begins to collapse under its own gravity which\nincreases the temperature of the core" + }, + { + "Chapter": "9", + "sentence_range": "2966-2969", + "Text": "Helium is not the only element that can be synthesized in the interior of\na star As the hydrogen in the core gets depleted and becomes helium, the\ncore starts to cool The star begins to collapse under its own gravity which\nincreases the temperature of the core If this temperature increases to about\n108 K, fusion takes place again, this time of helium nuclei into carbon" + }, + { + "Chapter": "9", + "sentence_range": "2967-2970", + "Text": "As the hydrogen in the core gets depleted and becomes helium, the\ncore starts to cool The star begins to collapse under its own gravity which\nincreases the temperature of the core If this temperature increases to about\n108 K, fusion takes place again, this time of helium nuclei into carbon This kind of process can generate through fusion higher and higher mass\nnumber elements" + }, + { + "Chapter": "9", + "sentence_range": "2968-2971", + "Text": "The star begins to collapse under its own gravity which\nincreases the temperature of the core If this temperature increases to about\n108 K, fusion takes place again, this time of helium nuclei into carbon This kind of process can generate through fusion higher and higher mass\nnumber elements But elements more massive than those near the peak of\nthe binding energy curve in Fig" + }, + { + "Chapter": "9", + "sentence_range": "2969-2972", + "Text": "If this temperature increases to about\n108 K, fusion takes place again, this time of helium nuclei into carbon This kind of process can generate through fusion higher and higher mass\nnumber elements But elements more massive than those near the peak of\nthe binding energy curve in Fig 13" + }, + { + "Chapter": "9", + "sentence_range": "2970-2973", + "Text": "This kind of process can generate through fusion higher and higher mass\nnumber elements But elements more massive than those near the peak of\nthe binding energy curve in Fig 13 1 cannot be so produced" + }, + { + "Chapter": "9", + "sentence_range": "2971-2974", + "Text": "But elements more massive than those near the peak of\nthe binding energy curve in Fig 13 1 cannot be so produced Rationalised 2023-24\n317\nNuclei\nThe age of the sun is about 5\u00d7109 y and it is estimated that there is\nenough hydrogen in the sun to keep it going for another 5 billion years" + }, + { + "Chapter": "9", + "sentence_range": "2972-2975", + "Text": "13 1 cannot be so produced Rationalised 2023-24\n317\nNuclei\nThe age of the sun is about 5\u00d7109 y and it is estimated that there is\nenough hydrogen in the sun to keep it going for another 5 billion years After that, the hydrogen burning will stop and the sun will begin to cool\nand will start to collapse under gravity, which will raise the core\ntemperature" + }, + { + "Chapter": "9", + "sentence_range": "2973-2976", + "Text": "1 cannot be so produced Rationalised 2023-24\n317\nNuclei\nThe age of the sun is about 5\u00d7109 y and it is estimated that there is\nenough hydrogen in the sun to keep it going for another 5 billion years After that, the hydrogen burning will stop and the sun will begin to cool\nand will start to collapse under gravity, which will raise the core\ntemperature The outer envelope of the sun will expand, turning it into\nthe so called red giant" + }, + { + "Chapter": "9", + "sentence_range": "2974-2977", + "Text": "Rationalised 2023-24\n317\nNuclei\nThe age of the sun is about 5\u00d7109 y and it is estimated that there is\nenough hydrogen in the sun to keep it going for another 5 billion years After that, the hydrogen burning will stop and the sun will begin to cool\nand will start to collapse under gravity, which will raise the core\ntemperature The outer envelope of the sun will expand, turning it into\nthe so called red giant 13" + }, + { + "Chapter": "9", + "sentence_range": "2975-2978", + "Text": "After that, the hydrogen burning will stop and the sun will begin to cool\nand will start to collapse under gravity, which will raise the core\ntemperature The outer envelope of the sun will expand, turning it into\nthe so called red giant 13 7" + }, + { + "Chapter": "9", + "sentence_range": "2976-2979", + "Text": "The outer envelope of the sun will expand, turning it into\nthe so called red giant 13 7 3 Controlled thermonuclear fusion\nThe natural thermonuclear fusion process in a star is replicated in a\nthermonuclear fusion device" + }, + { + "Chapter": "9", + "sentence_range": "2977-2980", + "Text": "13 7 3 Controlled thermonuclear fusion\nThe natural thermonuclear fusion process in a star is replicated in a\nthermonuclear fusion device In controlled fusion reactors, the aim is to\ngenerate steady power by heating the nuclear fuel to a temperature in the\nrange of 108 K" + }, + { + "Chapter": "9", + "sentence_range": "2978-2981", + "Text": "7 3 Controlled thermonuclear fusion\nThe natural thermonuclear fusion process in a star is replicated in a\nthermonuclear fusion device In controlled fusion reactors, the aim is to\ngenerate steady power by heating the nuclear fuel to a temperature in the\nrange of 108 K At these temperatures, the fuel is a mixture of positive\nions and electrons (plasma)" + }, + { + "Chapter": "9", + "sentence_range": "2979-2982", + "Text": "3 Controlled thermonuclear fusion\nThe natural thermonuclear fusion process in a star is replicated in a\nthermonuclear fusion device In controlled fusion reactors, the aim is to\ngenerate steady power by heating the nuclear fuel to a temperature in the\nrange of 108 K At these temperatures, the fuel is a mixture of positive\nions and electrons (plasma) The challenge is to confine this plasma, since\nno container can stand such a high temperature" + }, + { + "Chapter": "9", + "sentence_range": "2980-2983", + "Text": "In controlled fusion reactors, the aim is to\ngenerate steady power by heating the nuclear fuel to a temperature in the\nrange of 108 K At these temperatures, the fuel is a mixture of positive\nions and electrons (plasma) The challenge is to confine this plasma, since\nno container can stand such a high temperature Several countries\naround the world including India are developing techniques in this\nconnection" + }, + { + "Chapter": "9", + "sentence_range": "2981-2984", + "Text": "At these temperatures, the fuel is a mixture of positive\nions and electrons (plasma) The challenge is to confine this plasma, since\nno container can stand such a high temperature Several countries\naround the world including India are developing techniques in this\nconnection If successful, fusion reactors will hopefully supply almost\nunlimited power to humanity" + }, + { + "Chapter": "9", + "sentence_range": "2982-2985", + "Text": "The challenge is to confine this plasma, since\nno container can stand such a high temperature Several countries\naround the world including India are developing techniques in this\nconnection If successful, fusion reactors will hopefully supply almost\nunlimited power to humanity Example 13" + }, + { + "Chapter": "9", + "sentence_range": "2983-2986", + "Text": "Several countries\naround the world including India are developing techniques in this\nconnection If successful, fusion reactors will hopefully supply almost\nunlimited power to humanity Example 13 4 Answer the following questions:\n(a) Are the equations of nuclear reactions (such as those given in\nSection 13" + }, + { + "Chapter": "9", + "sentence_range": "2984-2987", + "Text": "If successful, fusion reactors will hopefully supply almost\nunlimited power to humanity Example 13 4 Answer the following questions:\n(a) Are the equations of nuclear reactions (such as those given in\nSection 13 7) \u2018balanced\u2019 in the sense a chemical equation (e" + }, + { + "Chapter": "9", + "sentence_range": "2985-2988", + "Text": "Example 13 4 Answer the following questions:\n(a) Are the equations of nuclear reactions (such as those given in\nSection 13 7) \u2018balanced\u2019 in the sense a chemical equation (e g" + }, + { + "Chapter": "9", + "sentence_range": "2986-2989", + "Text": "4 Answer the following questions:\n(a) Are the equations of nuclear reactions (such as those given in\nSection 13 7) \u2018balanced\u2019 in the sense a chemical equation (e g ,\n2H2 + O2\u00ae 2 H2O) is" + }, + { + "Chapter": "9", + "sentence_range": "2987-2990", + "Text": "7) \u2018balanced\u2019 in the sense a chemical equation (e g ,\n2H2 + O2\u00ae 2 H2O) is If not, in what sense are they balanced on\nboth sides" + }, + { + "Chapter": "9", + "sentence_range": "2988-2991", + "Text": "g ,\n2H2 + O2\u00ae 2 H2O) is If not, in what sense are they balanced on\nboth sides (b) If both the number of protons and the number of neutrons are\nconserved in each nuclear reaction, in what way is mass converted\ninto energy (or vice-versa) in a nuclear reaction" + }, + { + "Chapter": "9", + "sentence_range": "2989-2992", + "Text": ",\n2H2 + O2\u00ae 2 H2O) is If not, in what sense are they balanced on\nboth sides (b) If both the number of protons and the number of neutrons are\nconserved in each nuclear reaction, in what way is mass converted\ninto energy (or vice-versa) in a nuclear reaction (c) A general impression exists that mass-energy interconversion\ntakes place only in nuclear reaction and never in chemical\nreaction" + }, + { + "Chapter": "9", + "sentence_range": "2990-2993", + "Text": "If not, in what sense are they balanced on\nboth sides (b) If both the number of protons and the number of neutrons are\nconserved in each nuclear reaction, in what way is mass converted\ninto energy (or vice-versa) in a nuclear reaction (c) A general impression exists that mass-energy interconversion\ntakes place only in nuclear reaction and never in chemical\nreaction This is strictly speaking, incorrect" + }, + { + "Chapter": "9", + "sentence_range": "2991-2994", + "Text": "(b) If both the number of protons and the number of neutrons are\nconserved in each nuclear reaction, in what way is mass converted\ninto energy (or vice-versa) in a nuclear reaction (c) A general impression exists that mass-energy interconversion\ntakes place only in nuclear reaction and never in chemical\nreaction This is strictly speaking, incorrect Explain" + }, + { + "Chapter": "9", + "sentence_range": "2992-2995", + "Text": "(c) A general impression exists that mass-energy interconversion\ntakes place only in nuclear reaction and never in chemical\nreaction This is strictly speaking, incorrect Explain Solution\n(a) A chemical equation is balanced in the sense that the number of\natoms of each element is the same on both sides of the equation" + }, + { + "Chapter": "9", + "sentence_range": "2993-2996", + "Text": "This is strictly speaking, incorrect Explain Solution\n(a) A chemical equation is balanced in the sense that the number of\natoms of each element is the same on both sides of the equation A chemical reaction merely alters the original combinations of\natoms" + }, + { + "Chapter": "9", + "sentence_range": "2994-2997", + "Text": "Explain Solution\n(a) A chemical equation is balanced in the sense that the number of\natoms of each element is the same on both sides of the equation A chemical reaction merely alters the original combinations of\natoms In a nuclear reaction, elements may be transmuted" + }, + { + "Chapter": "9", + "sentence_range": "2995-2998", + "Text": "Solution\n(a) A chemical equation is balanced in the sense that the number of\natoms of each element is the same on both sides of the equation A chemical reaction merely alters the original combinations of\natoms In a nuclear reaction, elements may be transmuted Thus,\nthe number of atoms of each element is not necessarily conserved\nin a nuclear reaction" + }, + { + "Chapter": "9", + "sentence_range": "2996-2999", + "Text": "A chemical reaction merely alters the original combinations of\natoms In a nuclear reaction, elements may be transmuted Thus,\nthe number of atoms of each element is not necessarily conserved\nin a nuclear reaction However, the number of protons and the\nnumber of neutrons are both separately conserved in a nuclear\nreaction" + }, + { + "Chapter": "9", + "sentence_range": "2997-3000", + "Text": "In a nuclear reaction, elements may be transmuted Thus,\nthe number of atoms of each element is not necessarily conserved\nin a nuclear reaction However, the number of protons and the\nnumber of neutrons are both separately conserved in a nuclear\nreaction [Actually, even this is not strictly true in the realm of\nvery high energies \u2013 what is strictly conserved is the total charge\nand total \u2018baryon number\u2019" + }, + { + "Chapter": "9", + "sentence_range": "2998-3001", + "Text": "Thus,\nthe number of atoms of each element is not necessarily conserved\nin a nuclear reaction However, the number of protons and the\nnumber of neutrons are both separately conserved in a nuclear\nreaction [Actually, even this is not strictly true in the realm of\nvery high energies \u2013 what is strictly conserved is the total charge\nand total \u2018baryon number\u2019 We need not pursue this matter here" + }, + { + "Chapter": "9", + "sentence_range": "2999-3002", + "Text": "However, the number of protons and the\nnumber of neutrons are both separately conserved in a nuclear\nreaction [Actually, even this is not strictly true in the realm of\nvery high energies \u2013 what is strictly conserved is the total charge\nand total \u2018baryon number\u2019 We need not pursue this matter here ]\nIn nuclear reactions (e" + }, + { + "Chapter": "9", + "sentence_range": "3000-3003", + "Text": "[Actually, even this is not strictly true in the realm of\nvery high energies \u2013 what is strictly conserved is the total charge\nand total \u2018baryon number\u2019 We need not pursue this matter here ]\nIn nuclear reactions (e g" + }, + { + "Chapter": "9", + "sentence_range": "3001-3004", + "Text": "We need not pursue this matter here ]\nIn nuclear reactions (e g , Eq" + }, + { + "Chapter": "9", + "sentence_range": "3002-3005", + "Text": "]\nIn nuclear reactions (e g , Eq 13" + }, + { + "Chapter": "9", + "sentence_range": "3003-3006", + "Text": "g , Eq 13 10), the number of protons and\nthe number of neutrons are the same on the two sides of the equation" + }, + { + "Chapter": "9", + "sentence_range": "3004-3007", + "Text": ", Eq 13 10), the number of protons and\nthe number of neutrons are the same on the two sides of the equation (b) We know that the binding energy of a nucleus gives a negative\ncontribution to the mass of the nucleus (mass defect)" + }, + { + "Chapter": "9", + "sentence_range": "3005-3008", + "Text": "13 10), the number of protons and\nthe number of neutrons are the same on the two sides of the equation (b) We know that the binding energy of a nucleus gives a negative\ncontribution to the mass of the nucleus (mass defect) Now, since\nproton number and neutron number are conserved in a nuclear\nreaction, the total rest mass of neutrons and protons is the same\non either side of a reaction" + }, + { + "Chapter": "9", + "sentence_range": "3006-3009", + "Text": "10), the number of protons and\nthe number of neutrons are the same on the two sides of the equation (b) We know that the binding energy of a nucleus gives a negative\ncontribution to the mass of the nucleus (mass defect) Now, since\nproton number and neutron number are conserved in a nuclear\nreaction, the total rest mass of neutrons and protons is the same\non either side of a reaction But the total binding energy of nuclei\non the left side need not be the same as that on the right hand\nside" + }, + { + "Chapter": "9", + "sentence_range": "3007-3010", + "Text": "(b) We know that the binding energy of a nucleus gives a negative\ncontribution to the mass of the nucleus (mass defect) Now, since\nproton number and neutron number are conserved in a nuclear\nreaction, the total rest mass of neutrons and protons is the same\non either side of a reaction But the total binding energy of nuclei\non the left side need not be the same as that on the right hand\nside The difference in these binding energies appears as energy\nreleased or absorbed in a nuclear reaction" + }, + { + "Chapter": "9", + "sentence_range": "3008-3011", + "Text": "Now, since\nproton number and neutron number are conserved in a nuclear\nreaction, the total rest mass of neutrons and protons is the same\non either side of a reaction But the total binding energy of nuclei\non the left side need not be the same as that on the right hand\nside The difference in these binding energies appears as energy\nreleased or absorbed in a nuclear reaction Since binding energy\n EXAMPLE 13" + }, + { + "Chapter": "9", + "sentence_range": "3009-3012", + "Text": "But the total binding energy of nuclei\non the left side need not be the same as that on the right hand\nside The difference in these binding energies appears as energy\nreleased or absorbed in a nuclear reaction Since binding energy\n EXAMPLE 13 4\nRationalised 2023-24\nPhysics\n318\n EXAMPLE 13" + }, + { + "Chapter": "9", + "sentence_range": "3010-3013", + "Text": "The difference in these binding energies appears as energy\nreleased or absorbed in a nuclear reaction Since binding energy\n EXAMPLE 13 4\nRationalised 2023-24\nPhysics\n318\n EXAMPLE 13 4\ncontributes to mass, we say that the difference in the total mass\nof nuclei on the two sides get converted into energy or vice-versa" + }, + { + "Chapter": "9", + "sentence_range": "3011-3014", + "Text": "Since binding energy\n EXAMPLE 13 4\nRationalised 2023-24\nPhysics\n318\n EXAMPLE 13 4\ncontributes to mass, we say that the difference in the total mass\nof nuclei on the two sides get converted into energy or vice-versa It is in these sense that a nuclear reaction is an example of mass-\nenergy interconversion" + }, + { + "Chapter": "9", + "sentence_range": "3012-3015", + "Text": "4\nRationalised 2023-24\nPhysics\n318\n EXAMPLE 13 4\ncontributes to mass, we say that the difference in the total mass\nof nuclei on the two sides get converted into energy or vice-versa It is in these sense that a nuclear reaction is an example of mass-\nenergy interconversion (c) From the point of view of mass-energy interconversion, a chemical\nreaction is similar to a nuclear reaction in principle" + }, + { + "Chapter": "9", + "sentence_range": "3013-3016", + "Text": "4\ncontributes to mass, we say that the difference in the total mass\nof nuclei on the two sides get converted into energy or vice-versa It is in these sense that a nuclear reaction is an example of mass-\nenergy interconversion (c) From the point of view of mass-energy interconversion, a chemical\nreaction is similar to a nuclear reaction in principle The energy\nreleased or absorbed in a chemical reaction can be traced to the\ndifference in chemical (not nuclear) binding energies of atoms\nand molecules on the two sides of a reaction" + }, + { + "Chapter": "9", + "sentence_range": "3014-3017", + "Text": "It is in these sense that a nuclear reaction is an example of mass-\nenergy interconversion (c) From the point of view of mass-energy interconversion, a chemical\nreaction is similar to a nuclear reaction in principle The energy\nreleased or absorbed in a chemical reaction can be traced to the\ndifference in chemical (not nuclear) binding energies of atoms\nand molecules on the two sides of a reaction Since, strictly\nspeaking, chemical binding energy also gives a negative\ncontribution (mass defect) to the total mass of an atom or molecule,\nwe can equally well say that the difference in the total mass of\natoms or molecules, on the two sides of the chemical reaction\ngets converted into energy or vice-versa" + }, + { + "Chapter": "9", + "sentence_range": "3015-3018", + "Text": "(c) From the point of view of mass-energy interconversion, a chemical\nreaction is similar to a nuclear reaction in principle The energy\nreleased or absorbed in a chemical reaction can be traced to the\ndifference in chemical (not nuclear) binding energies of atoms\nand molecules on the two sides of a reaction Since, strictly\nspeaking, chemical binding energy also gives a negative\ncontribution (mass defect) to the total mass of an atom or molecule,\nwe can equally well say that the difference in the total mass of\natoms or molecules, on the two sides of the chemical reaction\ngets converted into energy or vice-versa However, the mass\ndefects involved in a chemical reaction are almost a million times\nsmaller than those in a nuclear reaction" + }, + { + "Chapter": "9", + "sentence_range": "3016-3019", + "Text": "The energy\nreleased or absorbed in a chemical reaction can be traced to the\ndifference in chemical (not nuclear) binding energies of atoms\nand molecules on the two sides of a reaction Since, strictly\nspeaking, chemical binding energy also gives a negative\ncontribution (mass defect) to the total mass of an atom or molecule,\nwe can equally well say that the difference in the total mass of\natoms or molecules, on the two sides of the chemical reaction\ngets converted into energy or vice-versa However, the mass\ndefects involved in a chemical reaction are almost a million times\nsmaller than those in a nuclear reaction This is the reason for\nthe general impression, (which is incorrect) that mass-energy\ninterconversion does not take place in a chemical reaction" + }, + { + "Chapter": "9", + "sentence_range": "3017-3020", + "Text": "Since, strictly\nspeaking, chemical binding energy also gives a negative\ncontribution (mass defect) to the total mass of an atom or molecule,\nwe can equally well say that the difference in the total mass of\natoms or molecules, on the two sides of the chemical reaction\ngets converted into energy or vice-versa However, the mass\ndefects involved in a chemical reaction are almost a million times\nsmaller than those in a nuclear reaction This is the reason for\nthe general impression, (which is incorrect) that mass-energy\ninterconversion does not take place in a chemical reaction SUMMARY\n1" + }, + { + "Chapter": "9", + "sentence_range": "3018-3021", + "Text": "However, the mass\ndefects involved in a chemical reaction are almost a million times\nsmaller than those in a nuclear reaction This is the reason for\nthe general impression, (which is incorrect) that mass-energy\ninterconversion does not take place in a chemical reaction SUMMARY\n1 An atom has a nucleus" + }, + { + "Chapter": "9", + "sentence_range": "3019-3022", + "Text": "This is the reason for\nthe general impression, (which is incorrect) that mass-energy\ninterconversion does not take place in a chemical reaction SUMMARY\n1 An atom has a nucleus The nucleus is positively charged" + }, + { + "Chapter": "9", + "sentence_range": "3020-3023", + "Text": "SUMMARY\n1 An atom has a nucleus The nucleus is positively charged The radius\nof the nucleus is smaller than the radius of an atom by a factor of\n104" + }, + { + "Chapter": "9", + "sentence_range": "3021-3024", + "Text": "An atom has a nucleus The nucleus is positively charged The radius\nof the nucleus is smaller than the radius of an atom by a factor of\n104 More than 99" + }, + { + "Chapter": "9", + "sentence_range": "3022-3025", + "Text": "The nucleus is positively charged The radius\nof the nucleus is smaller than the radius of an atom by a factor of\n104 More than 99 9% mass of the atom is concentrated in the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "3023-3026", + "Text": "The radius\nof the nucleus is smaller than the radius of an atom by a factor of\n104 More than 99 9% mass of the atom is concentrated in the nucleus 2" + }, + { + "Chapter": "9", + "sentence_range": "3024-3027", + "Text": "More than 99 9% mass of the atom is concentrated in the nucleus 2 On the atomic scale, mass is measured in atomic mass units (u)" + }, + { + "Chapter": "9", + "sentence_range": "3025-3028", + "Text": "9% mass of the atom is concentrated in the nucleus 2 On the atomic scale, mass is measured in atomic mass units (u) By\ndefinition, 1 atomic mass unit (1u) is 1/12th mass of one atom of 12C;\n1u = 1" + }, + { + "Chapter": "9", + "sentence_range": "3026-3029", + "Text": "2 On the atomic scale, mass is measured in atomic mass units (u) By\ndefinition, 1 atomic mass unit (1u) is 1/12th mass of one atom of 12C;\n1u = 1 660563 \u00d7 10\u201327 kg" + }, + { + "Chapter": "9", + "sentence_range": "3027-3030", + "Text": "On the atomic scale, mass is measured in atomic mass units (u) By\ndefinition, 1 atomic mass unit (1u) is 1/12th mass of one atom of 12C;\n1u = 1 660563 \u00d7 10\u201327 kg 3" + }, + { + "Chapter": "9", + "sentence_range": "3028-3031", + "Text": "By\ndefinition, 1 atomic mass unit (1u) is 1/12th mass of one atom of 12C;\n1u = 1 660563 \u00d7 10\u201327 kg 3 A nucleus contains a neutral particle called neutron" + }, + { + "Chapter": "9", + "sentence_range": "3029-3032", + "Text": "660563 \u00d7 10\u201327 kg 3 A nucleus contains a neutral particle called neutron Its mass is almost\nthe same as that of proton\n4" + }, + { + "Chapter": "9", + "sentence_range": "3030-3033", + "Text": "3 A nucleus contains a neutral particle called neutron Its mass is almost\nthe same as that of proton\n4 The atomic number Z is the number of protons in the atomic nucleus\nof an element" + }, + { + "Chapter": "9", + "sentence_range": "3031-3034", + "Text": "A nucleus contains a neutral particle called neutron Its mass is almost\nthe same as that of proton\n4 The atomic number Z is the number of protons in the atomic nucleus\nof an element The mass number A is the total number of protons and\nneutrons in the atomic nucleus; A = Z+N; Here N denotes the number\nof neutrons in the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "3032-3035", + "Text": "Its mass is almost\nthe same as that of proton\n4 The atomic number Z is the number of protons in the atomic nucleus\nof an element The mass number A is the total number of protons and\nneutrons in the atomic nucleus; A = Z+N; Here N denotes the number\nof neutrons in the nucleus A nuclear species or a nuclide is represented as \nZAX\n, where X is the\nchemical symbol of the species" + }, + { + "Chapter": "9", + "sentence_range": "3033-3036", + "Text": "The atomic number Z is the number of protons in the atomic nucleus\nof an element The mass number A is the total number of protons and\nneutrons in the atomic nucleus; A = Z+N; Here N denotes the number\nof neutrons in the nucleus A nuclear species or a nuclide is represented as \nZAX\n, where X is the\nchemical symbol of the species Nuclides with the same atomic number Z, but different neutron number\nN are called isotopes" + }, + { + "Chapter": "9", + "sentence_range": "3034-3037", + "Text": "The mass number A is the total number of protons and\nneutrons in the atomic nucleus; A = Z+N; Here N denotes the number\nof neutrons in the nucleus A nuclear species or a nuclide is represented as \nZAX\n, where X is the\nchemical symbol of the species Nuclides with the same atomic number Z, but different neutron number\nN are called isotopes Nuclides with the same A are isobars and those\nwith the same N are isotones" + }, + { + "Chapter": "9", + "sentence_range": "3035-3038", + "Text": "A nuclear species or a nuclide is represented as \nZAX\n, where X is the\nchemical symbol of the species Nuclides with the same atomic number Z, but different neutron number\nN are called isotopes Nuclides with the same A are isobars and those\nwith the same N are isotones Most elements are mixtures of two or more isotopes" + }, + { + "Chapter": "9", + "sentence_range": "3036-3039", + "Text": "Nuclides with the same atomic number Z, but different neutron number\nN are called isotopes Nuclides with the same A are isobars and those\nwith the same N are isotones Most elements are mixtures of two or more isotopes The atomic mass\nof an element is a weighted average of the masses of its isotopes and\ncalculated in accordance to the relative abundances of the isotopes" + }, + { + "Chapter": "9", + "sentence_range": "3037-3040", + "Text": "Nuclides with the same A are isobars and those\nwith the same N are isotones Most elements are mixtures of two or more isotopes The atomic mass\nof an element is a weighted average of the masses of its isotopes and\ncalculated in accordance to the relative abundances of the isotopes 5" + }, + { + "Chapter": "9", + "sentence_range": "3038-3041", + "Text": "Most elements are mixtures of two or more isotopes The atomic mass\nof an element is a weighted average of the masses of its isotopes and\ncalculated in accordance to the relative abundances of the isotopes 5 A nucleus can be considered to be spherical in shape and assigned a\nradius" + }, + { + "Chapter": "9", + "sentence_range": "3039-3042", + "Text": "The atomic mass\nof an element is a weighted average of the masses of its isotopes and\ncalculated in accordance to the relative abundances of the isotopes 5 A nucleus can be considered to be spherical in shape and assigned a\nradius Electron scattering experiments allow determination of the\nnuclear radius; it is found that radii of nuclei fit the formula\nR = R0 A1/3,\nwhere R0 = a constant = 1" + }, + { + "Chapter": "9", + "sentence_range": "3040-3043", + "Text": "5 A nucleus can be considered to be spherical in shape and assigned a\nradius Electron scattering experiments allow determination of the\nnuclear radius; it is found that radii of nuclei fit the formula\nR = R0 A1/3,\nwhere R0 = a constant = 1 2 fm" + }, + { + "Chapter": "9", + "sentence_range": "3041-3044", + "Text": "A nucleus can be considered to be spherical in shape and assigned a\nradius Electron scattering experiments allow determination of the\nnuclear radius; it is found that radii of nuclei fit the formula\nR = R0 A1/3,\nwhere R0 = a constant = 1 2 fm This implies that the nuclear density\nis independent of A" + }, + { + "Chapter": "9", + "sentence_range": "3042-3045", + "Text": "Electron scattering experiments allow determination of the\nnuclear radius; it is found that radii of nuclei fit the formula\nR = R0 A1/3,\nwhere R0 = a constant = 1 2 fm This implies that the nuclear density\nis independent of A It is of the order of 1017 kg/m3" + }, + { + "Chapter": "9", + "sentence_range": "3043-3046", + "Text": "2 fm This implies that the nuclear density\nis independent of A It is of the order of 1017 kg/m3 6" + }, + { + "Chapter": "9", + "sentence_range": "3044-3047", + "Text": "This implies that the nuclear density\nis independent of A It is of the order of 1017 kg/m3 6 Neutrons and protons are bound in a nucleus by the short-range strong\nnuclear force" + }, + { + "Chapter": "9", + "sentence_range": "3045-3048", + "Text": "It is of the order of 1017 kg/m3 6 Neutrons and protons are bound in a nucleus by the short-range strong\nnuclear force The nuclear force does not distinguish between neutron\nand proton" + }, + { + "Chapter": "9", + "sentence_range": "3046-3049", + "Text": "6 Neutrons and protons are bound in a nucleus by the short-range strong\nnuclear force The nuclear force does not distinguish between neutron\nand proton Rationalised 2023-24\n319\nNuclei\n7" + }, + { + "Chapter": "9", + "sentence_range": "3047-3050", + "Text": "Neutrons and protons are bound in a nucleus by the short-range strong\nnuclear force The nuclear force does not distinguish between neutron\nand proton Rationalised 2023-24\n319\nNuclei\n7 The nuclear mass M is always less than the total mass, Sm, of its\nconstituents" + }, + { + "Chapter": "9", + "sentence_range": "3048-3051", + "Text": "The nuclear force does not distinguish between neutron\nand proton Rationalised 2023-24\n319\nNuclei\n7 The nuclear mass M is always less than the total mass, Sm, of its\nconstituents The difference in mass of a nucleus and its constituents\nis called the mass defect,\nDM = (Z mp + (A \u2013 Z )mn) \u2013 M\nUsing Einstein\u2019s mass energy relation, we express this mass difference\nin terms of energy as\nDEb = DM c2\nThe energy DEb represents the binding energy of the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "3049-3052", + "Text": "Rationalised 2023-24\n319\nNuclei\n7 The nuclear mass M is always less than the total mass, Sm, of its\nconstituents The difference in mass of a nucleus and its constituents\nis called the mass defect,\nDM = (Z mp + (A \u2013 Z )mn) \u2013 M\nUsing Einstein\u2019s mass energy relation, we express this mass difference\nin terms of energy as\nDEb = DM c2\nThe energy DEb represents the binding energy of the nucleus In the\nmass number range A = 30 to 170, the binding energy per nucleon is\nnearly constant, about 8 MeV/nucleon" + }, + { + "Chapter": "9", + "sentence_range": "3050-3053", + "Text": "The nuclear mass M is always less than the total mass, Sm, of its\nconstituents The difference in mass of a nucleus and its constituents\nis called the mass defect,\nDM = (Z mp + (A \u2013 Z )mn) \u2013 M\nUsing Einstein\u2019s mass energy relation, we express this mass difference\nin terms of energy as\nDEb = DM c2\nThe energy DEb represents the binding energy of the nucleus In the\nmass number range A = 30 to 170, the binding energy per nucleon is\nnearly constant, about 8 MeV/nucleon 8" + }, + { + "Chapter": "9", + "sentence_range": "3051-3054", + "Text": "The difference in mass of a nucleus and its constituents\nis called the mass defect,\nDM = (Z mp + (A \u2013 Z )mn) \u2013 M\nUsing Einstein\u2019s mass energy relation, we express this mass difference\nin terms of energy as\nDEb = DM c2\nThe energy DEb represents the binding energy of the nucleus In the\nmass number range A = 30 to 170, the binding energy per nucleon is\nnearly constant, about 8 MeV/nucleon 8 Energies associated with nuclear processes are about a million times\nlarger than chemical process" + }, + { + "Chapter": "9", + "sentence_range": "3052-3055", + "Text": "In the\nmass number range A = 30 to 170, the binding energy per nucleon is\nnearly constant, about 8 MeV/nucleon 8 Energies associated with nuclear processes are about a million times\nlarger than chemical process 9" + }, + { + "Chapter": "9", + "sentence_range": "3053-3056", + "Text": "8 Energies associated with nuclear processes are about a million times\nlarger than chemical process 9 The Q-value of a nuclear process is\n Q = final kinetic energy \u2013 initial kinetic energy" + }, + { + "Chapter": "9", + "sentence_range": "3054-3057", + "Text": "Energies associated with nuclear processes are about a million times\nlarger than chemical process 9 The Q-value of a nuclear process is\n Q = final kinetic energy \u2013 initial kinetic energy Due to conservation of mass-energy, this is also,\nQ = (sum of initial masses \u2013 sum of final masses)c2\n10" + }, + { + "Chapter": "9", + "sentence_range": "3055-3058", + "Text": "9 The Q-value of a nuclear process is\n Q = final kinetic energy \u2013 initial kinetic energy Due to conservation of mass-energy, this is also,\nQ = (sum of initial masses \u2013 sum of final masses)c2\n10 Radioactivity is the phenomenon in which nuclei of a given species\ntransform by giving out a or b or g rays; a-rays are helium nuclei;\nb-rays are electrons" + }, + { + "Chapter": "9", + "sentence_range": "3056-3059", + "Text": "The Q-value of a nuclear process is\n Q = final kinetic energy \u2013 initial kinetic energy Due to conservation of mass-energy, this is also,\nQ = (sum of initial masses \u2013 sum of final masses)c2\n10 Radioactivity is the phenomenon in which nuclei of a given species\ntransform by giving out a or b or g rays; a-rays are helium nuclei;\nb-rays are electrons g-rays are electromagnetic radiation of wavelengths\nshorter than X-rays" + }, + { + "Chapter": "9", + "sentence_range": "3057-3060", + "Text": "Due to conservation of mass-energy, this is also,\nQ = (sum of initial masses \u2013 sum of final masses)c2\n10 Radioactivity is the phenomenon in which nuclei of a given species\ntransform by giving out a or b or g rays; a-rays are helium nuclei;\nb-rays are electrons g-rays are electromagnetic radiation of wavelengths\nshorter than X-rays 11" + }, + { + "Chapter": "9", + "sentence_range": "3058-3061", + "Text": "Radioactivity is the phenomenon in which nuclei of a given species\ntransform by giving out a or b or g rays; a-rays are helium nuclei;\nb-rays are electrons g-rays are electromagnetic radiation of wavelengths\nshorter than X-rays 11 Energy is released when less tightly bound nuclei are transmuted into\nmore tightly bound nuclei" + }, + { + "Chapter": "9", + "sentence_range": "3059-3062", + "Text": "g-rays are electromagnetic radiation of wavelengths\nshorter than X-rays 11 Energy is released when less tightly bound nuclei are transmuted into\nmore tightly bound nuclei In fission, a heavy nucleus like 235\n92 U breaks\ninto two smaller fragments, e" + }, + { + "Chapter": "9", + "sentence_range": "3060-3063", + "Text": "11 Energy is released when less tightly bound nuclei are transmuted into\nmore tightly bound nuclei In fission, a heavy nucleus like 235\n92 U breaks\ninto two smaller fragments, e g" + }, + { + "Chapter": "9", + "sentence_range": "3061-3064", + "Text": "Energy is released when less tightly bound nuclei are transmuted into\nmore tightly bound nuclei In fission, a heavy nucleus like 235\n92 U breaks\ninto two smaller fragments, e g , 235\n1\n133\n99\n1\n92\n0\n51\n41\n0\nU+ n\nSb\nNb + 4 n\n\u2192\n+\n12" + }, + { + "Chapter": "9", + "sentence_range": "3062-3065", + "Text": "In fission, a heavy nucleus like 235\n92 U breaks\ninto two smaller fragments, e g , 235\n1\n133\n99\n1\n92\n0\n51\n41\n0\nU+ n\nSb\nNb + 4 n\n\u2192\n+\n12 In fusion, lighter nuclei combine to form a larger nucleus" + }, + { + "Chapter": "9", + "sentence_range": "3063-3066", + "Text": "g , 235\n1\n133\n99\n1\n92\n0\n51\n41\n0\nU+ n\nSb\nNb + 4 n\n\u2192\n+\n12 In fusion, lighter nuclei combine to form a larger nucleus Fusion of\nhydrogen nuclei into helium nuclei is the source of energy of all stars\nincluding our sun" + }, + { + "Chapter": "9", + "sentence_range": "3064-3067", + "Text": ", 235\n1\n133\n99\n1\n92\n0\n51\n41\n0\nU+ n\nSb\nNb + 4 n\n\u2192\n+\n12 In fusion, lighter nuclei combine to form a larger nucleus Fusion of\nhydrogen nuclei into helium nuclei is the source of energy of all stars\nincluding our sun Physical Quantity\nSymbol\nDimensions\nUnits\nRemarks\nAtomic mass unit\n[M]\nu\nUnit of mass for\nexpressing atomic or\nnuclear masses" + }, + { + "Chapter": "9", + "sentence_range": "3065-3068", + "Text": "In fusion, lighter nuclei combine to form a larger nucleus Fusion of\nhydrogen nuclei into helium nuclei is the source of energy of all stars\nincluding our sun Physical Quantity\nSymbol\nDimensions\nUnits\nRemarks\nAtomic mass unit\n[M]\nu\nUnit of mass for\nexpressing atomic or\nnuclear masses One\natomic mass unit equals\n1/12th of the mass of 12C\natom" + }, + { + "Chapter": "9", + "sentence_range": "3066-3069", + "Text": "Fusion of\nhydrogen nuclei into helium nuclei is the source of energy of all stars\nincluding our sun Physical Quantity\nSymbol\nDimensions\nUnits\nRemarks\nAtomic mass unit\n[M]\nu\nUnit of mass for\nexpressing atomic or\nnuclear masses One\natomic mass unit equals\n1/12th of the mass of 12C\natom Disintegration or\nl\n[T \u20131]\ns\u20131\ndecay constant\nHalf-life\nT1/2\n[T]\ns\nTime taken for the decay\nof one-half of the initial\nnumber of nuclei present\nin a radioactive sample" + }, + { + "Chapter": "9", + "sentence_range": "3067-3070", + "Text": "Physical Quantity\nSymbol\nDimensions\nUnits\nRemarks\nAtomic mass unit\n[M]\nu\nUnit of mass for\nexpressing atomic or\nnuclear masses One\natomic mass unit equals\n1/12th of the mass of 12C\natom Disintegration or\nl\n[T \u20131]\ns\u20131\ndecay constant\nHalf-life\nT1/2\n[T]\ns\nTime taken for the decay\nof one-half of the initial\nnumber of nuclei present\nin a radioactive sample Mean life\nt\n[T]\ns\nTime at which number of\nnuclei has been reduced to\ne\u20131 of its initial value\nActivity of a radio-\nR\n[ T\u20131]\nBq\nMeasure of the activity\nactive sample\nof a radioactive source" + }, + { + "Chapter": "9", + "sentence_range": "3068-3071", + "Text": "One\natomic mass unit equals\n1/12th of the mass of 12C\natom Disintegration or\nl\n[T \u20131]\ns\u20131\ndecay constant\nHalf-life\nT1/2\n[T]\ns\nTime taken for the decay\nof one-half of the initial\nnumber of nuclei present\nin a radioactive sample Mean life\nt\n[T]\ns\nTime at which number of\nnuclei has been reduced to\ne\u20131 of its initial value\nActivity of a radio-\nR\n[ T\u20131]\nBq\nMeasure of the activity\nactive sample\nof a radioactive source Rationalised 2023-24\nPhysics\n320\nPOINTS TO PONDER\n1" + }, + { + "Chapter": "9", + "sentence_range": "3069-3072", + "Text": "Disintegration or\nl\n[T \u20131]\ns\u20131\ndecay constant\nHalf-life\nT1/2\n[T]\ns\nTime taken for the decay\nof one-half of the initial\nnumber of nuclei present\nin a radioactive sample Mean life\nt\n[T]\ns\nTime at which number of\nnuclei has been reduced to\ne\u20131 of its initial value\nActivity of a radio-\nR\n[ T\u20131]\nBq\nMeasure of the activity\nactive sample\nof a radioactive source Rationalised 2023-24\nPhysics\n320\nPOINTS TO PONDER\n1 The density of nuclear matter is independent of the size of the nucleus" + }, + { + "Chapter": "9", + "sentence_range": "3070-3073", + "Text": "Mean life\nt\n[T]\ns\nTime at which number of\nnuclei has been reduced to\ne\u20131 of its initial value\nActivity of a radio-\nR\n[ T\u20131]\nBq\nMeasure of the activity\nactive sample\nof a radioactive source Rationalised 2023-24\nPhysics\n320\nPOINTS TO PONDER\n1 The density of nuclear matter is independent of the size of the nucleus The mass density of the atom does not follow this rule" + }, + { + "Chapter": "9", + "sentence_range": "3071-3074", + "Text": "Rationalised 2023-24\nPhysics\n320\nPOINTS TO PONDER\n1 The density of nuclear matter is independent of the size of the nucleus The mass density of the atom does not follow this rule 2" + }, + { + "Chapter": "9", + "sentence_range": "3072-3075", + "Text": "The density of nuclear matter is independent of the size of the nucleus The mass density of the atom does not follow this rule 2 The radius of a nucleus determined by electron scattering is found to\nbe slightly different from that determined by alpha-particle scattering" + }, + { + "Chapter": "9", + "sentence_range": "3073-3076", + "Text": "The mass density of the atom does not follow this rule 2 The radius of a nucleus determined by electron scattering is found to\nbe slightly different from that determined by alpha-particle scattering This is because electron scattering senses the charge distribution of\nthe nucleus, whereas alpha and similar particles sense the nuclear\nmatter" + }, + { + "Chapter": "9", + "sentence_range": "3074-3077", + "Text": "2 The radius of a nucleus determined by electron scattering is found to\nbe slightly different from that determined by alpha-particle scattering This is because electron scattering senses the charge distribution of\nthe nucleus, whereas alpha and similar particles sense the nuclear\nmatter 3" + }, + { + "Chapter": "9", + "sentence_range": "3075-3078", + "Text": "The radius of a nucleus determined by electron scattering is found to\nbe slightly different from that determined by alpha-particle scattering This is because electron scattering senses the charge distribution of\nthe nucleus, whereas alpha and similar particles sense the nuclear\nmatter 3 After Einstein showed the equivalence of mass and energy, E = mc 2,\nwe cannot any longer speak of separate laws of conservation of mass\nand conservation of energy, but we have to speak of a unified law of\nconservation of mass and energy" + }, + { + "Chapter": "9", + "sentence_range": "3076-3079", + "Text": "This is because electron scattering senses the charge distribution of\nthe nucleus, whereas alpha and similar particles sense the nuclear\nmatter 3 After Einstein showed the equivalence of mass and energy, E = mc 2,\nwe cannot any longer speak of separate laws of conservation of mass\nand conservation of energy, but we have to speak of a unified law of\nconservation of mass and energy The most convincing evidence that\nthis principle operates in nature comes from nuclear physics" + }, + { + "Chapter": "9", + "sentence_range": "3077-3080", + "Text": "3 After Einstein showed the equivalence of mass and energy, E = mc 2,\nwe cannot any longer speak of separate laws of conservation of mass\nand conservation of energy, but we have to speak of a unified law of\nconservation of mass and energy The most convincing evidence that\nthis principle operates in nature comes from nuclear physics It is\ncentral to our understanding of nuclear energy and harnessing it as a\nsource of power" + }, + { + "Chapter": "9", + "sentence_range": "3078-3081", + "Text": "After Einstein showed the equivalence of mass and energy, E = mc 2,\nwe cannot any longer speak of separate laws of conservation of mass\nand conservation of energy, but we have to speak of a unified law of\nconservation of mass and energy The most convincing evidence that\nthis principle operates in nature comes from nuclear physics It is\ncentral to our understanding of nuclear energy and harnessing it as a\nsource of power Using the principle, Q of a nuclear process (decay or\nreaction) can be expressed also in terms of initial and final masses" + }, + { + "Chapter": "9", + "sentence_range": "3079-3082", + "Text": "The most convincing evidence that\nthis principle operates in nature comes from nuclear physics It is\ncentral to our understanding of nuclear energy and harnessing it as a\nsource of power Using the principle, Q of a nuclear process (decay or\nreaction) can be expressed also in terms of initial and final masses 4" + }, + { + "Chapter": "9", + "sentence_range": "3080-3083", + "Text": "It is\ncentral to our understanding of nuclear energy and harnessing it as a\nsource of power Using the principle, Q of a nuclear process (decay or\nreaction) can be expressed also in terms of initial and final masses 4 The nature of the binding energy (per nucleon) curve shows that\nexothermic nuclear reactions are possible, when two light nuclei fuse\nor when a heavy nucleus undergoes fission into nuclei with intermediate\nmass" + }, + { + "Chapter": "9", + "sentence_range": "3081-3084", + "Text": "Using the principle, Q of a nuclear process (decay or\nreaction) can be expressed also in terms of initial and final masses 4 The nature of the binding energy (per nucleon) curve shows that\nexothermic nuclear reactions are possible, when two light nuclei fuse\nor when a heavy nucleus undergoes fission into nuclei with intermediate\nmass 5" + }, + { + "Chapter": "9", + "sentence_range": "3082-3085", + "Text": "4 The nature of the binding energy (per nucleon) curve shows that\nexothermic nuclear reactions are possible, when two light nuclei fuse\nor when a heavy nucleus undergoes fission into nuclei with intermediate\nmass 5 For fusion, the light nuclei must have sufficient initial energy to\novercome the coulomb potential barrier" + }, + { + "Chapter": "9", + "sentence_range": "3083-3086", + "Text": "The nature of the binding energy (per nucleon) curve shows that\nexothermic nuclear reactions are possible, when two light nuclei fuse\nor when a heavy nucleus undergoes fission into nuclei with intermediate\nmass 5 For fusion, the light nuclei must have sufficient initial energy to\novercome the coulomb potential barrier That is why fusion requires\nvery high temperatures" + }, + { + "Chapter": "9", + "sentence_range": "3084-3087", + "Text": "5 For fusion, the light nuclei must have sufficient initial energy to\novercome the coulomb potential barrier That is why fusion requires\nvery high temperatures 6" + }, + { + "Chapter": "9", + "sentence_range": "3085-3088", + "Text": "For fusion, the light nuclei must have sufficient initial energy to\novercome the coulomb potential barrier That is why fusion requires\nvery high temperatures 6 Although the binding energy (per nucleon) curve is smooth and slowly\nvarying, it shows peaks at nuclides like 4He, 16O etc" + }, + { + "Chapter": "9", + "sentence_range": "3086-3089", + "Text": "That is why fusion requires\nvery high temperatures 6 Although the binding energy (per nucleon) curve is smooth and slowly\nvarying, it shows peaks at nuclides like 4He, 16O etc This is considered\nas evidence of atom-like shell structure in nuclei" + }, + { + "Chapter": "9", + "sentence_range": "3087-3090", + "Text": "6 Although the binding energy (per nucleon) curve is smooth and slowly\nvarying, it shows peaks at nuclides like 4He, 16O etc This is considered\nas evidence of atom-like shell structure in nuclei 7" + }, + { + "Chapter": "9", + "sentence_range": "3088-3091", + "Text": "Although the binding energy (per nucleon) curve is smooth and slowly\nvarying, it shows peaks at nuclides like 4He, 16O etc This is considered\nas evidence of atom-like shell structure in nuclei 7 Electrons and positron are a particle-antiparticle pair" + }, + { + "Chapter": "9", + "sentence_range": "3089-3092", + "Text": "This is considered\nas evidence of atom-like shell structure in nuclei 7 Electrons and positron are a particle-antiparticle pair They are\nidentical in mass; their charges are equal in magnitude and opposite" + }, + { + "Chapter": "9", + "sentence_range": "3090-3093", + "Text": "7 Electrons and positron are a particle-antiparticle pair They are\nidentical in mass; their charges are equal in magnitude and opposite (It is found that when an electron and a positron come together, they\nannihilate each other giving energy in the form of gamma-ray photons" + }, + { + "Chapter": "9", + "sentence_range": "3091-3094", + "Text": "Electrons and positron are a particle-antiparticle pair They are\nidentical in mass; their charges are equal in magnitude and opposite (It is found that when an electron and a positron come together, they\nannihilate each other giving energy in the form of gamma-ray photons )\n8" + }, + { + "Chapter": "9", + "sentence_range": "3092-3095", + "Text": "They are\nidentical in mass; their charges are equal in magnitude and opposite (It is found that when an electron and a positron come together, they\nannihilate each other giving energy in the form of gamma-ray photons )\n8 Radioactivity is an indication of the instability of nuclei" + }, + { + "Chapter": "9", + "sentence_range": "3093-3096", + "Text": "(It is found that when an electron and a positron come together, they\nannihilate each other giving energy in the form of gamma-ray photons )\n8 Radioactivity is an indication of the instability of nuclei Stability\nrequires the ratio of neutron to proton to be around 1:1 for light\nnuclei" + }, + { + "Chapter": "9", + "sentence_range": "3094-3097", + "Text": ")\n8 Radioactivity is an indication of the instability of nuclei Stability\nrequires the ratio of neutron to proton to be around 1:1 for light\nnuclei This ratio increases to about 3:2 for heavy nuclei" + }, + { + "Chapter": "9", + "sentence_range": "3095-3098", + "Text": "Radioactivity is an indication of the instability of nuclei Stability\nrequires the ratio of neutron to proton to be around 1:1 for light\nnuclei This ratio increases to about 3:2 for heavy nuclei (More\nneutrons are required to overcome the effect of repulsion among the\nprotons" + }, + { + "Chapter": "9", + "sentence_range": "3096-3099", + "Text": "Stability\nrequires the ratio of neutron to proton to be around 1:1 for light\nnuclei This ratio increases to about 3:2 for heavy nuclei (More\nneutrons are required to overcome the effect of repulsion among the\nprotons ) Nuclei which are away from the stability ratio, i" + }, + { + "Chapter": "9", + "sentence_range": "3097-3100", + "Text": "This ratio increases to about 3:2 for heavy nuclei (More\nneutrons are required to overcome the effect of repulsion among the\nprotons ) Nuclei which are away from the stability ratio, i e" + }, + { + "Chapter": "9", + "sentence_range": "3098-3101", + "Text": "(More\nneutrons are required to overcome the effect of repulsion among the\nprotons ) Nuclei which are away from the stability ratio, i e , nuclei\nwhich have an excess of neutrons or protons are unstable" + }, + { + "Chapter": "9", + "sentence_range": "3099-3102", + "Text": ") Nuclei which are away from the stability ratio, i e , nuclei\nwhich have an excess of neutrons or protons are unstable In fact,\nonly about 10% of knon isotopes (of all elements), are stable" + }, + { + "Chapter": "9", + "sentence_range": "3100-3103", + "Text": "e , nuclei\nwhich have an excess of neutrons or protons are unstable In fact,\nonly about 10% of knon isotopes (of all elements), are stable Others\nhave been either artificially produced in the laboratory by bombarding\na, p, d, n or other particles on targets of stable nuclear species or\nidentified in astronomical observations of matter in the universe" + }, + { + "Chapter": "9", + "sentence_range": "3101-3104", + "Text": ", nuclei\nwhich have an excess of neutrons or protons are unstable In fact,\nonly about 10% of knon isotopes (of all elements), are stable Others\nhave been either artificially produced in the laboratory by bombarding\na, p, d, n or other particles on targets of stable nuclear species or\nidentified in astronomical observations of matter in the universe Rationalised 2023-24\n321\nNuclei\nEXERCISES\nYou may find the following data useful in solving the exercises:\ne = 1" + }, + { + "Chapter": "9", + "sentence_range": "3102-3105", + "Text": "In fact,\nonly about 10% of knon isotopes (of all elements), are stable Others\nhave been either artificially produced in the laboratory by bombarding\na, p, d, n or other particles on targets of stable nuclear species or\nidentified in astronomical observations of matter in the universe Rationalised 2023-24\n321\nNuclei\nEXERCISES\nYou may find the following data useful in solving the exercises:\ne = 1 6\u00d710\u201319C\nN\n= 6" + }, + { + "Chapter": "9", + "sentence_range": "3103-3106", + "Text": "Others\nhave been either artificially produced in the laboratory by bombarding\na, p, d, n or other particles on targets of stable nuclear species or\nidentified in astronomical observations of matter in the universe Rationalised 2023-24\n321\nNuclei\nEXERCISES\nYou may find the following data useful in solving the exercises:\ne = 1 6\u00d710\u201319C\nN\n= 6 023\u00d71023 per mole\n1/(4pe0) = 9 \u00d7 109 N m2/C2\nk\n= 1" + }, + { + "Chapter": "9", + "sentence_range": "3104-3107", + "Text": "Rationalised 2023-24\n321\nNuclei\nEXERCISES\nYou may find the following data useful in solving the exercises:\ne = 1 6\u00d710\u201319C\nN\n= 6 023\u00d71023 per mole\n1/(4pe0) = 9 \u00d7 109 N m2/C2\nk\n= 1 381\u00d710\u201323J K\u20131\n1 MeV = 1" + }, + { + "Chapter": "9", + "sentence_range": "3105-3108", + "Text": "6\u00d710\u201319C\nN\n= 6 023\u00d71023 per mole\n1/(4pe0) = 9 \u00d7 109 N m2/C2\nk\n= 1 381\u00d710\u201323J K\u20131\n1 MeV = 1 6\u00d710\u201313J\n1 u = 931" + }, + { + "Chapter": "9", + "sentence_range": "3106-3109", + "Text": "023\u00d71023 per mole\n1/(4pe0) = 9 \u00d7 109 N m2/C2\nk\n= 1 381\u00d710\u201323J K\u20131\n1 MeV = 1 6\u00d710\u201313J\n1 u = 931 5 MeV/c2\n1 year = 3" + }, + { + "Chapter": "9", + "sentence_range": "3107-3110", + "Text": "381\u00d710\u201323J K\u20131\n1 MeV = 1 6\u00d710\u201313J\n1 u = 931 5 MeV/c2\n1 year = 3 154\u00d7107 s\nmH = 1" + }, + { + "Chapter": "9", + "sentence_range": "3108-3111", + "Text": "6\u00d710\u201313J\n1 u = 931 5 MeV/c2\n1 year = 3 154\u00d7107 s\nmH = 1 007825 u\nmn = 1" + }, + { + "Chapter": "9", + "sentence_range": "3109-3112", + "Text": "5 MeV/c2\n1 year = 3 154\u00d7107 s\nmH = 1 007825 u\nmn = 1 008665 u\nm( 4\n2He ) = 4" + }, + { + "Chapter": "9", + "sentence_range": "3110-3113", + "Text": "154\u00d7107 s\nmH = 1 007825 u\nmn = 1 008665 u\nm( 4\n2He ) = 4 002603 u\nme = 0" + }, + { + "Chapter": "9", + "sentence_range": "3111-3114", + "Text": "007825 u\nmn = 1 008665 u\nm( 4\n2He ) = 4 002603 u\nme = 0 000548 u\n13" + }, + { + "Chapter": "9", + "sentence_range": "3112-3115", + "Text": "008665 u\nm( 4\n2He ) = 4 002603 u\nme = 0 000548 u\n13 1\nObtain the binding energy (in MeV) of a nitrogen nucleus (\n)\n14\n7 N ,\ngiven m (\n)\n14\n7 N =14" + }, + { + "Chapter": "9", + "sentence_range": "3113-3116", + "Text": "002603 u\nme = 0 000548 u\n13 1\nObtain the binding energy (in MeV) of a nitrogen nucleus (\n)\n14\n7 N ,\ngiven m (\n)\n14\n7 N =14 00307 u\n13" + }, + { + "Chapter": "9", + "sentence_range": "3114-3117", + "Text": "000548 u\n13 1\nObtain the binding energy (in MeV) of a nitrogen nucleus (\n)\n14\n7 N ,\ngiven m (\n)\n14\n7 N =14 00307 u\n13 2\nObtain the binding energy of the nuclei 56\n26Fe and 209\n83 Bi in units of\nMeV from the following data:\nm ( 56\n26Fe ) = 55" + }, + { + "Chapter": "9", + "sentence_range": "3115-3118", + "Text": "1\nObtain the binding energy (in MeV) of a nitrogen nucleus (\n)\n14\n7 N ,\ngiven m (\n)\n14\n7 N =14 00307 u\n13 2\nObtain the binding energy of the nuclei 56\n26Fe and 209\n83 Bi in units of\nMeV from the following data:\nm ( 56\n26Fe ) = 55 934939 u m ( 209\n83 Bi ) = 208" + }, + { + "Chapter": "9", + "sentence_range": "3116-3119", + "Text": "00307 u\n13 2\nObtain the binding energy of the nuclei 56\n26Fe and 209\n83 Bi in units of\nMeV from the following data:\nm ( 56\n26Fe ) = 55 934939 u m ( 209\n83 Bi ) = 208 980388 u\n13" + }, + { + "Chapter": "9", + "sentence_range": "3117-3120", + "Text": "2\nObtain the binding energy of the nuclei 56\n26Fe and 209\n83 Bi in units of\nMeV from the following data:\nm ( 56\n26Fe ) = 55 934939 u m ( 209\n83 Bi ) = 208 980388 u\n13 3\nA given coin has a mass of 3" + }, + { + "Chapter": "9", + "sentence_range": "3118-3121", + "Text": "934939 u m ( 209\n83 Bi ) = 208 980388 u\n13 3\nA given coin has a mass of 3 0 g" + }, + { + "Chapter": "9", + "sentence_range": "3119-3122", + "Text": "980388 u\n13 3\nA given coin has a mass of 3 0 g Calculate the nuclear energy that\nwould be required to separate all the neutrons and protons from\neach other" + }, + { + "Chapter": "9", + "sentence_range": "3120-3123", + "Text": "3\nA given coin has a mass of 3 0 g Calculate the nuclear energy that\nwould be required to separate all the neutrons and protons from\neach other For simplicity assume that the coin is entirely made of\n63\n29Cu atoms (of mass 62" + }, + { + "Chapter": "9", + "sentence_range": "3121-3124", + "Text": "0 g Calculate the nuclear energy that\nwould be required to separate all the neutrons and protons from\neach other For simplicity assume that the coin is entirely made of\n63\n29Cu atoms (of mass 62 92960 u)" + }, + { + "Chapter": "9", + "sentence_range": "3122-3125", + "Text": "Calculate the nuclear energy that\nwould be required to separate all the neutrons and protons from\neach other For simplicity assume that the coin is entirely made of\n63\n29Cu atoms (of mass 62 92960 u) 13" + }, + { + "Chapter": "9", + "sentence_range": "3123-3126", + "Text": "For simplicity assume that the coin is entirely made of\n63\n29Cu atoms (of mass 62 92960 u) 13 4\nObtain approximately the ratio of the nuclear radii of the gold isotope\n197\n79 Au and the silver isotope 107\n47 Ag" + }, + { + "Chapter": "9", + "sentence_range": "3124-3127", + "Text": "92960 u) 13 4\nObtain approximately the ratio of the nuclear radii of the gold isotope\n197\n79 Au and the silver isotope 107\n47 Ag 13" + }, + { + "Chapter": "9", + "sentence_range": "3125-3128", + "Text": "13 4\nObtain approximately the ratio of the nuclear radii of the gold isotope\n197\n79 Au and the silver isotope 107\n47 Ag 13 5\nThe Q value of a nuclear reaction A + b \u00ae C + d is defined by\nQ = [ mA + mb \u2013 mC \u2013 md]c2\n where the masses refer to the respective nuclei" + }, + { + "Chapter": "9", + "sentence_range": "3126-3129", + "Text": "4\nObtain approximately the ratio of the nuclear radii of the gold isotope\n197\n79 Au and the silver isotope 107\n47 Ag 13 5\nThe Q value of a nuclear reaction A + b \u00ae C + d is defined by\nQ = [ mA + mb \u2013 mC \u2013 md]c2\n where the masses refer to the respective nuclei Determine from the\ngiven data the Q-value of the following reactions and state whether\nthe reactions are exothermic or endothermic" + }, + { + "Chapter": "9", + "sentence_range": "3127-3130", + "Text": "13 5\nThe Q value of a nuclear reaction A + b \u00ae C + d is defined by\nQ = [ mA + mb \u2013 mC \u2013 md]c2\n where the masses refer to the respective nuclei Determine from the\ngiven data the Q-value of the following reactions and state whether\nthe reactions are exothermic or endothermic (i) 1\n3\n2\n2\n1\n1\n1\n1\nH+ H\nH+ H\n\u2192\n(ii) 12\n12\n20\n4\n6\n6\n10\n2\nC+ C\nNe+ He\n\u2192\nAtomic masses are given to be\nm ( 2\nm ( 31 H ) = 2" + }, + { + "Chapter": "9", + "sentence_range": "3128-3131", + "Text": "5\nThe Q value of a nuclear reaction A + b \u00ae C + d is defined by\nQ = [ mA + mb \u2013 mC \u2013 md]c2\n where the masses refer to the respective nuclei Determine from the\ngiven data the Q-value of the following reactions and state whether\nthe reactions are exothermic or endothermic (i) 1\n3\n2\n2\n1\n1\n1\n1\nH+ H\nH+ H\n\u2192\n(ii) 12\n12\n20\n4\n6\n6\n10\n2\nC+ C\nNe+ He\n\u2192\nAtomic masses are given to be\nm ( 2\nm ( 31 H ) = 2 014102 u\n1 H) = 3" + }, + { + "Chapter": "9", + "sentence_range": "3129-3132", + "Text": "Determine from the\ngiven data the Q-value of the following reactions and state whether\nthe reactions are exothermic or endothermic (i) 1\n3\n2\n2\n1\n1\n1\n1\nH+ H\nH+ H\n\u2192\n(ii) 12\n12\n20\n4\n6\n6\n10\n2\nC+ C\nNe+ He\n\u2192\nAtomic masses are given to be\nm ( 2\nm ( 31 H ) = 2 014102 u\n1 H) = 3 016049 u\nm ( 12\nm ( 206 C ) = 12" + }, + { + "Chapter": "9", + "sentence_range": "3130-3133", + "Text": "(i) 1\n3\n2\n2\n1\n1\n1\n1\nH+ H\nH+ H\n\u2192\n(ii) 12\n12\n20\n4\n6\n6\n10\n2\nC+ C\nNe+ He\n\u2192\nAtomic masses are given to be\nm ( 2\nm ( 31 H ) = 2 014102 u\n1 H) = 3 016049 u\nm ( 12\nm ( 206 C ) = 12 000000 u\n10 Ne ) = 19" + }, + { + "Chapter": "9", + "sentence_range": "3131-3134", + "Text": "014102 u\n1 H) = 3 016049 u\nm ( 12\nm ( 206 C ) = 12 000000 u\n10 Ne ) = 19 992439 u\n13" + }, + { + "Chapter": "9", + "sentence_range": "3132-3135", + "Text": "016049 u\nm ( 12\nm ( 206 C ) = 12 000000 u\n10 Ne ) = 19 992439 u\n13 6\nSuppose, we think of fission of a 56\n26Fe nucleus into two equal\nfragments, 28\n13 Al" + }, + { + "Chapter": "9", + "sentence_range": "3133-3136", + "Text": "000000 u\n10 Ne ) = 19 992439 u\n13 6\nSuppose, we think of fission of a 56\n26Fe nucleus into two equal\nfragments, 28\n13 Al Is the fission energetically possible" + }, + { + "Chapter": "9", + "sentence_range": "3134-3137", + "Text": "992439 u\n13 6\nSuppose, we think of fission of a 56\n26Fe nucleus into two equal\nfragments, 28\n13 Al Is the fission energetically possible Argue by\nworking out Q of the process" + }, + { + "Chapter": "9", + "sentence_range": "3135-3138", + "Text": "6\nSuppose, we think of fission of a 56\n26Fe nucleus into two equal\nfragments, 28\n13 Al Is the fission energetically possible Argue by\nworking out Q of the process Given m ( 56\n26Fe ) = 55" + }, + { + "Chapter": "9", + "sentence_range": "3136-3139", + "Text": "Is the fission energetically possible Argue by\nworking out Q of the process Given m ( 56\n26Fe ) = 55 93494 u and\nm ( 28\n13 Al ) = 27" + }, + { + "Chapter": "9", + "sentence_range": "3137-3140", + "Text": "Argue by\nworking out Q of the process Given m ( 56\n26Fe ) = 55 93494 u and\nm ( 28\n13 Al ) = 27 98191 u" + }, + { + "Chapter": "9", + "sentence_range": "3138-3141", + "Text": "Given m ( 56\n26Fe ) = 55 93494 u and\nm ( 28\n13 Al ) = 27 98191 u Rationalised 2023-24\nPhysics\n322\n13" + }, + { + "Chapter": "9", + "sentence_range": "3139-3142", + "Text": "93494 u and\nm ( 28\n13 Al ) = 27 98191 u Rationalised 2023-24\nPhysics\n322\n13 7\nThe fission properties of 239\n94 Pu are very similar to those of 235\n92 U" + }, + { + "Chapter": "9", + "sentence_range": "3140-3143", + "Text": "98191 u Rationalised 2023-24\nPhysics\n322\n13 7\nThe fission properties of 239\n94 Pu are very similar to those of 235\n92 U The\naverage energy released per fission is 180 MeV" + }, + { + "Chapter": "9", + "sentence_range": "3141-3144", + "Text": "Rationalised 2023-24\nPhysics\n322\n13 7\nThe fission properties of 239\n94 Pu are very similar to those of 235\n92 U The\naverage energy released per fission is 180 MeV How much energy,\nin MeV, is released if all the atoms in 1 kg of pure 239\n94 Pu undergo\nfission" + }, + { + "Chapter": "9", + "sentence_range": "3142-3145", + "Text": "7\nThe fission properties of 239\n94 Pu are very similar to those of 235\n92 U The\naverage energy released per fission is 180 MeV How much energy,\nin MeV, is released if all the atoms in 1 kg of pure 239\n94 Pu undergo\nfission 13" + }, + { + "Chapter": "9", + "sentence_range": "3143-3146", + "Text": "The\naverage energy released per fission is 180 MeV How much energy,\nin MeV, is released if all the atoms in 1 kg of pure 239\n94 Pu undergo\nfission 13 8\nHow long can an electric lamp of 100W be kept glowing by fusion of\n2" + }, + { + "Chapter": "9", + "sentence_range": "3144-3147", + "Text": "How much energy,\nin MeV, is released if all the atoms in 1 kg of pure 239\n94 Pu undergo\nfission 13 8\nHow long can an electric lamp of 100W be kept glowing by fusion of\n2 0 kg of deuterium" + }, + { + "Chapter": "9", + "sentence_range": "3145-3148", + "Text": "13 8\nHow long can an electric lamp of 100W be kept glowing by fusion of\n2 0 kg of deuterium Take the fusion reaction as\n2\n2\n3\n1\n1\n2\nH+ H\nHe+n+3" + }, + { + "Chapter": "9", + "sentence_range": "3146-3149", + "Text": "8\nHow long can an electric lamp of 100W be kept glowing by fusion of\n2 0 kg of deuterium Take the fusion reaction as\n2\n2\n3\n1\n1\n2\nH+ H\nHe+n+3 27 MeV\n\u2192\n13" + }, + { + "Chapter": "9", + "sentence_range": "3147-3150", + "Text": "0 kg of deuterium Take the fusion reaction as\n2\n2\n3\n1\n1\n2\nH+ H\nHe+n+3 27 MeV\n\u2192\n13 9\nCalculate the height of the potential barrier for a head on collision\nof two deuterons" + }, + { + "Chapter": "9", + "sentence_range": "3148-3151", + "Text": "Take the fusion reaction as\n2\n2\n3\n1\n1\n2\nH+ H\nHe+n+3 27 MeV\n\u2192\n13 9\nCalculate the height of the potential barrier for a head on collision\nof two deuterons (Hint: The height of the potential barrier is given\nby the Coulomb repulsion between the two deuterons when they\njust touch each other" + }, + { + "Chapter": "9", + "sentence_range": "3149-3152", + "Text": "27 MeV\n\u2192\n13 9\nCalculate the height of the potential barrier for a head on collision\nof two deuterons (Hint: The height of the potential barrier is given\nby the Coulomb repulsion between the two deuterons when they\njust touch each other Assume that they can be taken as hard\nspheres of radius 2" + }, + { + "Chapter": "9", + "sentence_range": "3150-3153", + "Text": "9\nCalculate the height of the potential barrier for a head on collision\nof two deuterons (Hint: The height of the potential barrier is given\nby the Coulomb repulsion between the two deuterons when they\njust touch each other Assume that they can be taken as hard\nspheres of radius 2 0 fm" + }, + { + "Chapter": "9", + "sentence_range": "3151-3154", + "Text": "(Hint: The height of the potential barrier is given\nby the Coulomb repulsion between the two deuterons when they\njust touch each other Assume that they can be taken as hard\nspheres of radius 2 0 fm )\n13" + }, + { + "Chapter": "9", + "sentence_range": "3152-3155", + "Text": "Assume that they can be taken as hard\nspheres of radius 2 0 fm )\n13 10 From the relation R = R0A1/3, where R0 is a constant and A is the\nmass number of a nucleus, show that the nuclear matter density is\nnearly constant (i" + }, + { + "Chapter": "9", + "sentence_range": "3153-3156", + "Text": "0 fm )\n13 10 From the relation R = R0A1/3, where R0 is a constant and A is the\nmass number of a nucleus, show that the nuclear matter density is\nnearly constant (i e" + }, + { + "Chapter": "9", + "sentence_range": "3154-3157", + "Text": ")\n13 10 From the relation R = R0A1/3, where R0 is a constant and A is the\nmass number of a nucleus, show that the nuclear matter density is\nnearly constant (i e independent of A)" + }, + { + "Chapter": "9", + "sentence_range": "3155-3158", + "Text": "10 From the relation R = R0A1/3, where R0 is a constant and A is the\nmass number of a nucleus, show that the nuclear matter density is\nnearly constant (i e independent of A) Rationalised 2023-24\n14" + }, + { + "Chapter": "9", + "sentence_range": "3156-3159", + "Text": "e independent of A) Rationalised 2023-24\n14 1 INTRODUCTION\nDevices in which a controlled flow of electrons can be obtained are the\nbasic building blocks of all the electronic circuits" + }, + { + "Chapter": "9", + "sentence_range": "3157-3160", + "Text": "independent of A) Rationalised 2023-24\n14 1 INTRODUCTION\nDevices in which a controlled flow of electrons can be obtained are the\nbasic building blocks of all the electronic circuits Before the discovery of\ntransistor in 1948, such devices were mostly vacuum tubes (also called\nvalves) like the vacuum diode which has two electrodes, viz" + }, + { + "Chapter": "9", + "sentence_range": "3158-3161", + "Text": "Rationalised 2023-24\n14 1 INTRODUCTION\nDevices in which a controlled flow of electrons can be obtained are the\nbasic building blocks of all the electronic circuits Before the discovery of\ntransistor in 1948, such devices were mostly vacuum tubes (also called\nvalves) like the vacuum diode which has two electrodes, viz , anode (often\ncalled plate) and cathode; triode which has three electrodes \u2013 cathode,\nplate and grid; tetrode and pentode (respectively with 4 and 5 electrodes)" + }, + { + "Chapter": "9", + "sentence_range": "3159-3162", + "Text": "1 INTRODUCTION\nDevices in which a controlled flow of electrons can be obtained are the\nbasic building blocks of all the electronic circuits Before the discovery of\ntransistor in 1948, such devices were mostly vacuum tubes (also called\nvalves) like the vacuum diode which has two electrodes, viz , anode (often\ncalled plate) and cathode; triode which has three electrodes \u2013 cathode,\nplate and grid; tetrode and pentode (respectively with 4 and 5 electrodes) In a vacuum tube, the electrons are supplied by a heated cathode and\nthe controlled flow of these electrons in vacuum is obtained by varying\nthe voltage between its different electrodes" + }, + { + "Chapter": "9", + "sentence_range": "3160-3163", + "Text": "Before the discovery of\ntransistor in 1948, such devices were mostly vacuum tubes (also called\nvalves) like the vacuum diode which has two electrodes, viz , anode (often\ncalled plate) and cathode; triode which has three electrodes \u2013 cathode,\nplate and grid; tetrode and pentode (respectively with 4 and 5 electrodes) In a vacuum tube, the electrons are supplied by a heated cathode and\nthe controlled flow of these electrons in vacuum is obtained by varying\nthe voltage between its different electrodes Vacuum is required in the\ninter-electrode space; otherwise the moving electrons may lose their\nenergy on collision with the air molecules in their path" + }, + { + "Chapter": "9", + "sentence_range": "3161-3164", + "Text": ", anode (often\ncalled plate) and cathode; triode which has three electrodes \u2013 cathode,\nplate and grid; tetrode and pentode (respectively with 4 and 5 electrodes) In a vacuum tube, the electrons are supplied by a heated cathode and\nthe controlled flow of these electrons in vacuum is obtained by varying\nthe voltage between its different electrodes Vacuum is required in the\ninter-electrode space; otherwise the moving electrons may lose their\nenergy on collision with the air molecules in their path In these devices\nthe electrons can flow only from the cathode to the anode (i" + }, + { + "Chapter": "9", + "sentence_range": "3162-3165", + "Text": "In a vacuum tube, the electrons are supplied by a heated cathode and\nthe controlled flow of these electrons in vacuum is obtained by varying\nthe voltage between its different electrodes Vacuum is required in the\ninter-electrode space; otherwise the moving electrons may lose their\nenergy on collision with the air molecules in their path In these devices\nthe electrons can flow only from the cathode to the anode (i e" + }, + { + "Chapter": "9", + "sentence_range": "3163-3166", + "Text": "Vacuum is required in the\ninter-electrode space; otherwise the moving electrons may lose their\nenergy on collision with the air molecules in their path In these devices\nthe electrons can flow only from the cathode to the anode (i e , only in one\ndirection)" + }, + { + "Chapter": "9", + "sentence_range": "3164-3167", + "Text": "In these devices\nthe electrons can flow only from the cathode to the anode (i e , only in one\ndirection) Therefore, such devices are generally referred to as valves" + }, + { + "Chapter": "9", + "sentence_range": "3165-3168", + "Text": "e , only in one\ndirection) Therefore, such devices are generally referred to as valves These vacuum tube devices are bulky, consume high power, operate\ngenerally at high voltages (~100 V) and have limited life and low reliability" + }, + { + "Chapter": "9", + "sentence_range": "3166-3169", + "Text": ", only in one\ndirection) Therefore, such devices are generally referred to as valves These vacuum tube devices are bulky, consume high power, operate\ngenerally at high voltages (~100 V) and have limited life and low reliability The seed of the development of modern solid-state semiconductor\nelectronics goes back to 1930\u2019s when it was realised that some solid-\nstate semiconductors and their junctions offer the possibility of controlling\nthe number and the direction of flow of charge carriers through them" + }, + { + "Chapter": "9", + "sentence_range": "3167-3170", + "Text": "Therefore, such devices are generally referred to as valves These vacuum tube devices are bulky, consume high power, operate\ngenerally at high voltages (~100 V) and have limited life and low reliability The seed of the development of modern solid-state semiconductor\nelectronics goes back to 1930\u2019s when it was realised that some solid-\nstate semiconductors and their junctions offer the possibility of controlling\nthe number and the direction of flow of charge carriers through them Simple excitations like light, heat or small applied voltage can change\nthe number of mobile charges in a semiconductor" + }, + { + "Chapter": "9", + "sentence_range": "3168-3171", + "Text": "These vacuum tube devices are bulky, consume high power, operate\ngenerally at high voltages (~100 V) and have limited life and low reliability The seed of the development of modern solid-state semiconductor\nelectronics goes back to 1930\u2019s when it was realised that some solid-\nstate semiconductors and their junctions offer the possibility of controlling\nthe number and the direction of flow of charge carriers through them Simple excitations like light, heat or small applied voltage can change\nthe number of mobile charges in a semiconductor Note that the supply\nChapter Fourteen\nSEMICONDUCTOR\nELECTRONICS:\nMATERIALS, DEVICES\nAND SIMPLE CIRCUITS\nRationalised 2023-24\nPhysics\n324\nand flow of charge carriers in the semiconductor devices are within the\nsolid itself, while in the earlier vacuum tubes/valves, the mobile electrons\nwere obtained from a heated cathode and they were made to flow in an\nevacuated space or vacuum" + }, + { + "Chapter": "9", + "sentence_range": "3169-3172", + "Text": "The seed of the development of modern solid-state semiconductor\nelectronics goes back to 1930\u2019s when it was realised that some solid-\nstate semiconductors and their junctions offer the possibility of controlling\nthe number and the direction of flow of charge carriers through them Simple excitations like light, heat or small applied voltage can change\nthe number of mobile charges in a semiconductor Note that the supply\nChapter Fourteen\nSEMICONDUCTOR\nELECTRONICS:\nMATERIALS, DEVICES\nAND SIMPLE CIRCUITS\nRationalised 2023-24\nPhysics\n324\nand flow of charge carriers in the semiconductor devices are within the\nsolid itself, while in the earlier vacuum tubes/valves, the mobile electrons\nwere obtained from a heated cathode and they were made to flow in an\nevacuated space or vacuum No external heating or large evacuated space\nis required by the semiconductor devices" + }, + { + "Chapter": "9", + "sentence_range": "3170-3173", + "Text": "Simple excitations like light, heat or small applied voltage can change\nthe number of mobile charges in a semiconductor Note that the supply\nChapter Fourteen\nSEMICONDUCTOR\nELECTRONICS:\nMATERIALS, DEVICES\nAND SIMPLE CIRCUITS\nRationalised 2023-24\nPhysics\n324\nand flow of charge carriers in the semiconductor devices are within the\nsolid itself, while in the earlier vacuum tubes/valves, the mobile electrons\nwere obtained from a heated cathode and they were made to flow in an\nevacuated space or vacuum No external heating or large evacuated space\nis required by the semiconductor devices They are small in size, consume\nlow power, operate at low voltages and have long life and high reliability" + }, + { + "Chapter": "9", + "sentence_range": "3171-3174", + "Text": "Note that the supply\nChapter Fourteen\nSEMICONDUCTOR\nELECTRONICS:\nMATERIALS, DEVICES\nAND SIMPLE CIRCUITS\nRationalised 2023-24\nPhysics\n324\nand flow of charge carriers in the semiconductor devices are within the\nsolid itself, while in the earlier vacuum tubes/valves, the mobile electrons\nwere obtained from a heated cathode and they were made to flow in an\nevacuated space or vacuum No external heating or large evacuated space\nis required by the semiconductor devices They are small in size, consume\nlow power, operate at low voltages and have long life and high reliability Even the Cathode Ray Tubes (CRT) used in television and computer\nmonitors which work on the principle of vacuum tubes are being replaced\nby Liquid Crystal Display (LCD) monitors with supporting solid state\nelectronics" + }, + { + "Chapter": "9", + "sentence_range": "3172-3175", + "Text": "No external heating or large evacuated space\nis required by the semiconductor devices They are small in size, consume\nlow power, operate at low voltages and have long life and high reliability Even the Cathode Ray Tubes (CRT) used in television and computer\nmonitors which work on the principle of vacuum tubes are being replaced\nby Liquid Crystal Display (LCD) monitors with supporting solid state\nelectronics Much before the full implications of the semiconductor devices\nwas formally understood, a naturally occurring crystal of galena (Lead\nsulphide, PbS) with a metal point contact attached to it was used as\ndetector of radio waves" + }, + { + "Chapter": "9", + "sentence_range": "3173-3176", + "Text": "They are small in size, consume\nlow power, operate at low voltages and have long life and high reliability Even the Cathode Ray Tubes (CRT) used in television and computer\nmonitors which work on the principle of vacuum tubes are being replaced\nby Liquid Crystal Display (LCD) monitors with supporting solid state\nelectronics Much before the full implications of the semiconductor devices\nwas formally understood, a naturally occurring crystal of galena (Lead\nsulphide, PbS) with a metal point contact attached to it was used as\ndetector of radio waves In the following sections, we will introduce the basic concepts of\nsemiconductor physics and discuss some semiconductor devices like\njunction diodes (a 2-electrode device) and bipolar junction transistor (a\n3-electrode device)" + }, + { + "Chapter": "9", + "sentence_range": "3174-3177", + "Text": "Even the Cathode Ray Tubes (CRT) used in television and computer\nmonitors which work on the principle of vacuum tubes are being replaced\nby Liquid Crystal Display (LCD) monitors with supporting solid state\nelectronics Much before the full implications of the semiconductor devices\nwas formally understood, a naturally occurring crystal of galena (Lead\nsulphide, PbS) with a metal point contact attached to it was used as\ndetector of radio waves In the following sections, we will introduce the basic concepts of\nsemiconductor physics and discuss some semiconductor devices like\njunction diodes (a 2-electrode device) and bipolar junction transistor (a\n3-electrode device) A few circuits illustrating their applications will also\nbe described" + }, + { + "Chapter": "9", + "sentence_range": "3175-3178", + "Text": "Much before the full implications of the semiconductor devices\nwas formally understood, a naturally occurring crystal of galena (Lead\nsulphide, PbS) with a metal point contact attached to it was used as\ndetector of radio waves In the following sections, we will introduce the basic concepts of\nsemiconductor physics and discuss some semiconductor devices like\njunction diodes (a 2-electrode device) and bipolar junction transistor (a\n3-electrode device) A few circuits illustrating their applications will also\nbe described 14" + }, + { + "Chapter": "9", + "sentence_range": "3176-3179", + "Text": "In the following sections, we will introduce the basic concepts of\nsemiconductor physics and discuss some semiconductor devices like\njunction diodes (a 2-electrode device) and bipolar junction transistor (a\n3-electrode device) A few circuits illustrating their applications will also\nbe described 14 2 CLASSIFICATION OF METALS, CONDUCTORS AND\nSEMICONDUCTORS\nOn the basis of conductivity\nOn the basis of the relative values of electrical conductivity (s ) or resistivity\n(r = 1/s ), the solids are broadly classified as:\n(i) Metals: They possess very low resistivity (or high conductivity)" + }, + { + "Chapter": "9", + "sentence_range": "3177-3180", + "Text": "A few circuits illustrating their applications will also\nbe described 14 2 CLASSIFICATION OF METALS, CONDUCTORS AND\nSEMICONDUCTORS\nOn the basis of conductivity\nOn the basis of the relative values of electrical conductivity (s ) or resistivity\n(r = 1/s ), the solids are broadly classified as:\n(i) Metals: They possess very low resistivity (or high conductivity) r ~ 10\u20132 \u2013 10\u20138 W m\ns ~ 102 \u2013 108 S m\u20131\n(ii) Semiconductors: They have resistivity or conductivity intermediate\nto metals and insulators" + }, + { + "Chapter": "9", + "sentence_range": "3178-3181", + "Text": "14 2 CLASSIFICATION OF METALS, CONDUCTORS AND\nSEMICONDUCTORS\nOn the basis of conductivity\nOn the basis of the relative values of electrical conductivity (s ) or resistivity\n(r = 1/s ), the solids are broadly classified as:\n(i) Metals: They possess very low resistivity (or high conductivity) r ~ 10\u20132 \u2013 10\u20138 W m\ns ~ 102 \u2013 108 S m\u20131\n(ii) Semiconductors: They have resistivity or conductivity intermediate\nto metals and insulators r ~ 10\u20135 \u2013 106 W m\ns ~ 105 \u2013 10\u20136 S m\u20131\n(iii)Insulators: They have high resistivity (or low conductivity)" + }, + { + "Chapter": "9", + "sentence_range": "3179-3182", + "Text": "2 CLASSIFICATION OF METALS, CONDUCTORS AND\nSEMICONDUCTORS\nOn the basis of conductivity\nOn the basis of the relative values of electrical conductivity (s ) or resistivity\n(r = 1/s ), the solids are broadly classified as:\n(i) Metals: They possess very low resistivity (or high conductivity) r ~ 10\u20132 \u2013 10\u20138 W m\ns ~ 102 \u2013 108 S m\u20131\n(ii) Semiconductors: They have resistivity or conductivity intermediate\nto metals and insulators r ~ 10\u20135 \u2013 106 W m\ns ~ 105 \u2013 10\u20136 S m\u20131\n(iii)Insulators: They have high resistivity (or low conductivity) r ~ 1011 \u2013 1019 W m\ns ~ 10\u201311 \u2013 10\u201319 S m\u20131\nThe values of r and s given above are indicative of magnitude and\ncould well go outside the ranges as well" + }, + { + "Chapter": "9", + "sentence_range": "3180-3183", + "Text": "r ~ 10\u20132 \u2013 10\u20138 W m\ns ~ 102 \u2013 108 S m\u20131\n(ii) Semiconductors: They have resistivity or conductivity intermediate\nto metals and insulators r ~ 10\u20135 \u2013 106 W m\ns ~ 105 \u2013 10\u20136 S m\u20131\n(iii)Insulators: They have high resistivity (or low conductivity) r ~ 1011 \u2013 1019 W m\ns ~ 10\u201311 \u2013 10\u201319 S m\u20131\nThe values of r and s given above are indicative of magnitude and\ncould well go outside the ranges as well Relative values of the resistivity\nare not the only criteria for distinguishing metals, insulators and\nsemiconductors from each other" + }, + { + "Chapter": "9", + "sentence_range": "3181-3184", + "Text": "r ~ 10\u20135 \u2013 106 W m\ns ~ 105 \u2013 10\u20136 S m\u20131\n(iii)Insulators: They have high resistivity (or low conductivity) r ~ 1011 \u2013 1019 W m\ns ~ 10\u201311 \u2013 10\u201319 S m\u20131\nThe values of r and s given above are indicative of magnitude and\ncould well go outside the ranges as well Relative values of the resistivity\nare not the only criteria for distinguishing metals, insulators and\nsemiconductors from each other There are some other differences, which\nwill become clear as we go along in this chapter" + }, + { + "Chapter": "9", + "sentence_range": "3182-3185", + "Text": "r ~ 1011 \u2013 1019 W m\ns ~ 10\u201311 \u2013 10\u201319 S m\u20131\nThe values of r and s given above are indicative of magnitude and\ncould well go outside the ranges as well Relative values of the resistivity\nare not the only criteria for distinguishing metals, insulators and\nsemiconductors from each other There are some other differences, which\nwill become clear as we go along in this chapter Our interest in this chapter is in the study of semiconductors which\ncould be:\n(i)\nElemental semiconductors: Si and Ge\n(ii) Compound semiconductors: Examples are:\n\u00b7 Inorganic: CdS, GaAs, CdSe, InP, etc" + }, + { + "Chapter": "9", + "sentence_range": "3183-3186", + "Text": "Relative values of the resistivity\nare not the only criteria for distinguishing metals, insulators and\nsemiconductors from each other There are some other differences, which\nwill become clear as we go along in this chapter Our interest in this chapter is in the study of semiconductors which\ncould be:\n(i)\nElemental semiconductors: Si and Ge\n(ii) Compound semiconductors: Examples are:\n\u00b7 Inorganic: CdS, GaAs, CdSe, InP, etc \u00b7 Organic: anthracene, doped pthalocyanines, etc" + }, + { + "Chapter": "9", + "sentence_range": "3184-3187", + "Text": "There are some other differences, which\nwill become clear as we go along in this chapter Our interest in this chapter is in the study of semiconductors which\ncould be:\n(i)\nElemental semiconductors: Si and Ge\n(ii) Compound semiconductors: Examples are:\n\u00b7 Inorganic: CdS, GaAs, CdSe, InP, etc \u00b7 Organic: anthracene, doped pthalocyanines, etc \u00b7 Organic polymers: polypyrrole, polyaniline, polythiophene, etc" + }, + { + "Chapter": "9", + "sentence_range": "3185-3188", + "Text": "Our interest in this chapter is in the study of semiconductors which\ncould be:\n(i)\nElemental semiconductors: Si and Ge\n(ii) Compound semiconductors: Examples are:\n\u00b7 Inorganic: CdS, GaAs, CdSe, InP, etc \u00b7 Organic: anthracene, doped pthalocyanines, etc \u00b7 Organic polymers: polypyrrole, polyaniline, polythiophene, etc Most of the currently available semiconductor devices are based on\nelemental semiconductors Si or Ge and compound inorganic\nsemiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3186-3189", + "Text": "\u00b7 Organic: anthracene, doped pthalocyanines, etc \u00b7 Organic polymers: polypyrrole, polyaniline, polythiophene, etc Most of the currently available semiconductor devices are based on\nelemental semiconductors Si or Ge and compound inorganic\nsemiconductors However, after 1990, a few semiconductor devices using\nRationalised 2023-24\n325\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\norganic semiconductors and semiconducting polymers have been\ndeveloped signalling the birth of a futuristic technology of polymer-\nelectronics and molecular-electronics" + }, + { + "Chapter": "9", + "sentence_range": "3187-3190", + "Text": "\u00b7 Organic polymers: polypyrrole, polyaniline, polythiophene, etc Most of the currently available semiconductor devices are based on\nelemental semiconductors Si or Ge and compound inorganic\nsemiconductors However, after 1990, a few semiconductor devices using\nRationalised 2023-24\n325\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\norganic semiconductors and semiconducting polymers have been\ndeveloped signalling the birth of a futuristic technology of polymer-\nelectronics and molecular-electronics In this chapter, we will restrict\nourselves to the study of inorganic semiconductors, particularly\nelemental semiconductors Si and Ge" + }, + { + "Chapter": "9", + "sentence_range": "3188-3191", + "Text": "Most of the currently available semiconductor devices are based on\nelemental semiconductors Si or Ge and compound inorganic\nsemiconductors However, after 1990, a few semiconductor devices using\nRationalised 2023-24\n325\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\norganic semiconductors and semiconducting polymers have been\ndeveloped signalling the birth of a futuristic technology of polymer-\nelectronics and molecular-electronics In this chapter, we will restrict\nourselves to the study of inorganic semiconductors, particularly\nelemental semiconductors Si and Ge The general concepts introduced\nhere for discussing the elemental semiconductors, by-and-large, apply\nto most of the compound semiconductors as well" + }, + { + "Chapter": "9", + "sentence_range": "3189-3192", + "Text": "However, after 1990, a few semiconductor devices using\nRationalised 2023-24\n325\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\norganic semiconductors and semiconducting polymers have been\ndeveloped signalling the birth of a futuristic technology of polymer-\nelectronics and molecular-electronics In this chapter, we will restrict\nourselves to the study of inorganic semiconductors, particularly\nelemental semiconductors Si and Ge The general concepts introduced\nhere for discussing the elemental semiconductors, by-and-large, apply\nto most of the compound semiconductors as well On the basis of energy bands\nAccording to the Bohr atomic model, in an isolated atom the energy of\nany of its electrons is decided by the orbit in which it revolves" + }, + { + "Chapter": "9", + "sentence_range": "3190-3193", + "Text": "In this chapter, we will restrict\nourselves to the study of inorganic semiconductors, particularly\nelemental semiconductors Si and Ge The general concepts introduced\nhere for discussing the elemental semiconductors, by-and-large, apply\nto most of the compound semiconductors as well On the basis of energy bands\nAccording to the Bohr atomic model, in an isolated atom the energy of\nany of its electrons is decided by the orbit in which it revolves But when\nthe atoms come together to form a solid they are close to each other" + }, + { + "Chapter": "9", + "sentence_range": "3191-3194", + "Text": "The general concepts introduced\nhere for discussing the elemental semiconductors, by-and-large, apply\nto most of the compound semiconductors as well On the basis of energy bands\nAccording to the Bohr atomic model, in an isolated atom the energy of\nany of its electrons is decided by the orbit in which it revolves But when\nthe atoms come together to form a solid they are close to each other So\nthe outer orbits of electrons from neighbouring atoms would come very\nclose or could even overlap" + }, + { + "Chapter": "9", + "sentence_range": "3192-3195", + "Text": "On the basis of energy bands\nAccording to the Bohr atomic model, in an isolated atom the energy of\nany of its electrons is decided by the orbit in which it revolves But when\nthe atoms come together to form a solid they are close to each other So\nthe outer orbits of electrons from neighbouring atoms would come very\nclose or could even overlap This would make the nature of electron motion\nin a solid very different from that in an isolated atom" + }, + { + "Chapter": "9", + "sentence_range": "3193-3196", + "Text": "But when\nthe atoms come together to form a solid they are close to each other So\nthe outer orbits of electrons from neighbouring atoms would come very\nclose or could even overlap This would make the nature of electron motion\nin a solid very different from that in an isolated atom Inside the crystal each electron has a unique position and no two\nelectrons see exactly the same pattern of surrounding charges" + }, + { + "Chapter": "9", + "sentence_range": "3194-3197", + "Text": "So\nthe outer orbits of electrons from neighbouring atoms would come very\nclose or could even overlap This would make the nature of electron motion\nin a solid very different from that in an isolated atom Inside the crystal each electron has a unique position and no two\nelectrons see exactly the same pattern of surrounding charges Because\nof this, each electron will have a different energy level" + }, + { + "Chapter": "9", + "sentence_range": "3195-3198", + "Text": "This would make the nature of electron motion\nin a solid very different from that in an isolated atom Inside the crystal each electron has a unique position and no two\nelectrons see exactly the same pattern of surrounding charges Because\nof this, each electron will have a different energy level These different\nenergy levels with continuous energy variation form what are called\nenergy bands" + }, + { + "Chapter": "9", + "sentence_range": "3196-3199", + "Text": "Inside the crystal each electron has a unique position and no two\nelectrons see exactly the same pattern of surrounding charges Because\nof this, each electron will have a different energy level These different\nenergy levels with continuous energy variation form what are called\nenergy bands The energy band which includes the energy levels of the\nvalence electrons is called the valence band" + }, + { + "Chapter": "9", + "sentence_range": "3197-3200", + "Text": "Because\nof this, each electron will have a different energy level These different\nenergy levels with continuous energy variation form what are called\nenergy bands The energy band which includes the energy levels of the\nvalence electrons is called the valence band The energy band above the\nvalence band is called the conduction band" + }, + { + "Chapter": "9", + "sentence_range": "3198-3201", + "Text": "These different\nenergy levels with continuous energy variation form what are called\nenergy bands The energy band which includes the energy levels of the\nvalence electrons is called the valence band The energy band above the\nvalence band is called the conduction band With no external energy, all\nthe valence electrons will reside in the valence band" + }, + { + "Chapter": "9", + "sentence_range": "3199-3202", + "Text": "The energy band which includes the energy levels of the\nvalence electrons is called the valence band The energy band above the\nvalence band is called the conduction band With no external energy, all\nthe valence electrons will reside in the valence band If the lowest level in\nthe conduction band happens to be lower than the highest level of the\nvalence band, the electrons from the valence band can easily move into\nthe conduction band" + }, + { + "Chapter": "9", + "sentence_range": "3200-3203", + "Text": "The energy band above the\nvalence band is called the conduction band With no external energy, all\nthe valence electrons will reside in the valence band If the lowest level in\nthe conduction band happens to be lower than the highest level of the\nvalence band, the electrons from the valence band can easily move into\nthe conduction band Normally the conduction band is empty" + }, + { + "Chapter": "9", + "sentence_range": "3201-3204", + "Text": "With no external energy, all\nthe valence electrons will reside in the valence band If the lowest level in\nthe conduction band happens to be lower than the highest level of the\nvalence band, the electrons from the valence band can easily move into\nthe conduction band Normally the conduction band is empty But when\nit overlaps on the valence band electrons can move freely into it" + }, + { + "Chapter": "9", + "sentence_range": "3202-3205", + "Text": "If the lowest level in\nthe conduction band happens to be lower than the highest level of the\nvalence band, the electrons from the valence band can easily move into\nthe conduction band Normally the conduction band is empty But when\nit overlaps on the valence band electrons can move freely into it This is\nthe case with metallic conductors" + }, + { + "Chapter": "9", + "sentence_range": "3203-3206", + "Text": "Normally the conduction band is empty But when\nit overlaps on the valence band electrons can move freely into it This is\nthe case with metallic conductors If there is some gap between the conduction band and the valence\nband, electrons in the valence band all remain bound and no free electrons\nare available in the conduction band" + }, + { + "Chapter": "9", + "sentence_range": "3204-3207", + "Text": "But when\nit overlaps on the valence band electrons can move freely into it This is\nthe case with metallic conductors If there is some gap between the conduction band and the valence\nband, electrons in the valence band all remain bound and no free electrons\nare available in the conduction band This makes the material an\ninsulator" + }, + { + "Chapter": "9", + "sentence_range": "3205-3208", + "Text": "This is\nthe case with metallic conductors If there is some gap between the conduction band and the valence\nband, electrons in the valence band all remain bound and no free electrons\nare available in the conduction band This makes the material an\ninsulator But some of the electrons from the valence band may gain\nexternal energy to cross the gap between the conduction band and the\nvalence band" + }, + { + "Chapter": "9", + "sentence_range": "3206-3209", + "Text": "If there is some gap between the conduction band and the valence\nband, electrons in the valence band all remain bound and no free electrons\nare available in the conduction band This makes the material an\ninsulator But some of the electrons from the valence band may gain\nexternal energy to cross the gap between the conduction band and the\nvalence band Then these electrons will move into the conduction band" + }, + { + "Chapter": "9", + "sentence_range": "3207-3210", + "Text": "This makes the material an\ninsulator But some of the electrons from the valence band may gain\nexternal energy to cross the gap between the conduction band and the\nvalence band Then these electrons will move into the conduction band At the same time they will create vacant energy levels in the valence band\nwhere other valence electrons can move" + }, + { + "Chapter": "9", + "sentence_range": "3208-3211", + "Text": "But some of the electrons from the valence band may gain\nexternal energy to cross the gap between the conduction band and the\nvalence band Then these electrons will move into the conduction band At the same time they will create vacant energy levels in the valence band\nwhere other valence electrons can move Thus the process creates the\npossibility of conduction due to electrons in conduction band as well as\ndue to vacancies in the valence band" + }, + { + "Chapter": "9", + "sentence_range": "3209-3212", + "Text": "Then these electrons will move into the conduction band At the same time they will create vacant energy levels in the valence band\nwhere other valence electrons can move Thus the process creates the\npossibility of conduction due to electrons in conduction band as well as\ndue to vacancies in the valence band Let us consider what happens in the case of Si or Ge crystal containing\nN atoms" + }, + { + "Chapter": "9", + "sentence_range": "3210-3213", + "Text": "At the same time they will create vacant energy levels in the valence band\nwhere other valence electrons can move Thus the process creates the\npossibility of conduction due to electrons in conduction band as well as\ndue to vacancies in the valence band Let us consider what happens in the case of Si or Ge crystal containing\nN atoms For Si, the outermost orbit is the third orbit (n = 3), while for Ge\nit is the fourth orbit (n = 4)" + }, + { + "Chapter": "9", + "sentence_range": "3211-3214", + "Text": "Thus the process creates the\npossibility of conduction due to electrons in conduction band as well as\ndue to vacancies in the valence band Let us consider what happens in the case of Si or Ge crystal containing\nN atoms For Si, the outermost orbit is the third orbit (n = 3), while for Ge\nit is the fourth orbit (n = 4) The number of electrons in the outermost\norbit is 4 (2s and 2p electrons)" + }, + { + "Chapter": "9", + "sentence_range": "3212-3215", + "Text": "Let us consider what happens in the case of Si or Ge crystal containing\nN atoms For Si, the outermost orbit is the third orbit (n = 3), while for Ge\nit is the fourth orbit (n = 4) The number of electrons in the outermost\norbit is 4 (2s and 2p electrons) Hence, the total number of outer electrons\nin the crystal is 4N" + }, + { + "Chapter": "9", + "sentence_range": "3213-3216", + "Text": "For Si, the outermost orbit is the third orbit (n = 3), while for Ge\nit is the fourth orbit (n = 4) The number of electrons in the outermost\norbit is 4 (2s and 2p electrons) Hence, the total number of outer electrons\nin the crystal is 4N The maximum possible number of electrons in the\nouter orbit is 8 (2s + 6p electrons)" + }, + { + "Chapter": "9", + "sentence_range": "3214-3217", + "Text": "The number of electrons in the outermost\norbit is 4 (2s and 2p electrons) Hence, the total number of outer electrons\nin the crystal is 4N The maximum possible number of electrons in the\nouter orbit is 8 (2s + 6p electrons) So, for the 4N valence electrons there\nare 8N available energy states" + }, + { + "Chapter": "9", + "sentence_range": "3215-3218", + "Text": "Hence, the total number of outer electrons\nin the crystal is 4N The maximum possible number of electrons in the\nouter orbit is 8 (2s + 6p electrons) So, for the 4N valence electrons there\nare 8N available energy states These 8N discrete energy levels can either\nform a continuous band or they may be grouped in different bands\ndepending upon the distance between the atoms in the crystal (see box\non Band Theory of Solids)" + }, + { + "Chapter": "9", + "sentence_range": "3216-3219", + "Text": "The maximum possible number of electrons in the\nouter orbit is 8 (2s + 6p electrons) So, for the 4N valence electrons there\nare 8N available energy states These 8N discrete energy levels can either\nform a continuous band or they may be grouped in different bands\ndepending upon the distance between the atoms in the crystal (see box\non Band Theory of Solids) At the distance between the atoms in the crystal lattices of Si and Ge,\nthe energy band of these 8N states is split apart into two which are\nseparated by an energy gap Eg (Fig" + }, + { + "Chapter": "9", + "sentence_range": "3217-3220", + "Text": "So, for the 4N valence electrons there\nare 8N available energy states These 8N discrete energy levels can either\nform a continuous band or they may be grouped in different bands\ndepending upon the distance between the atoms in the crystal (see box\non Band Theory of Solids) At the distance between the atoms in the crystal lattices of Si and Ge,\nthe energy band of these 8N states is split apart into two which are\nseparated by an energy gap Eg (Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3218-3221", + "Text": "These 8N discrete energy levels can either\nform a continuous band or they may be grouped in different bands\ndepending upon the distance between the atoms in the crystal (see box\non Band Theory of Solids) At the distance between the atoms in the crystal lattices of Si and Ge,\nthe energy band of these 8N states is split apart into two which are\nseparated by an energy gap Eg (Fig 14 1)" + }, + { + "Chapter": "9", + "sentence_range": "3219-3222", + "Text": "At the distance between the atoms in the crystal lattices of Si and Ge,\nthe energy band of these 8N states is split apart into two which are\nseparated by an energy gap Eg (Fig 14 1) The lower band which is\ncompletely occupied by the 4N valence electrons at temperature of absolute\nzero is the valence band" + }, + { + "Chapter": "9", + "sentence_range": "3220-3223", + "Text": "14 1) The lower band which is\ncompletely occupied by the 4N valence electrons at temperature of absolute\nzero is the valence band The other band consisting of 4N energy states,\ncalled the conduction band, is completely empty at absolute zero" + }, + { + "Chapter": "9", + "sentence_range": "3221-3224", + "Text": "1) The lower band which is\ncompletely occupied by the 4N valence electrons at temperature of absolute\nzero is the valence band The other band consisting of 4N energy states,\ncalled the conduction band, is completely empty at absolute zero Rationalised 2023-24\nPhysics\n326\nThe lowest energy level in the\nconduction band is shown as EC and\nhighest energy level in the valence band\nis shown as EV" + }, + { + "Chapter": "9", + "sentence_range": "3222-3225", + "Text": "The lower band which is\ncompletely occupied by the 4N valence electrons at temperature of absolute\nzero is the valence band The other band consisting of 4N energy states,\ncalled the conduction band, is completely empty at absolute zero Rationalised 2023-24\nPhysics\n326\nThe lowest energy level in the\nconduction band is shown as EC and\nhighest energy level in the valence band\nis shown as EV Above EC and below EV\nthere are a large number of closely spaced\nenergy levels, as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3223-3226", + "Text": "The other band consisting of 4N energy states,\ncalled the conduction band, is completely empty at absolute zero Rationalised 2023-24\nPhysics\n326\nThe lowest energy level in the\nconduction band is shown as EC and\nhighest energy level in the valence band\nis shown as EV Above EC and below EV\nthere are a large number of closely spaced\nenergy levels, as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3224-3227", + "Text": "Rationalised 2023-24\nPhysics\n326\nThe lowest energy level in the\nconduction band is shown as EC and\nhighest energy level in the valence band\nis shown as EV Above EC and below EV\nthere are a large number of closely spaced\nenergy levels, as shown in Fig 14 1" + }, + { + "Chapter": "9", + "sentence_range": "3225-3228", + "Text": "Above EC and below EV\nthere are a large number of closely spaced\nenergy levels, as shown in Fig 14 1 The gap between the top of the valence\nband and bottom of the conduction band\nis called the energy band gap (Energy gap\nEg)" + }, + { + "Chapter": "9", + "sentence_range": "3226-3229", + "Text": "14 1 The gap between the top of the valence\nband and bottom of the conduction band\nis called the energy band gap (Energy gap\nEg) It may be large, small, or zero,\ndepending upon the material" + }, + { + "Chapter": "9", + "sentence_range": "3227-3230", + "Text": "1 The gap between the top of the valence\nband and bottom of the conduction band\nis called the energy band gap (Energy gap\nEg) It may be large, small, or zero,\ndepending upon the material These\ndifferent situations, are depicted in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3228-3231", + "Text": "The gap between the top of the valence\nband and bottom of the conduction band\nis called the energy band gap (Energy gap\nEg) It may be large, small, or zero,\ndepending upon the material These\ndifferent situations, are depicted in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3229-3232", + "Text": "It may be large, small, or zero,\ndepending upon the material These\ndifferent situations, are depicted in Fig 14 2 and discussed below:\nCase I: This refers to a situation, as\nshown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3230-3233", + "Text": "These\ndifferent situations, are depicted in Fig 14 2 and discussed below:\nCase I: This refers to a situation, as\nshown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3231-3234", + "Text": "14 2 and discussed below:\nCase I: This refers to a situation, as\nshown in Fig 14 2(a)" + }, + { + "Chapter": "9", + "sentence_range": "3232-3235", + "Text": "2 and discussed below:\nCase I: This refers to a situation, as\nshown in Fig 14 2(a) One can have a\nmetal either when the conduction band\nis partially filled and the balanced band\nis partially empty or when the conduction\nand valance bands overlap" + }, + { + "Chapter": "9", + "sentence_range": "3233-3236", + "Text": "14 2(a) One can have a\nmetal either when the conduction band\nis partially filled and the balanced band\nis partially empty or when the conduction\nand valance bands overlap When there\nis overlap electrons from valence band can\neasily move into the conduction band" + }, + { + "Chapter": "9", + "sentence_range": "3234-3237", + "Text": "2(a) One can have a\nmetal either when the conduction band\nis partially filled and the balanced band\nis partially empty or when the conduction\nand valance bands overlap When there\nis overlap electrons from valence band can\neasily move into the conduction band This situation makes a large number of\nelectrons available for electrical conduction" + }, + { + "Chapter": "9", + "sentence_range": "3235-3238", + "Text": "One can have a\nmetal either when the conduction band\nis partially filled and the balanced band\nis partially empty or when the conduction\nand valance bands overlap When there\nis overlap electrons from valence band can\neasily move into the conduction band This situation makes a large number of\nelectrons available for electrical conduction When the valence band is\npartially empty, electrons from its lower level can move to higher level\nmaking conduction possible" + }, + { + "Chapter": "9", + "sentence_range": "3236-3239", + "Text": "When there\nis overlap electrons from valence band can\neasily move into the conduction band This situation makes a large number of\nelectrons available for electrical conduction When the valence band is\npartially empty, electrons from its lower level can move to higher level\nmaking conduction possible Therefore, the resistance of such materials\nis low or the conductivity is high" + }, + { + "Chapter": "9", + "sentence_range": "3237-3240", + "Text": "This situation makes a large number of\nelectrons available for electrical conduction When the valence band is\npartially empty, electrons from its lower level can move to higher level\nmaking conduction possible Therefore, the resistance of such materials\nis low or the conductivity is high FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3238-3241", + "Text": "When the valence band is\npartially empty, electrons from its lower level can move to higher level\nmaking conduction possible Therefore, the resistance of such materials\nis low or the conductivity is high FIGURE 14 2 Difference between energy bands of (a) metals,\n(b) insulators and (c) semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3239-3242", + "Text": "Therefore, the resistance of such materials\nis low or the conductivity is high FIGURE 14 2 Difference between energy bands of (a) metals,\n(b) insulators and (c) semiconductors FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3240-3243", + "Text": "FIGURE 14 2 Difference between energy bands of (a) metals,\n(b) insulators and (c) semiconductors FIGURE 14 1 The energy band positions in a\nsemiconductor at 0 K" + }, + { + "Chapter": "9", + "sentence_range": "3241-3244", + "Text": "2 Difference between energy bands of (a) metals,\n(b) insulators and (c) semiconductors FIGURE 14 1 The energy band positions in a\nsemiconductor at 0 K The upper band, called the\nconduction band, consists of infinitely large number\nof closely spaced energy states" + }, + { + "Chapter": "9", + "sentence_range": "3242-3245", + "Text": "FIGURE 14 1 The energy band positions in a\nsemiconductor at 0 K The upper band, called the\nconduction band, consists of infinitely large number\nof closely spaced energy states The lower band,\ncalled the valence band, consists of closely spaced\ncompletely filled energy states" + }, + { + "Chapter": "9", + "sentence_range": "3243-3246", + "Text": "1 The energy band positions in a\nsemiconductor at 0 K The upper band, called the\nconduction band, consists of infinitely large number\nof closely spaced energy states The lower band,\ncalled the valence band, consists of closely spaced\ncompletely filled energy states Rationalised 2023-24\n327\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nCase II: In this case, as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3244-3247", + "Text": "The upper band, called the\nconduction band, consists of infinitely large number\nof closely spaced energy states The lower band,\ncalled the valence band, consists of closely spaced\ncompletely filled energy states Rationalised 2023-24\n327\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nCase II: In this case, as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3245-3248", + "Text": "The lower band,\ncalled the valence band, consists of closely spaced\ncompletely filled energy states Rationalised 2023-24\n327\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nCase II: In this case, as shown in Fig 14 2(b), a large band gap Eg exists\n(Eg > 3 eV)" + }, + { + "Chapter": "9", + "sentence_range": "3246-3249", + "Text": "Rationalised 2023-24\n327\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nCase II: In this case, as shown in Fig 14 2(b), a large band gap Eg exists\n(Eg > 3 eV) There are no electrons in the conduction band, and therefore\nno electrical conduction is possible" + }, + { + "Chapter": "9", + "sentence_range": "3247-3250", + "Text": "14 2(b), a large band gap Eg exists\n(Eg > 3 eV) There are no electrons in the conduction band, and therefore\nno electrical conduction is possible Note that the energy gap is so large\nthat electrons cannot be excited from the valence band to the conduction\nband by thermal excitation" + }, + { + "Chapter": "9", + "sentence_range": "3248-3251", + "Text": "2(b), a large band gap Eg exists\n(Eg > 3 eV) There are no electrons in the conduction band, and therefore\nno electrical conduction is possible Note that the energy gap is so large\nthat electrons cannot be excited from the valence band to the conduction\nband by thermal excitation This is the case of insulators" + }, + { + "Chapter": "9", + "sentence_range": "3249-3252", + "Text": "There are no electrons in the conduction band, and therefore\nno electrical conduction is possible Note that the energy gap is so large\nthat electrons cannot be excited from the valence band to the conduction\nband by thermal excitation This is the case of insulators Case III: This situation is shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3250-3253", + "Text": "Note that the energy gap is so large\nthat electrons cannot be excited from the valence band to the conduction\nband by thermal excitation This is the case of insulators Case III: This situation is shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3251-3254", + "Text": "This is the case of insulators Case III: This situation is shown in Fig 14 2(c)" + }, + { + "Chapter": "9", + "sentence_range": "3252-3255", + "Text": "Case III: This situation is shown in Fig 14 2(c) Here a finite but small\nband gap (Eg < 3 eV) exists" + }, + { + "Chapter": "9", + "sentence_range": "3253-3256", + "Text": "14 2(c) Here a finite but small\nband gap (Eg < 3 eV) exists Because of the small band gap, at room\ntemperature some electrons from valence band can acquire enough\nenergy to cross the energy gap and enter the conduction band" + }, + { + "Chapter": "9", + "sentence_range": "3254-3257", + "Text": "2(c) Here a finite but small\nband gap (Eg < 3 eV) exists Because of the small band gap, at room\ntemperature some electrons from valence band can acquire enough\nenergy to cross the energy gap and enter the conduction band These\nelectrons (though small in numbers) can move in the conduction band" + }, + { + "Chapter": "9", + "sentence_range": "3255-3258", + "Text": "Here a finite but small\nband gap (Eg < 3 eV) exists Because of the small band gap, at room\ntemperature some electrons from valence band can acquire enough\nenergy to cross the energy gap and enter the conduction band These\nelectrons (though small in numbers) can move in the conduction band Hence, the resistance of semiconductors is not as high as that of the\ninsulators" + }, + { + "Chapter": "9", + "sentence_range": "3256-3259", + "Text": "Because of the small band gap, at room\ntemperature some electrons from valence band can acquire enough\nenergy to cross the energy gap and enter the conduction band These\nelectrons (though small in numbers) can move in the conduction band Hence, the resistance of semiconductors is not as high as that of the\ninsulators In this section we have made a broad classification of metals,\nconductors and semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3257-3260", + "Text": "These\nelectrons (though small in numbers) can move in the conduction band Hence, the resistance of semiconductors is not as high as that of the\ninsulators In this section we have made a broad classification of metals,\nconductors and semiconductors In the section which follows you will\nlearn the conduction process in semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3258-3261", + "Text": "Hence, the resistance of semiconductors is not as high as that of the\ninsulators In this section we have made a broad classification of metals,\nconductors and semiconductors In the section which follows you will\nlearn the conduction process in semiconductors 14" + }, + { + "Chapter": "9", + "sentence_range": "3259-3262", + "Text": "In this section we have made a broad classification of metals,\nconductors and semiconductors In the section which follows you will\nlearn the conduction process in semiconductors 14 3 INTRINSIC SEMICONDUCTOR\nWe shall take the most common case of Ge and Si whose\nlattice structure is shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3260-3263", + "Text": "In the section which follows you will\nlearn the conduction process in semiconductors 14 3 INTRINSIC SEMICONDUCTOR\nWe shall take the most common case of Ge and Si whose\nlattice structure is shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3261-3264", + "Text": "14 3 INTRINSIC SEMICONDUCTOR\nWe shall take the most common case of Ge and Si whose\nlattice structure is shown in Fig 14 3" + }, + { + "Chapter": "9", + "sentence_range": "3262-3265", + "Text": "3 INTRINSIC SEMICONDUCTOR\nWe shall take the most common case of Ge and Si whose\nlattice structure is shown in Fig 14 3 These structures\nare called the diamond-like structures" + }, + { + "Chapter": "9", + "sentence_range": "3263-3266", + "Text": "14 3 These structures\nare called the diamond-like structures Each atom is\nsurrounded by four nearest neighbours" + }, + { + "Chapter": "9", + "sentence_range": "3264-3267", + "Text": "3 These structures\nare called the diamond-like structures Each atom is\nsurrounded by four nearest neighbours We know that\nSi and Ge have four valence electrons" + }, + { + "Chapter": "9", + "sentence_range": "3265-3268", + "Text": "These structures\nare called the diamond-like structures Each atom is\nsurrounded by four nearest neighbours We know that\nSi and Ge have four valence electrons In its crystalline\nstructure, every Si or Ge atom tends to share one of its\nfour valence electrons with each of its four nearest\nneighbour atoms, and also to take share of one electron\nfrom each such neighbour" + }, + { + "Chapter": "9", + "sentence_range": "3266-3269", + "Text": "Each atom is\nsurrounded by four nearest neighbours We know that\nSi and Ge have four valence electrons In its crystalline\nstructure, every Si or Ge atom tends to share one of its\nfour valence electrons with each of its four nearest\nneighbour atoms, and also to take share of one electron\nfrom each such neighbour These shared electron pairs\nare referred to as forming a covalent bond or simply a\nvalence bond" + }, + { + "Chapter": "9", + "sentence_range": "3267-3270", + "Text": "We know that\nSi and Ge have four valence electrons In its crystalline\nstructure, every Si or Ge atom tends to share one of its\nfour valence electrons with each of its four nearest\nneighbour atoms, and also to take share of one electron\nfrom each such neighbour These shared electron pairs\nare referred to as forming a covalent bond or simply a\nvalence bond The two shared electrons can be assumed\nto shuttle back-and-forth between the associated atoms\nholding them together strongly" + }, + { + "Chapter": "9", + "sentence_range": "3268-3271", + "Text": "In its crystalline\nstructure, every Si or Ge atom tends to share one of its\nfour valence electrons with each of its four nearest\nneighbour atoms, and also to take share of one electron\nfrom each such neighbour These shared electron pairs\nare referred to as forming a covalent bond or simply a\nvalence bond The two shared electrons can be assumed\nto shuttle back-and-forth between the associated atoms\nholding them together strongly Figure 14" + }, + { + "Chapter": "9", + "sentence_range": "3269-3272", + "Text": "These shared electron pairs\nare referred to as forming a covalent bond or simply a\nvalence bond The two shared electrons can be assumed\nto shuttle back-and-forth between the associated atoms\nholding them together strongly Figure 14 4 schematically\nshows the 2-dimensional representation of Si or Ge\nstructure shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3270-3273", + "Text": "The two shared electrons can be assumed\nto shuttle back-and-forth between the associated atoms\nholding them together strongly Figure 14 4 schematically\nshows the 2-dimensional representation of Si or Ge\nstructure shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3271-3274", + "Text": "Figure 14 4 schematically\nshows the 2-dimensional representation of Si or Ge\nstructure shown in Fig 14 3 which overemphasises the\ncovalent bond" + }, + { + "Chapter": "9", + "sentence_range": "3272-3275", + "Text": "4 schematically\nshows the 2-dimensional representation of Si or Ge\nstructure shown in Fig 14 3 which overemphasises the\ncovalent bond It shows an idealised picture in which no\nbonds are broken (all bonds are intact)" + }, + { + "Chapter": "9", + "sentence_range": "3273-3276", + "Text": "14 3 which overemphasises the\ncovalent bond It shows an idealised picture in which no\nbonds are broken (all bonds are intact) Such a situation\narises at low temperatures" + }, + { + "Chapter": "9", + "sentence_range": "3274-3277", + "Text": "3 which overemphasises the\ncovalent bond It shows an idealised picture in which no\nbonds are broken (all bonds are intact) Such a situation\narises at low temperatures As the temperature increases,\nmore thermal energy becomes available to these electrons and some of\nthese electrons may break\u2013away (becoming free electrons contributing to\nconduction)" + }, + { + "Chapter": "9", + "sentence_range": "3275-3278", + "Text": "It shows an idealised picture in which no\nbonds are broken (all bonds are intact) Such a situation\narises at low temperatures As the temperature increases,\nmore thermal energy becomes available to these electrons and some of\nthese electrons may break\u2013away (becoming free electrons contributing to\nconduction) The thermal energy effectively ionises only a few atoms in the\ncrystalline lattice and creates a vacancy in the bond as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3276-3279", + "Text": "Such a situation\narises at low temperatures As the temperature increases,\nmore thermal energy becomes available to these electrons and some of\nthese electrons may break\u2013away (becoming free electrons contributing to\nconduction) The thermal energy effectively ionises only a few atoms in the\ncrystalline lattice and creates a vacancy in the bond as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3277-3280", + "Text": "As the temperature increases,\nmore thermal energy becomes available to these electrons and some of\nthese electrons may break\u2013away (becoming free electrons contributing to\nconduction) The thermal energy effectively ionises only a few atoms in the\ncrystalline lattice and creates a vacancy in the bond as shown in Fig 14 5(a)" + }, + { + "Chapter": "9", + "sentence_range": "3278-3281", + "Text": "The thermal energy effectively ionises only a few atoms in the\ncrystalline lattice and creates a vacancy in the bond as shown in Fig 14 5(a) The neighbourhood, from which the free electron (with charge \u2013q) has come\nout leaves a vacancy with an effective charge (+q)" + }, + { + "Chapter": "9", + "sentence_range": "3279-3282", + "Text": "14 5(a) The neighbourhood, from which the free electron (with charge \u2013q) has come\nout leaves a vacancy with an effective charge (+q) This vacancy with the\neffective positive electronic charge is called a hole" + }, + { + "Chapter": "9", + "sentence_range": "3280-3283", + "Text": "5(a) The neighbourhood, from which the free electron (with charge \u2013q) has come\nout leaves a vacancy with an effective charge (+q) This vacancy with the\neffective positive electronic charge is called a hole The hole behaves as an\napparent free particle with effective positive charge" + }, + { + "Chapter": "9", + "sentence_range": "3281-3284", + "Text": "The neighbourhood, from which the free electron (with charge \u2013q) has come\nout leaves a vacancy with an effective charge (+q) This vacancy with the\neffective positive electronic charge is called a hole The hole behaves as an\napparent free particle with effective positive charge In intrinsic semiconductors, the number of free electrons, ne is equal to\nthe number of holes, nh" + }, + { + "Chapter": "9", + "sentence_range": "3282-3285", + "Text": "This vacancy with the\neffective positive electronic charge is called a hole The hole behaves as an\napparent free particle with effective positive charge In intrinsic semiconductors, the number of free electrons, ne is equal to\nthe number of holes, nh That is\nne = nh = ni\n(14" + }, + { + "Chapter": "9", + "sentence_range": "3283-3286", + "Text": "The hole behaves as an\napparent free particle with effective positive charge In intrinsic semiconductors, the number of free electrons, ne is equal to\nthe number of holes, nh That is\nne = nh = ni\n(14 1)\nwhere ni is called intrinsic carrier concentration" + }, + { + "Chapter": "9", + "sentence_range": "3284-3287", + "Text": "In intrinsic semiconductors, the number of free electrons, ne is equal to\nthe number of holes, nh That is\nne = nh = ni\n(14 1)\nwhere ni is called intrinsic carrier concentration Semiconductors posses the unique property in which, apart from\nelectrons, the holes also move" + }, + { + "Chapter": "9", + "sentence_range": "3285-3288", + "Text": "That is\nne = nh = ni\n(14 1)\nwhere ni is called intrinsic carrier concentration Semiconductors posses the unique property in which, apart from\nelectrons, the holes also move Suppose there is a hole at site 1 as shown\nFIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3286-3289", + "Text": "1)\nwhere ni is called intrinsic carrier concentration Semiconductors posses the unique property in which, apart from\nelectrons, the holes also move Suppose there is a hole at site 1 as shown\nFIGURE 14 3 Three-dimensional dia-\nmond-like crystal structure for Carbon,\nSilicon or Germanium with\nrespective lattice spacing a equal\nto 3" + }, + { + "Chapter": "9", + "sentence_range": "3287-3290", + "Text": "Semiconductors posses the unique property in which, apart from\nelectrons, the holes also move Suppose there is a hole at site 1 as shown\nFIGURE 14 3 Three-dimensional dia-\nmond-like crystal structure for Carbon,\nSilicon or Germanium with\nrespective lattice spacing a equal\nto 3 56, 5" + }, + { + "Chapter": "9", + "sentence_range": "3288-3291", + "Text": "Suppose there is a hole at site 1 as shown\nFIGURE 14 3 Three-dimensional dia-\nmond-like crystal structure for Carbon,\nSilicon or Germanium with\nrespective lattice spacing a equal\nto 3 56, 5 43 and 5" + }, + { + "Chapter": "9", + "sentence_range": "3289-3292", + "Text": "3 Three-dimensional dia-\nmond-like crystal structure for Carbon,\nSilicon or Germanium with\nrespective lattice spacing a equal\nto 3 56, 5 43 and 5 66 \u00c5" + }, + { + "Chapter": "9", + "sentence_range": "3290-3293", + "Text": "56, 5 43 and 5 66 \u00c5 Rationalised 2023-24\nPhysics\n328\nin Fig" + }, + { + "Chapter": "9", + "sentence_range": "3291-3294", + "Text": "43 and 5 66 \u00c5 Rationalised 2023-24\nPhysics\n328\nin Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3292-3295", + "Text": "66 \u00c5 Rationalised 2023-24\nPhysics\n328\nin Fig 14 5(a)" + }, + { + "Chapter": "9", + "sentence_range": "3293-3296", + "Text": "Rationalised 2023-24\nPhysics\n328\nin Fig 14 5(a) The movement of holes can be\nvisualised as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3294-3297", + "Text": "14 5(a) The movement of holes can be\nvisualised as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3295-3298", + "Text": "5(a) The movement of holes can be\nvisualised as shown in Fig 14 5(b)" + }, + { + "Chapter": "9", + "sentence_range": "3296-3299", + "Text": "The movement of holes can be\nvisualised as shown in Fig 14 5(b) An electron\nfrom the covalent bond at site 2 may jump to\nthe vacant site 1 (hole)" + }, + { + "Chapter": "9", + "sentence_range": "3297-3300", + "Text": "14 5(b) An electron\nfrom the covalent bond at site 2 may jump to\nthe vacant site 1 (hole) Thus, after such a jump,\nthe hole is at site 2 and the site 1 has now an\nelectron" + }, + { + "Chapter": "9", + "sentence_range": "3298-3301", + "Text": "5(b) An electron\nfrom the covalent bond at site 2 may jump to\nthe vacant site 1 (hole) Thus, after such a jump,\nthe hole is at site 2 and the site 1 has now an\nelectron Therefore, apparently, the hole has\nmoved from site 1 to site 2" + }, + { + "Chapter": "9", + "sentence_range": "3299-3302", + "Text": "An electron\nfrom the covalent bond at site 2 may jump to\nthe vacant site 1 (hole) Thus, after such a jump,\nthe hole is at site 2 and the site 1 has now an\nelectron Therefore, apparently, the hole has\nmoved from site 1 to site 2 Note that the electron\noriginally set free [Fig" + }, + { + "Chapter": "9", + "sentence_range": "3300-3303", + "Text": "Thus, after such a jump,\nthe hole is at site 2 and the site 1 has now an\nelectron Therefore, apparently, the hole has\nmoved from site 1 to site 2 Note that the electron\noriginally set free [Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3301-3304", + "Text": "Therefore, apparently, the hole has\nmoved from site 1 to site 2 Note that the electron\noriginally set free [Fig 14 5(a)] is not involved\nin this process of hole motion" + }, + { + "Chapter": "9", + "sentence_range": "3302-3305", + "Text": "Note that the electron\noriginally set free [Fig 14 5(a)] is not involved\nin this process of hole motion The free electron\nmoves completely independently as conduction\nelectron and gives rise to an electron current, Ie\nunder an applied electric field" + }, + { + "Chapter": "9", + "sentence_range": "3303-3306", + "Text": "14 5(a)] is not involved\nin this process of hole motion The free electron\nmoves completely independently as conduction\nelectron and gives rise to an electron current, Ie\nunder an applied electric field Remember that\nthe motion of hole is only a convenient way of\ndescribing the actual motion of bound electrons,\nwhenever there is an empty bond anywhere in\nthe crystal" + }, + { + "Chapter": "9", + "sentence_range": "3304-3307", + "Text": "5(a)] is not involved\nin this process of hole motion The free electron\nmoves completely independently as conduction\nelectron and gives rise to an electron current, Ie\nunder an applied electric field Remember that\nthe motion of hole is only a convenient way of\ndescribing the actual motion of bound electrons,\nwhenever there is an empty bond anywhere in\nthe crystal Under the action of an electric field,\nthese holes move towards negative potential\ngiving the hole current, Ih" + }, + { + "Chapter": "9", + "sentence_range": "3305-3308", + "Text": "The free electron\nmoves completely independently as conduction\nelectron and gives rise to an electron current, Ie\nunder an applied electric field Remember that\nthe motion of hole is only a convenient way of\ndescribing the actual motion of bound electrons,\nwhenever there is an empty bond anywhere in\nthe crystal Under the action of an electric field,\nthese holes move towards negative potential\ngiving the hole current, Ih The total current, I is\nthus the sum of the electron current Ie and the\nhole current Ih:\nI = Ie + Ih\n(14" + }, + { + "Chapter": "9", + "sentence_range": "3306-3309", + "Text": "Remember that\nthe motion of hole is only a convenient way of\ndescribing the actual motion of bound electrons,\nwhenever there is an empty bond anywhere in\nthe crystal Under the action of an electric field,\nthese holes move towards negative potential\ngiving the hole current, Ih The total current, I is\nthus the sum of the electron current Ie and the\nhole current Ih:\nI = Ie + Ih\n(14 2)\nIt may be noted that apart from the process of generation of conduction\nelectrons and holes, a simultaneous process of recombination occurs in\nwhich the electrons recombine with the holes" + }, + { + "Chapter": "9", + "sentence_range": "3307-3310", + "Text": "Under the action of an electric field,\nthese holes move towards negative potential\ngiving the hole current, Ih The total current, I is\nthus the sum of the electron current Ie and the\nhole current Ih:\nI = Ie + Ih\n(14 2)\nIt may be noted that apart from the process of generation of conduction\nelectrons and holes, a simultaneous process of recombination occurs in\nwhich the electrons recombine with the holes At equilibrium, the rate of\ngeneration is equal to the rate of recombination of charge carriers" + }, + { + "Chapter": "9", + "sentence_range": "3308-3311", + "Text": "The total current, I is\nthus the sum of the electron current Ie and the\nhole current Ih:\nI = Ie + Ih\n(14 2)\nIt may be noted that apart from the process of generation of conduction\nelectrons and holes, a simultaneous process of recombination occurs in\nwhich the electrons recombine with the holes At equilibrium, the rate of\ngeneration is equal to the rate of recombination of charge carriers The\nrecombination occurs due to an electron colliding with a hole" + }, + { + "Chapter": "9", + "sentence_range": "3309-3312", + "Text": "2)\nIt may be noted that apart from the process of generation of conduction\nelectrons and holes, a simultaneous process of recombination occurs in\nwhich the electrons recombine with the holes At equilibrium, the rate of\ngeneration is equal to the rate of recombination of charge carriers The\nrecombination occurs due to an electron colliding with a hole FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3310-3313", + "Text": "At equilibrium, the rate of\ngeneration is equal to the rate of recombination of charge carriers The\nrecombination occurs due to an electron colliding with a hole FIGURE 14 4 Schematic two-dimensional\nrepresentation of Si or Ge structure showing\ncovalent bonds at low temperature\n(all bonds intact)" + }, + { + "Chapter": "9", + "sentence_range": "3311-3314", + "Text": "The\nrecombination occurs due to an electron colliding with a hole FIGURE 14 4 Schematic two-dimensional\nrepresentation of Si or Ge structure showing\ncovalent bonds at low temperature\n(all bonds intact) +4 symbol\nindicates inner cores of Si or Ge" + }, + { + "Chapter": "9", + "sentence_range": "3312-3315", + "Text": "FIGURE 14 4 Schematic two-dimensional\nrepresentation of Si or Ge structure showing\ncovalent bonds at low temperature\n(all bonds intact) +4 symbol\nindicates inner cores of Si or Ge FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3313-3316", + "Text": "4 Schematic two-dimensional\nrepresentation of Si or Ge structure showing\ncovalent bonds at low temperature\n(all bonds intact) +4 symbol\nindicates inner cores of Si or Ge FIGURE 14 5 (a) Schematic model of generation of hole at site 1 and conduction electron\ndue to thermal energy at moderate temperatures" + }, + { + "Chapter": "9", + "sentence_range": "3314-3317", + "Text": "+4 symbol\nindicates inner cores of Si or Ge FIGURE 14 5 (a) Schematic model of generation of hole at site 1 and conduction electron\ndue to thermal energy at moderate temperatures (b) Simplified representation of\npossible thermal motion of a hole" + }, + { + "Chapter": "9", + "sentence_range": "3315-3318", + "Text": "FIGURE 14 5 (a) Schematic model of generation of hole at site 1 and conduction electron\ndue to thermal energy at moderate temperatures (b) Simplified representation of\npossible thermal motion of a hole The electron from the lower left hand covalent bond\n(site 2) goes to the earlier hole site1, leaving a hole at its site indicating an\napparent movement of the hole from site 1 to site 2" + }, + { + "Chapter": "9", + "sentence_range": "3316-3319", + "Text": "5 (a) Schematic model of generation of hole at site 1 and conduction electron\ndue to thermal energy at moderate temperatures (b) Simplified representation of\npossible thermal motion of a hole The electron from the lower left hand covalent bond\n(site 2) goes to the earlier hole site1, leaving a hole at its site indicating an\napparent movement of the hole from site 1 to site 2 (a)\n(b)\nRationalised 2023-24\n329\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n EXAMPLE 14" + }, + { + "Chapter": "9", + "sentence_range": "3317-3320", + "Text": "(b) Simplified representation of\npossible thermal motion of a hole The electron from the lower left hand covalent bond\n(site 2) goes to the earlier hole site1, leaving a hole at its site indicating an\napparent movement of the hole from site 1 to site 2 (a)\n(b)\nRationalised 2023-24\n329\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n EXAMPLE 14 1\nAn intrinsic semiconductor\nwill behave like an insulator at\nT = 0 K as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3318-3321", + "Text": "The electron from the lower left hand covalent bond\n(site 2) goes to the earlier hole site1, leaving a hole at its site indicating an\napparent movement of the hole from site 1 to site 2 (a)\n(b)\nRationalised 2023-24\n329\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n EXAMPLE 14 1\nAn intrinsic semiconductor\nwill behave like an insulator at\nT = 0 K as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3319-3322", + "Text": "(a)\n(b)\nRationalised 2023-24\n329\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n EXAMPLE 14 1\nAn intrinsic semiconductor\nwill behave like an insulator at\nT = 0 K as shown in Fig 14 6(a)" + }, + { + "Chapter": "9", + "sentence_range": "3320-3323", + "Text": "1\nAn intrinsic semiconductor\nwill behave like an insulator at\nT = 0 K as shown in Fig 14 6(a) It is the thermal energy at\nhigher temperatures (T > 0K),\nwhich excites some electrons\nfrom the valence band to the\nconduction band" + }, + { + "Chapter": "9", + "sentence_range": "3321-3324", + "Text": "14 6(a) It is the thermal energy at\nhigher temperatures (T > 0K),\nwhich excites some electrons\nfrom the valence band to the\nconduction band These\nthermally excited electrons at\nT > 0 K, partially occupy the\nconduction band" + }, + { + "Chapter": "9", + "sentence_range": "3322-3325", + "Text": "6(a) It is the thermal energy at\nhigher temperatures (T > 0K),\nwhich excites some electrons\nfrom the valence band to the\nconduction band These\nthermally excited electrons at\nT > 0 K, partially occupy the\nconduction band Therefore,\nthe energy-band diagram of an\nintrinsic semiconductor will be\nas shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3323-3326", + "Text": "It is the thermal energy at\nhigher temperatures (T > 0K),\nwhich excites some electrons\nfrom the valence band to the\nconduction band These\nthermally excited electrons at\nT > 0 K, partially occupy the\nconduction band Therefore,\nthe energy-band diagram of an\nintrinsic semiconductor will be\nas shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3324-3327", + "Text": "These\nthermally excited electrons at\nT > 0 K, partially occupy the\nconduction band Therefore,\nthe energy-band diagram of an\nintrinsic semiconductor will be\nas shown in Fig 14 6(b)" + }, + { + "Chapter": "9", + "sentence_range": "3325-3328", + "Text": "Therefore,\nthe energy-band diagram of an\nintrinsic semiconductor will be\nas shown in Fig 14 6(b) Here,\nsome electrons are shown in\nthe conduction band" + }, + { + "Chapter": "9", + "sentence_range": "3326-3329", + "Text": "14 6(b) Here,\nsome electrons are shown in\nthe conduction band These\nhave come from the valence\nband leaving equal number of\nholes there" + }, + { + "Chapter": "9", + "sentence_range": "3327-3330", + "Text": "6(b) Here,\nsome electrons are shown in\nthe conduction band These\nhave come from the valence\nband leaving equal number of\nholes there Example 14" + }, + { + "Chapter": "9", + "sentence_range": "3328-3331", + "Text": "Here,\nsome electrons are shown in\nthe conduction band These\nhave come from the valence\nband leaving equal number of\nholes there Example 14 1 C, Si and Ge have same lattice structure" + }, + { + "Chapter": "9", + "sentence_range": "3329-3332", + "Text": "These\nhave come from the valence\nband leaving equal number of\nholes there Example 14 1 C, Si and Ge have same lattice structure Why is C\ninsulator while Si and Ge intrinsic semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3330-3333", + "Text": "Example 14 1 C, Si and Ge have same lattice structure Why is C\ninsulator while Si and Ge intrinsic semiconductors Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in\nthe second, third and fourth orbit" + }, + { + "Chapter": "9", + "sentence_range": "3331-3334", + "Text": "1 C, Si and Ge have same lattice structure Why is C\ninsulator while Si and Ge intrinsic semiconductors Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in\nthe second, third and fourth orbit Hence, energy required to take\nout an electron from these atoms (i" + }, + { + "Chapter": "9", + "sentence_range": "3332-3335", + "Text": "Why is C\ninsulator while Si and Ge intrinsic semiconductors Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in\nthe second, third and fourth orbit Hence, energy required to take\nout an electron from these atoms (i e" + }, + { + "Chapter": "9", + "sentence_range": "3333-3336", + "Text": "Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in\nthe second, third and fourth orbit Hence, energy required to take\nout an electron from these atoms (i e , ionisation energy Eg) will be\nleast for Ge, followed by Si and highest for C" + }, + { + "Chapter": "9", + "sentence_range": "3334-3337", + "Text": "Hence, energy required to take\nout an electron from these atoms (i e , ionisation energy Eg) will be\nleast for Ge, followed by Si and highest for C Hence, number of free\nelectrons for conduction in Ge and Si are significant but negligibly\nsmall for C" + }, + { + "Chapter": "9", + "sentence_range": "3335-3338", + "Text": "e , ionisation energy Eg) will be\nleast for Ge, followed by Si and highest for C Hence, number of free\nelectrons for conduction in Ge and Si are significant but negligibly\nsmall for C 14" + }, + { + "Chapter": "9", + "sentence_range": "3336-3339", + "Text": ", ionisation energy Eg) will be\nleast for Ge, followed by Si and highest for C Hence, number of free\nelectrons for conduction in Ge and Si are significant but negligibly\nsmall for C 14 4 EXTRINSIC SEMICONDUCTOR\nThe conductivity of an intrinsic semiconductor depends on its\ntemperature, but at room temperature its conductivity is very low" + }, + { + "Chapter": "9", + "sentence_range": "3337-3340", + "Text": "Hence, number of free\nelectrons for conduction in Ge and Si are significant but negligibly\nsmall for C 14 4 EXTRINSIC SEMICONDUCTOR\nThe conductivity of an intrinsic semiconductor depends on its\ntemperature, but at room temperature its conductivity is very low As\nsuch, no important electronic devices can be developed using these\nsemiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3338-3341", + "Text": "14 4 EXTRINSIC SEMICONDUCTOR\nThe conductivity of an intrinsic semiconductor depends on its\ntemperature, but at room temperature its conductivity is very low As\nsuch, no important electronic devices can be developed using these\nsemiconductors Hence there is a necessity of improving their\nconductivity" + }, + { + "Chapter": "9", + "sentence_range": "3339-3342", + "Text": "4 EXTRINSIC SEMICONDUCTOR\nThe conductivity of an intrinsic semiconductor depends on its\ntemperature, but at room temperature its conductivity is very low As\nsuch, no important electronic devices can be developed using these\nsemiconductors Hence there is a necessity of improving their\nconductivity This can be done by making use of impurities" + }, + { + "Chapter": "9", + "sentence_range": "3340-3343", + "Text": "As\nsuch, no important electronic devices can be developed using these\nsemiconductors Hence there is a necessity of improving their\nconductivity This can be done by making use of impurities When a small amount, say, a few parts per million (ppm), of a suitable\nimpurity is added to the pure semiconductor, the conductivity of the\nsemiconductor is increased manifold" + }, + { + "Chapter": "9", + "sentence_range": "3341-3344", + "Text": "Hence there is a necessity of improving their\nconductivity This can be done by making use of impurities When a small amount, say, a few parts per million (ppm), of a suitable\nimpurity is added to the pure semiconductor, the conductivity of the\nsemiconductor is increased manifold Such materials are known as\nextrinsic semiconductors or impurity semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3342-3345", + "Text": "This can be done by making use of impurities When a small amount, say, a few parts per million (ppm), of a suitable\nimpurity is added to the pure semiconductor, the conductivity of the\nsemiconductor is increased manifold Such materials are known as\nextrinsic semiconductors or impurity semiconductors The deliberate\naddition of a desirable impurity is called doping and the impurity atoms\nare called dopants" + }, + { + "Chapter": "9", + "sentence_range": "3343-3346", + "Text": "When a small amount, say, a few parts per million (ppm), of a suitable\nimpurity is added to the pure semiconductor, the conductivity of the\nsemiconductor is increased manifold Such materials are known as\nextrinsic semiconductors or impurity semiconductors The deliberate\naddition of a desirable impurity is called doping and the impurity atoms\nare called dopants Such a material is also called a doped semiconductor" + }, + { + "Chapter": "9", + "sentence_range": "3344-3347", + "Text": "Such materials are known as\nextrinsic semiconductors or impurity semiconductors The deliberate\naddition of a desirable impurity is called doping and the impurity atoms\nare called dopants Such a material is also called a doped semiconductor The dopant has to be such that it does not distort the original pure\nsemiconductor lattice" + }, + { + "Chapter": "9", + "sentence_range": "3345-3348", + "Text": "The deliberate\naddition of a desirable impurity is called doping and the impurity atoms\nare called dopants Such a material is also called a doped semiconductor The dopant has to be such that it does not distort the original pure\nsemiconductor lattice It occupies only a very few of the original\nsemiconductor atom sites in the crystal" + }, + { + "Chapter": "9", + "sentence_range": "3346-3349", + "Text": "Such a material is also called a doped semiconductor The dopant has to be such that it does not distort the original pure\nsemiconductor lattice It occupies only a very few of the original\nsemiconductor atom sites in the crystal A necessary condition to attain\nthis is that the sizes of the dopant and the semiconductor atoms should\nbe nearly the same" + }, + { + "Chapter": "9", + "sentence_range": "3347-3350", + "Text": "The dopant has to be such that it does not distort the original pure\nsemiconductor lattice It occupies only a very few of the original\nsemiconductor atom sites in the crystal A necessary condition to attain\nthis is that the sizes of the dopant and the semiconductor atoms should\nbe nearly the same There are two types of dopants used in doping the tetravalent Si\nor Ge:\n(i)\nPentavalent (valency 5); like Arsenic (As), Antimony (Sb), Phosphorous\n(P), etc" + }, + { + "Chapter": "9", + "sentence_range": "3348-3351", + "Text": "It occupies only a very few of the original\nsemiconductor atom sites in the crystal A necessary condition to attain\nthis is that the sizes of the dopant and the semiconductor atoms should\nbe nearly the same There are two types of dopants used in doping the tetravalent Si\nor Ge:\n(i)\nPentavalent (valency 5); like Arsenic (As), Antimony (Sb), Phosphorous\n(P), etc FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3349-3352", + "Text": "A necessary condition to attain\nthis is that the sizes of the dopant and the semiconductor atoms should\nbe nearly the same There are two types of dopants used in doping the tetravalent Si\nor Ge:\n(i)\nPentavalent (valency 5); like Arsenic (As), Antimony (Sb), Phosphorous\n(P), etc FIGURE 14 6 (a) An intrinsic semiconductor at T = 0 K\nbehaves like insulator" + }, + { + "Chapter": "9", + "sentence_range": "3350-3353", + "Text": "There are two types of dopants used in doping the tetravalent Si\nor Ge:\n(i)\nPentavalent (valency 5); like Arsenic (As), Antimony (Sb), Phosphorous\n(P), etc FIGURE 14 6 (a) An intrinsic semiconductor at T = 0 K\nbehaves like insulator (b) At T > 0 K, four thermally generated\nelectron-hole pairs" + }, + { + "Chapter": "9", + "sentence_range": "3351-3354", + "Text": "FIGURE 14 6 (a) An intrinsic semiconductor at T = 0 K\nbehaves like insulator (b) At T > 0 K, four thermally generated\nelectron-hole pairs The filled circles ( ) represent electrons\nand empty circles ( ) represent holes" + }, + { + "Chapter": "9", + "sentence_range": "3352-3355", + "Text": "6 (a) An intrinsic semiconductor at T = 0 K\nbehaves like insulator (b) At T > 0 K, four thermally generated\nelectron-hole pairs The filled circles ( ) represent electrons\nand empty circles ( ) represent holes Rationalised 2023-24\nPhysics\n330\n(ii) Trivalent (valency 3); like Indium (In),\nBoron (B), Aluminium (Al), etc" + }, + { + "Chapter": "9", + "sentence_range": "3353-3356", + "Text": "(b) At T > 0 K, four thermally generated\nelectron-hole pairs The filled circles ( ) represent electrons\nand empty circles ( ) represent holes Rationalised 2023-24\nPhysics\n330\n(ii) Trivalent (valency 3); like Indium (In),\nBoron (B), Aluminium (Al), etc We shall now discuss how the doping\nchanges the number of charge carriers (and\nhence the conductivity) of semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3354-3357", + "Text": "The filled circles ( ) represent electrons\nand empty circles ( ) represent holes Rationalised 2023-24\nPhysics\n330\n(ii) Trivalent (valency 3); like Indium (In),\nBoron (B), Aluminium (Al), etc We shall now discuss how the doping\nchanges the number of charge carriers (and\nhence the conductivity) of semiconductors Si or Ge belongs to the fourth group in the\nPeriodic table and, therefore, we choose the\ndopant element from nearby fifth or third\ngroup, expecting and taking care that the\nsize of the dopant atom is nearly the same as\nthat of Si or Ge" + }, + { + "Chapter": "9", + "sentence_range": "3355-3358", + "Text": "Rationalised 2023-24\nPhysics\n330\n(ii) Trivalent (valency 3); like Indium (In),\nBoron (B), Aluminium (Al), etc We shall now discuss how the doping\nchanges the number of charge carriers (and\nhence the conductivity) of semiconductors Si or Ge belongs to the fourth group in the\nPeriodic table and, therefore, we choose the\ndopant element from nearby fifth or third\ngroup, expecting and taking care that the\nsize of the dopant atom is nearly the same as\nthat of Si or Ge Interestingly, the pentavalent\nand trivalent dopants in Si or Ge give two\nentirely different types of semiconductors as\ndiscussed below" + }, + { + "Chapter": "9", + "sentence_range": "3356-3359", + "Text": "We shall now discuss how the doping\nchanges the number of charge carriers (and\nhence the conductivity) of semiconductors Si or Ge belongs to the fourth group in the\nPeriodic table and, therefore, we choose the\ndopant element from nearby fifth or third\ngroup, expecting and taking care that the\nsize of the dopant atom is nearly the same as\nthat of Si or Ge Interestingly, the pentavalent\nand trivalent dopants in Si or Ge give two\nentirely different types of semiconductors as\ndiscussed below (i) n-type semiconductor\nSuppose we dope Si or Ge with a pentavalent\nelement as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3357-3360", + "Text": "Si or Ge belongs to the fourth group in the\nPeriodic table and, therefore, we choose the\ndopant element from nearby fifth or third\ngroup, expecting and taking care that the\nsize of the dopant atom is nearly the same as\nthat of Si or Ge Interestingly, the pentavalent\nand trivalent dopants in Si or Ge give two\nentirely different types of semiconductors as\ndiscussed below (i) n-type semiconductor\nSuppose we dope Si or Ge with a pentavalent\nelement as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3358-3361", + "Text": "Interestingly, the pentavalent\nand trivalent dopants in Si or Ge give two\nentirely different types of semiconductors as\ndiscussed below (i) n-type semiconductor\nSuppose we dope Si or Ge with a pentavalent\nelement as shown in Fig 14 7" + }, + { + "Chapter": "9", + "sentence_range": "3359-3362", + "Text": "(i) n-type semiconductor\nSuppose we dope Si or Ge with a pentavalent\nelement as shown in Fig 14 7 When an atom\nof +5 valency element occupies the position\nof an atom in the crystal lattice of Si, four of\nits electrons bond with the four silicon\nneighbours while the fifth remains very\nweakly bound to its parent atom" + }, + { + "Chapter": "9", + "sentence_range": "3360-3363", + "Text": "14 7 When an atom\nof +5 valency element occupies the position\nof an atom in the crystal lattice of Si, four of\nits electrons bond with the four silicon\nneighbours while the fifth remains very\nweakly bound to its parent atom This is\nbecause the four electrons participating in\nbonding are seen as part of the effective core\nof the atom by the fifth electron" + }, + { + "Chapter": "9", + "sentence_range": "3361-3364", + "Text": "7 When an atom\nof +5 valency element occupies the position\nof an atom in the crystal lattice of Si, four of\nits electrons bond with the four silicon\nneighbours while the fifth remains very\nweakly bound to its parent atom This is\nbecause the four electrons participating in\nbonding are seen as part of the effective core\nof the atom by the fifth electron As a result\nthe ionisation energy required to set this\nelectron free is very small and even at room\ntemperature it will be free to move in the\nlattice of the semiconductor" + }, + { + "Chapter": "9", + "sentence_range": "3362-3365", + "Text": "When an atom\nof +5 valency element occupies the position\nof an atom in the crystal lattice of Si, four of\nits electrons bond with the four silicon\nneighbours while the fifth remains very\nweakly bound to its parent atom This is\nbecause the four electrons participating in\nbonding are seen as part of the effective core\nof the atom by the fifth electron As a result\nthe ionisation energy required to set this\nelectron free is very small and even at room\ntemperature it will be free to move in the\nlattice of the semiconductor For example, the\nenergy required is ~ 0" + }, + { + "Chapter": "9", + "sentence_range": "3363-3366", + "Text": "This is\nbecause the four electrons participating in\nbonding are seen as part of the effective core\nof the atom by the fifth electron As a result\nthe ionisation energy required to set this\nelectron free is very small and even at room\ntemperature it will be free to move in the\nlattice of the semiconductor For example, the\nenergy required is ~ 0 01 eV for germanium,\nand 0" + }, + { + "Chapter": "9", + "sentence_range": "3364-3367", + "Text": "As a result\nthe ionisation energy required to set this\nelectron free is very small and even at room\ntemperature it will be free to move in the\nlattice of the semiconductor For example, the\nenergy required is ~ 0 01 eV for germanium,\nand 0 05 eV for silicon, to separate this\nelectron from its atom" + }, + { + "Chapter": "9", + "sentence_range": "3365-3368", + "Text": "For example, the\nenergy required is ~ 0 01 eV for germanium,\nand 0 05 eV for silicon, to separate this\nelectron from its atom This is in contrast to the energy required to jump\nthe forbidden band (about 0" + }, + { + "Chapter": "9", + "sentence_range": "3366-3369", + "Text": "01 eV for germanium,\nand 0 05 eV for silicon, to separate this\nelectron from its atom This is in contrast to the energy required to jump\nthe forbidden band (about 0 72 eV for germanium and about 1" + }, + { + "Chapter": "9", + "sentence_range": "3367-3370", + "Text": "05 eV for silicon, to separate this\nelectron from its atom This is in contrast to the energy required to jump\nthe forbidden band (about 0 72 eV for germanium and about 1 1 eV for\nsilicon) at room temperature in the intrinsic semiconductor" + }, + { + "Chapter": "9", + "sentence_range": "3368-3371", + "Text": "This is in contrast to the energy required to jump\nthe forbidden band (about 0 72 eV for germanium and about 1 1 eV for\nsilicon) at room temperature in the intrinsic semiconductor Thus, the\npentavalent dopant is donating one extra electron for conduction and\nhence is known as donor impurity" + }, + { + "Chapter": "9", + "sentence_range": "3369-3372", + "Text": "72 eV for germanium and about 1 1 eV for\nsilicon) at room temperature in the intrinsic semiconductor Thus, the\npentavalent dopant is donating one extra electron for conduction and\nhence is known as donor impurity The number of electrons made\navailable for conduction by dopant atoms depends strongly upon the\ndoping level and is independent of any increase in ambient temperature" + }, + { + "Chapter": "9", + "sentence_range": "3370-3373", + "Text": "1 eV for\nsilicon) at room temperature in the intrinsic semiconductor Thus, the\npentavalent dopant is donating one extra electron for conduction and\nhence is known as donor impurity The number of electrons made\navailable for conduction by dopant atoms depends strongly upon the\ndoping level and is independent of any increase in ambient temperature On the other hand, the number of free electrons (with an equal number\nof holes) generated by Si atoms, increases weakly with temperature" + }, + { + "Chapter": "9", + "sentence_range": "3371-3374", + "Text": "Thus, the\npentavalent dopant is donating one extra electron for conduction and\nhence is known as donor impurity The number of electrons made\navailable for conduction by dopant atoms depends strongly upon the\ndoping level and is independent of any increase in ambient temperature On the other hand, the number of free electrons (with an equal number\nof holes) generated by Si atoms, increases weakly with temperature In a doped semiconductor the total number of conduction electrons\nne is due to the electrons contributed by donors and those generated\nintrinsically, while the total number of holes nh is only due to the holes\nfrom the intrinsic source" + }, + { + "Chapter": "9", + "sentence_range": "3372-3375", + "Text": "The number of electrons made\navailable for conduction by dopant atoms depends strongly upon the\ndoping level and is independent of any increase in ambient temperature On the other hand, the number of free electrons (with an equal number\nof holes) generated by Si atoms, increases weakly with temperature In a doped semiconductor the total number of conduction electrons\nne is due to the electrons contributed by donors and those generated\nintrinsically, while the total number of holes nh is only due to the holes\nfrom the intrinsic source But the rate of recombination of holes would\nincrease due to the increase in the number of electrons" + }, + { + "Chapter": "9", + "sentence_range": "3373-3376", + "Text": "On the other hand, the number of free electrons (with an equal number\nof holes) generated by Si atoms, increases weakly with temperature In a doped semiconductor the total number of conduction electrons\nne is due to the electrons contributed by donors and those generated\nintrinsically, while the total number of holes nh is only due to the holes\nfrom the intrinsic source But the rate of recombination of holes would\nincrease due to the increase in the number of electrons As a result, the\nnumber of holes would get reduced further" + }, + { + "Chapter": "9", + "sentence_range": "3374-3377", + "Text": "In a doped semiconductor the total number of conduction electrons\nne is due to the electrons contributed by donors and those generated\nintrinsically, while the total number of holes nh is only due to the holes\nfrom the intrinsic source But the rate of recombination of holes would\nincrease due to the increase in the number of electrons As a result, the\nnumber of holes would get reduced further Thus, with proper level of doping the number of conduction electrons\ncan be made much larger than the number of holes" + }, + { + "Chapter": "9", + "sentence_range": "3375-3378", + "Text": "But the rate of recombination of holes would\nincrease due to the increase in the number of electrons As a result, the\nnumber of holes would get reduced further Thus, with proper level of doping the number of conduction electrons\ncan be made much larger than the number of holes Hence in an extrinsic\nFIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3376-3379", + "Text": "As a result, the\nnumber of holes would get reduced further Thus, with proper level of doping the number of conduction electrons\ncan be made much larger than the number of holes Hence in an extrinsic\nFIGURE 14 7 (a) Pentavalent donor atom (As, Sb,\nP, etc" + }, + { + "Chapter": "9", + "sentence_range": "3377-3380", + "Text": "Thus, with proper level of doping the number of conduction electrons\ncan be made much larger than the number of holes Hence in an extrinsic\nFIGURE 14 7 (a) Pentavalent donor atom (As, Sb,\nP, etc ) doped for tetravalent Si or Ge giving n-\ntype semiconductor, and (b) Commonly used\nschematic representation of n-type material\nwhich shows only the fixed cores of the\nsubstituent donors with one additional effective\npositive charge and its associated extra electron" + }, + { + "Chapter": "9", + "sentence_range": "3378-3381", + "Text": "Hence in an extrinsic\nFIGURE 14 7 (a) Pentavalent donor atom (As, Sb,\nP, etc ) doped for tetravalent Si or Ge giving n-\ntype semiconductor, and (b) Commonly used\nschematic representation of n-type material\nwhich shows only the fixed cores of the\nsubstituent donors with one additional effective\npositive charge and its associated extra electron Rationalised 2023-24\n331\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nsemiconductor doped with pentavalent impurity, electrons\nbecome the majority carriers and holes the minority carriers" + }, + { + "Chapter": "9", + "sentence_range": "3379-3382", + "Text": "7 (a) Pentavalent donor atom (As, Sb,\nP, etc ) doped for tetravalent Si or Ge giving n-\ntype semiconductor, and (b) Commonly used\nschematic representation of n-type material\nwhich shows only the fixed cores of the\nsubstituent donors with one additional effective\npositive charge and its associated extra electron Rationalised 2023-24\n331\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nsemiconductor doped with pentavalent impurity, electrons\nbecome the majority carriers and holes the minority carriers These semiconductors are, therefore, known as n-type\nsemiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3380-3383", + "Text": ") doped for tetravalent Si or Ge giving n-\ntype semiconductor, and (b) Commonly used\nschematic representation of n-type material\nwhich shows only the fixed cores of the\nsubstituent donors with one additional effective\npositive charge and its associated extra electron Rationalised 2023-24\n331\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nsemiconductor doped with pentavalent impurity, electrons\nbecome the majority carriers and holes the minority carriers These semiconductors are, therefore, known as n-type\nsemiconductors For n-type semiconductors, we have,\nne >> nh\n(14" + }, + { + "Chapter": "9", + "sentence_range": "3381-3384", + "Text": "Rationalised 2023-24\n331\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nsemiconductor doped with pentavalent impurity, electrons\nbecome the majority carriers and holes the minority carriers These semiconductors are, therefore, known as n-type\nsemiconductors For n-type semiconductors, we have,\nne >> nh\n(14 3)\n(ii) p-type semiconductor\nThis is obtained when Si or Ge is doped with a trivalent impurity\nlike Al, B, In, etc" + }, + { + "Chapter": "9", + "sentence_range": "3382-3385", + "Text": "These semiconductors are, therefore, known as n-type\nsemiconductors For n-type semiconductors, we have,\nne >> nh\n(14 3)\n(ii) p-type semiconductor\nThis is obtained when Si or Ge is doped with a trivalent impurity\nlike Al, B, In, etc The dopant has one valence electron less than\nSi or Ge and, therefore, this atom can form covalent bonds with\nneighbouring three Si atoms but does not have any electron to\noffer to the fourth Si atom" + }, + { + "Chapter": "9", + "sentence_range": "3383-3386", + "Text": "For n-type semiconductors, we have,\nne >> nh\n(14 3)\n(ii) p-type semiconductor\nThis is obtained when Si or Ge is doped with a trivalent impurity\nlike Al, B, In, etc The dopant has one valence electron less than\nSi or Ge and, therefore, this atom can form covalent bonds with\nneighbouring three Si atoms but does not have any electron to\noffer to the fourth Si atom So the bond between the fourth\nneighbour and the trivalent atom has a vacancy or hole as\nshown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3384-3387", + "Text": "3)\n(ii) p-type semiconductor\nThis is obtained when Si or Ge is doped with a trivalent impurity\nlike Al, B, In, etc The dopant has one valence electron less than\nSi or Ge and, therefore, this atom can form covalent bonds with\nneighbouring three Si atoms but does not have any electron to\noffer to the fourth Si atom So the bond between the fourth\nneighbour and the trivalent atom has a vacancy or hole as\nshown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3385-3388", + "Text": "The dopant has one valence electron less than\nSi or Ge and, therefore, this atom can form covalent bonds with\nneighbouring three Si atoms but does not have any electron to\noffer to the fourth Si atom So the bond between the fourth\nneighbour and the trivalent atom has a vacancy or hole as\nshown in Fig 14 8" + }, + { + "Chapter": "9", + "sentence_range": "3386-3389", + "Text": "So the bond between the fourth\nneighbour and the trivalent atom has a vacancy or hole as\nshown in Fig 14 8 Since the neighbouring Si atom in the lattice\nwants an electron in place of a hole, an electron in the outer\norbit of an atom in the neighbourhood may jump to fill this\nvacancy, leaving a vacancy or hole at its own site" + }, + { + "Chapter": "9", + "sentence_range": "3387-3390", + "Text": "14 8 Since the neighbouring Si atom in the lattice\nwants an electron in place of a hole, an electron in the outer\norbit of an atom in the neighbourhood may jump to fill this\nvacancy, leaving a vacancy or hole at its own site Thus the hole\nis available for conduction" + }, + { + "Chapter": "9", + "sentence_range": "3388-3391", + "Text": "8 Since the neighbouring Si atom in the lattice\nwants an electron in place of a hole, an electron in the outer\norbit of an atom in the neighbourhood may jump to fill this\nvacancy, leaving a vacancy or hole at its own site Thus the hole\nis available for conduction Note that the trivalent foreign atom\nbecomes effectively negatively charged when it shares fourth\nelectron with neighbouring Si atom" + }, + { + "Chapter": "9", + "sentence_range": "3389-3392", + "Text": "Since the neighbouring Si atom in the lattice\nwants an electron in place of a hole, an electron in the outer\norbit of an atom in the neighbourhood may jump to fill this\nvacancy, leaving a vacancy or hole at its own site Thus the hole\nis available for conduction Note that the trivalent foreign atom\nbecomes effectively negatively charged when it shares fourth\nelectron with neighbouring Si atom Therefore, the dopant atom\nof p-type material can be treated as core of one negative charge\nalong with its associated hole as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3390-3393", + "Text": "Thus the hole\nis available for conduction Note that the trivalent foreign atom\nbecomes effectively negatively charged when it shares fourth\nelectron with neighbouring Si atom Therefore, the dopant atom\nof p-type material can be treated as core of one negative charge\nalong with its associated hole as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3391-3394", + "Text": "Note that the trivalent foreign atom\nbecomes effectively negatively charged when it shares fourth\nelectron with neighbouring Si atom Therefore, the dopant atom\nof p-type material can be treated as core of one negative charge\nalong with its associated hole as shown in Fig 14 8(b)" + }, + { + "Chapter": "9", + "sentence_range": "3392-3395", + "Text": "Therefore, the dopant atom\nof p-type material can be treated as core of one negative charge\nalong with its associated hole as shown in Fig 14 8(b) It is\nobvious that one acceptor atom gives one hole" + }, + { + "Chapter": "9", + "sentence_range": "3393-3396", + "Text": "14 8(b) It is\nobvious that one acceptor atom gives one hole These holes are\nin addition to the intrinsically generated holes while the source\nof conduction electrons is only intrinsic generation" + }, + { + "Chapter": "9", + "sentence_range": "3394-3397", + "Text": "8(b) It is\nobvious that one acceptor atom gives one hole These holes are\nin addition to the intrinsically generated holes while the source\nof conduction electrons is only intrinsic generation Thus, for\nsuch a material, the holes are the majority carriers and electrons\nare minority carriers" + }, + { + "Chapter": "9", + "sentence_range": "3395-3398", + "Text": "It is\nobvious that one acceptor atom gives one hole These holes are\nin addition to the intrinsically generated holes while the source\nof conduction electrons is only intrinsic generation Thus, for\nsuch a material, the holes are the majority carriers and electrons\nare minority carriers Therefore, extrinsic semiconductors doped\nwith trivalent impurity are called p-type semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3396-3399", + "Text": "These holes are\nin addition to the intrinsically generated holes while the source\nof conduction electrons is only intrinsic generation Thus, for\nsuch a material, the holes are the majority carriers and electrons\nare minority carriers Therefore, extrinsic semiconductors doped\nwith trivalent impurity are called p-type semiconductors For\np-type semiconductors, the recombination process will reduce\nthe number (ni)of intrinsically generated electrons to ne" + }, + { + "Chapter": "9", + "sentence_range": "3397-3400", + "Text": "Thus, for\nsuch a material, the holes are the majority carriers and electrons\nare minority carriers Therefore, extrinsic semiconductors doped\nwith trivalent impurity are called p-type semiconductors For\np-type semiconductors, the recombination process will reduce\nthe number (ni)of intrinsically generated electrons to ne We have, for p-type semiconductors\nnh >> ne\n(14" + }, + { + "Chapter": "9", + "sentence_range": "3398-3401", + "Text": "Therefore, extrinsic semiconductors doped\nwith trivalent impurity are called p-type semiconductors For\np-type semiconductors, the recombination process will reduce\nthe number (ni)of intrinsically generated electrons to ne We have, for p-type semiconductors\nnh >> ne\n(14 4)\nNote that the crystal maintains an overall charge neutrality\nas the charge of additional charge carriers is just equal and\nopposite to that of the ionised cores in the lattice" + }, + { + "Chapter": "9", + "sentence_range": "3399-3402", + "Text": "For\np-type semiconductors, the recombination process will reduce\nthe number (ni)of intrinsically generated electrons to ne We have, for p-type semiconductors\nnh >> ne\n(14 4)\nNote that the crystal maintains an overall charge neutrality\nas the charge of additional charge carriers is just equal and\nopposite to that of the ionised cores in the lattice In extrinsic semiconductors, because of the abundance of\nmajority current carriers, the minority carriers produced\nthermally have more chance of meeting majority carriers and\nthus getting destroyed" + }, + { + "Chapter": "9", + "sentence_range": "3400-3403", + "Text": "We have, for p-type semiconductors\nnh >> ne\n(14 4)\nNote that the crystal maintains an overall charge neutrality\nas the charge of additional charge carriers is just equal and\nopposite to that of the ionised cores in the lattice In extrinsic semiconductors, because of the abundance of\nmajority current carriers, the minority carriers produced\nthermally have more chance of meeting majority carriers and\nthus getting destroyed Hence, the dopant, by adding a large number of\ncurrent carriers of one type, which become the majority carriers, indirectly\nhelps to reduce the intrinsic concentration of minority carriers" + }, + { + "Chapter": "9", + "sentence_range": "3401-3404", + "Text": "4)\nNote that the crystal maintains an overall charge neutrality\nas the charge of additional charge carriers is just equal and\nopposite to that of the ionised cores in the lattice In extrinsic semiconductors, because of the abundance of\nmajority current carriers, the minority carriers produced\nthermally have more chance of meeting majority carriers and\nthus getting destroyed Hence, the dopant, by adding a large number of\ncurrent carriers of one type, which become the majority carriers, indirectly\nhelps to reduce the intrinsic concentration of minority carriers The semiconductor\u2019s energy band structure is affected by doping" + }, + { + "Chapter": "9", + "sentence_range": "3402-3405", + "Text": "In extrinsic semiconductors, because of the abundance of\nmajority current carriers, the minority carriers produced\nthermally have more chance of meeting majority carriers and\nthus getting destroyed Hence, the dopant, by adding a large number of\ncurrent carriers of one type, which become the majority carriers, indirectly\nhelps to reduce the intrinsic concentration of minority carriers The semiconductor\u2019s energy band structure is affected by doping In\nthe case of extrinsic semiconductors, additional energy states due to donor\nimpurities (ED) and acceptor impurities (EA) also exist" + }, + { + "Chapter": "9", + "sentence_range": "3403-3406", + "Text": "Hence, the dopant, by adding a large number of\ncurrent carriers of one type, which become the majority carriers, indirectly\nhelps to reduce the intrinsic concentration of minority carriers The semiconductor\u2019s energy band structure is affected by doping In\nthe case of extrinsic semiconductors, additional energy states due to donor\nimpurities (ED) and acceptor impurities (EA) also exist In the energy band\ndiagram of n-type Si semiconductor, the donor energy level ED is slightly\nbelow the bottom EC of the conduction band and electrons from this level\nmove into the conduction band with very small supply of energy" + }, + { + "Chapter": "9", + "sentence_range": "3404-3407", + "Text": "The semiconductor\u2019s energy band structure is affected by doping In\nthe case of extrinsic semiconductors, additional energy states due to donor\nimpurities (ED) and acceptor impurities (EA) also exist In the energy band\ndiagram of n-type Si semiconductor, the donor energy level ED is slightly\nbelow the bottom EC of the conduction band and electrons from this level\nmove into the conduction band with very small supply of energy At room\ntemperature, most of the donor atoms get ionised but very few (~1012)\natoms of Si get ionised" + }, + { + "Chapter": "9", + "sentence_range": "3405-3408", + "Text": "In\nthe case of extrinsic semiconductors, additional energy states due to donor\nimpurities (ED) and acceptor impurities (EA) also exist In the energy band\ndiagram of n-type Si semiconductor, the donor energy level ED is slightly\nbelow the bottom EC of the conduction band and electrons from this level\nmove into the conduction band with very small supply of energy At room\ntemperature, most of the donor atoms get ionised but very few (~1012)\natoms of Si get ionised So the conduction band will have most electrons\ncoming from the donor impurities, as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3406-3409", + "Text": "In the energy band\ndiagram of n-type Si semiconductor, the donor energy level ED is slightly\nbelow the bottom EC of the conduction band and electrons from this level\nmove into the conduction band with very small supply of energy At room\ntemperature, most of the donor atoms get ionised but very few (~1012)\natoms of Si get ionised So the conduction band will have most electrons\ncoming from the donor impurities, as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3407-3410", + "Text": "At room\ntemperature, most of the donor atoms get ionised but very few (~1012)\natoms of Si get ionised So the conduction band will have most electrons\ncoming from the donor impurities, as shown in Fig 14 9(a)" + }, + { + "Chapter": "9", + "sentence_range": "3408-3411", + "Text": "So the conduction band will have most electrons\ncoming from the donor impurities, as shown in Fig 14 9(a) Similarly,\nFIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3409-3412", + "Text": "14 9(a) Similarly,\nFIGURE 14 8 (a) Trivalent\nacceptor atom (In, Al, B etc" + }, + { + "Chapter": "9", + "sentence_range": "3410-3413", + "Text": "9(a) Similarly,\nFIGURE 14 8 (a) Trivalent\nacceptor atom (In, Al, B etc )\ndoped in tetravalent Si or Ge\nlattice giving p-type semicon-\nductor" + }, + { + "Chapter": "9", + "sentence_range": "3411-3414", + "Text": "Similarly,\nFIGURE 14 8 (a) Trivalent\nacceptor atom (In, Al, B etc )\ndoped in tetravalent Si or Ge\nlattice giving p-type semicon-\nductor (b) Commonly used\nschematic representation of\np-type material which shows\nonly the fixed core of the\nsubstituent acceptor with\none effective additional\nnegative charge and its\nassociated hole" + }, + { + "Chapter": "9", + "sentence_range": "3412-3415", + "Text": "8 (a) Trivalent\nacceptor atom (In, Al, B etc )\ndoped in tetravalent Si or Ge\nlattice giving p-type semicon-\nductor (b) Commonly used\nschematic representation of\np-type material which shows\nonly the fixed core of the\nsubstituent acceptor with\none effective additional\nnegative charge and its\nassociated hole Rationalised 2023-24\nPhysics\n332\n EXAMPLE 14" + }, + { + "Chapter": "9", + "sentence_range": "3413-3416", + "Text": ")\ndoped in tetravalent Si or Ge\nlattice giving p-type semicon-\nductor (b) Commonly used\nschematic representation of\np-type material which shows\nonly the fixed core of the\nsubstituent acceptor with\none effective additional\nnegative charge and its\nassociated hole Rationalised 2023-24\nPhysics\n332\n EXAMPLE 14 2\nfor p-type semiconductor, the acceptor energy level EA is slightly above\nthe top EV of the valence band as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3414-3417", + "Text": "(b) Commonly used\nschematic representation of\np-type material which shows\nonly the fixed core of the\nsubstituent acceptor with\none effective additional\nnegative charge and its\nassociated hole Rationalised 2023-24\nPhysics\n332\n EXAMPLE 14 2\nfor p-type semiconductor, the acceptor energy level EA is slightly above\nthe top EV of the valence band as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3415-3418", + "Text": "Rationalised 2023-24\nPhysics\n332\n EXAMPLE 14 2\nfor p-type semiconductor, the acceptor energy level EA is slightly above\nthe top EV of the valence band as shown in Fig 14 9(b)" + }, + { + "Chapter": "9", + "sentence_range": "3416-3419", + "Text": "2\nfor p-type semiconductor, the acceptor energy level EA is slightly above\nthe top EV of the valence band as shown in Fig 14 9(b) With very small\nsupply of energy an electron from the valence band can jump to the level\nEA and ionise the acceptor negatively" + }, + { + "Chapter": "9", + "sentence_range": "3417-3420", + "Text": "14 9(b) With very small\nsupply of energy an electron from the valence band can jump to the level\nEA and ionise the acceptor negatively (Alternately, we can also say that\nwith very small supply of energy the hole from level EA sinks down into\nthe valence band" + }, + { + "Chapter": "9", + "sentence_range": "3418-3421", + "Text": "9(b) With very small\nsupply of energy an electron from the valence band can jump to the level\nEA and ionise the acceptor negatively (Alternately, we can also say that\nwith very small supply of energy the hole from level EA sinks down into\nthe valence band Electrons rise up and holes fall down when they gain\nexternal energy" + }, + { + "Chapter": "9", + "sentence_range": "3419-3422", + "Text": "With very small\nsupply of energy an electron from the valence band can jump to the level\nEA and ionise the acceptor negatively (Alternately, we can also say that\nwith very small supply of energy the hole from level EA sinks down into\nthe valence band Electrons rise up and holes fall down when they gain\nexternal energy ) At room temperature, most of the acceptor atoms get\nionised leaving holes in the valence band" + }, + { + "Chapter": "9", + "sentence_range": "3420-3423", + "Text": "(Alternately, we can also say that\nwith very small supply of energy the hole from level EA sinks down into\nthe valence band Electrons rise up and holes fall down when they gain\nexternal energy ) At room temperature, most of the acceptor atoms get\nionised leaving holes in the valence band Thus at room temperature the\ndensity of holes in the valence band is predominantly due to impurity in\nthe extrinsic semiconductor" + }, + { + "Chapter": "9", + "sentence_range": "3421-3424", + "Text": "Electrons rise up and holes fall down when they gain\nexternal energy ) At room temperature, most of the acceptor atoms get\nionised leaving holes in the valence band Thus at room temperature the\ndensity of holes in the valence band is predominantly due to impurity in\nthe extrinsic semiconductor The electron and hole concentration in a\nsemiconductor in thermal equilibrium is given by\nnenh = ni\n2\n(14" + }, + { + "Chapter": "9", + "sentence_range": "3422-3425", + "Text": ") At room temperature, most of the acceptor atoms get\nionised leaving holes in the valence band Thus at room temperature the\ndensity of holes in the valence band is predominantly due to impurity in\nthe extrinsic semiconductor The electron and hole concentration in a\nsemiconductor in thermal equilibrium is given by\nnenh = ni\n2\n(14 5)\nThough the above description is grossly approximate and\nhypothetical, it helps in understanding the difference between metals,\ninsulators and semiconductors (extrinsic and intrinsic) in a simple\nmanner" + }, + { + "Chapter": "9", + "sentence_range": "3423-3426", + "Text": "Thus at room temperature the\ndensity of holes in the valence band is predominantly due to impurity in\nthe extrinsic semiconductor The electron and hole concentration in a\nsemiconductor in thermal equilibrium is given by\nnenh = ni\n2\n(14 5)\nThough the above description is grossly approximate and\nhypothetical, it helps in understanding the difference between metals,\ninsulators and semiconductors (extrinsic and intrinsic) in a simple\nmanner The difference in the resistivity of C, Si and Ge depends upon\nthe energy gap between their conduction and valence bands" + }, + { + "Chapter": "9", + "sentence_range": "3424-3427", + "Text": "The electron and hole concentration in a\nsemiconductor in thermal equilibrium is given by\nnenh = ni\n2\n(14 5)\nThough the above description is grossly approximate and\nhypothetical, it helps in understanding the difference between metals,\ninsulators and semiconductors (extrinsic and intrinsic) in a simple\nmanner The difference in the resistivity of C, Si and Ge depends upon\nthe energy gap between their conduction and valence bands For C\n(diamond), Si and Ge, the energy gaps are 5" + }, + { + "Chapter": "9", + "sentence_range": "3425-3428", + "Text": "5)\nThough the above description is grossly approximate and\nhypothetical, it helps in understanding the difference between metals,\ninsulators and semiconductors (extrinsic and intrinsic) in a simple\nmanner The difference in the resistivity of C, Si and Ge depends upon\nthe energy gap between their conduction and valence bands For C\n(diamond), Si and Ge, the energy gaps are 5 4 eV, 1" + }, + { + "Chapter": "9", + "sentence_range": "3426-3429", + "Text": "The difference in the resistivity of C, Si and Ge depends upon\nthe energy gap between their conduction and valence bands For C\n(diamond), Si and Ge, the energy gaps are 5 4 eV, 1 1 eV and 0" + }, + { + "Chapter": "9", + "sentence_range": "3427-3430", + "Text": "For C\n(diamond), Si and Ge, the energy gaps are 5 4 eV, 1 1 eV and 0 7 eV,\nrespectively" + }, + { + "Chapter": "9", + "sentence_range": "3428-3431", + "Text": "4 eV, 1 1 eV and 0 7 eV,\nrespectively Sn also is a group IV element but it is a metal because the\nenergy gap in its case is 0 eV" + }, + { + "Chapter": "9", + "sentence_range": "3429-3432", + "Text": "1 eV and 0 7 eV,\nrespectively Sn also is a group IV element but it is a metal because the\nenergy gap in its case is 0 eV FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3430-3433", + "Text": "7 eV,\nrespectively Sn also is a group IV element but it is a metal because the\nenergy gap in its case is 0 eV FIGURE 14 9 Energy bands of (a) n-type semiconductor at T > 0K, (b) p-type\nsemiconductor at T > 0K" + }, + { + "Chapter": "9", + "sentence_range": "3431-3434", + "Text": "Sn also is a group IV element but it is a metal because the\nenergy gap in its case is 0 eV FIGURE 14 9 Energy bands of (a) n-type semiconductor at T > 0K, (b) p-type\nsemiconductor at T > 0K Example 14" + }, + { + "Chapter": "9", + "sentence_range": "3432-3435", + "Text": "FIGURE 14 9 Energy bands of (a) n-type semiconductor at T > 0K, (b) p-type\nsemiconductor at T > 0K Example 14 2 Suppose a pure Si crystal has 5 \u00d7 1028 atoms m\u20133" + }, + { + "Chapter": "9", + "sentence_range": "3433-3436", + "Text": "9 Energy bands of (a) n-type semiconductor at T > 0K, (b) p-type\nsemiconductor at T > 0K Example 14 2 Suppose a pure Si crystal has 5 \u00d7 1028 atoms m\u20133 It is\ndoped by 1 ppm concentration of pentavalent As" + }, + { + "Chapter": "9", + "sentence_range": "3434-3437", + "Text": "Example 14 2 Suppose a pure Si crystal has 5 \u00d7 1028 atoms m\u20133 It is\ndoped by 1 ppm concentration of pentavalent As Calculate the\nnumber of electrons and holes" + }, + { + "Chapter": "9", + "sentence_range": "3435-3438", + "Text": "2 Suppose a pure Si crystal has 5 \u00d7 1028 atoms m\u20133 It is\ndoped by 1 ppm concentration of pentavalent As Calculate the\nnumber of electrons and holes Given that ni =1" + }, + { + "Chapter": "9", + "sentence_range": "3436-3439", + "Text": "It is\ndoped by 1 ppm concentration of pentavalent As Calculate the\nnumber of electrons and holes Given that ni =1 5 \u00d7 1016 m\u20133" + }, + { + "Chapter": "9", + "sentence_range": "3437-3440", + "Text": "Calculate the\nnumber of electrons and holes Given that ni =1 5 \u00d7 1016 m\u20133 Solution Note that thermally generated electrons (ni ~1016 m\u20133) are\nnegligibly small as compared to those produced by doping" + }, + { + "Chapter": "9", + "sentence_range": "3438-3441", + "Text": "Given that ni =1 5 \u00d7 1016 m\u20133 Solution Note that thermally generated electrons (ni ~1016 m\u20133) are\nnegligibly small as compared to those produced by doping Therefore, ne \u00bb\u00bb\u00bb\u00bb\u00bb ND" + }, + { + "Chapter": "9", + "sentence_range": "3439-3442", + "Text": "5 \u00d7 1016 m\u20133 Solution Note that thermally generated electrons (ni ~1016 m\u20133) are\nnegligibly small as compared to those produced by doping Therefore, ne \u00bb\u00bb\u00bb\u00bb\u00bb ND Since nenh = ni\n2, The number of holes\nnh = (2" + }, + { + "Chapter": "9", + "sentence_range": "3440-3443", + "Text": "Solution Note that thermally generated electrons (ni ~1016 m\u20133) are\nnegligibly small as compared to those produced by doping Therefore, ne \u00bb\u00bb\u00bb\u00bb\u00bb ND Since nenh = ni\n2, The number of holes\nnh = (2 25 \u00d7 1032)/(5 \u00d71022)\n ~ 4" + }, + { + "Chapter": "9", + "sentence_range": "3441-3444", + "Text": "Therefore, ne \u00bb\u00bb\u00bb\u00bb\u00bb ND Since nenh = ni\n2, The number of holes\nnh = (2 25 \u00d7 1032)/(5 \u00d71022)\n ~ 4 5 \u00d7 109 m\u20133\nRationalised 2023-24\n333\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n14" + }, + { + "Chapter": "9", + "sentence_range": "3442-3445", + "Text": "Since nenh = ni\n2, The number of holes\nnh = (2 25 \u00d7 1032)/(5 \u00d71022)\n ~ 4 5 \u00d7 109 m\u20133\nRationalised 2023-24\n333\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n14 5 p-n JUNCTION\nA p-n junction is the basic building block of many semiconductor devices\nlike diodes, transistor, etc" + }, + { + "Chapter": "9", + "sentence_range": "3443-3446", + "Text": "25 \u00d7 1032)/(5 \u00d71022)\n ~ 4 5 \u00d7 109 m\u20133\nRationalised 2023-24\n333\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n14 5 p-n JUNCTION\nA p-n junction is the basic building block of many semiconductor devices\nlike diodes, transistor, etc A clear understanding of the junction behaviour\nis important to analyse the working of other semiconductor devices" + }, + { + "Chapter": "9", + "sentence_range": "3444-3447", + "Text": "5 \u00d7 109 m\u20133\nRationalised 2023-24\n333\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n14 5 p-n JUNCTION\nA p-n junction is the basic building block of many semiconductor devices\nlike diodes, transistor, etc A clear understanding of the junction behaviour\nis important to analyse the working of other semiconductor devices We will now try to understand how a junction is formed and how the\njunction behaves under the influence of external applied voltage (also\ncalled bias)" + }, + { + "Chapter": "9", + "sentence_range": "3445-3448", + "Text": "5 p-n JUNCTION\nA p-n junction is the basic building block of many semiconductor devices\nlike diodes, transistor, etc A clear understanding of the junction behaviour\nis important to analyse the working of other semiconductor devices We will now try to understand how a junction is formed and how the\njunction behaves under the influence of external applied voltage (also\ncalled bias) 14" + }, + { + "Chapter": "9", + "sentence_range": "3446-3449", + "Text": "A clear understanding of the junction behaviour\nis important to analyse the working of other semiconductor devices We will now try to understand how a junction is formed and how the\njunction behaves under the influence of external applied voltage (also\ncalled bias) 14 5" + }, + { + "Chapter": "9", + "sentence_range": "3447-3450", + "Text": "We will now try to understand how a junction is formed and how the\njunction behaves under the influence of external applied voltage (also\ncalled bias) 14 5 1 p-n junction formation\nConsider a thin p-type silicon (p-Si) semiconductor wafer" + }, + { + "Chapter": "9", + "sentence_range": "3448-3451", + "Text": "14 5 1 p-n junction formation\nConsider a thin p-type silicon (p-Si) semiconductor wafer By adding\nprecisely a small quantity of pentavelent impurity, part of the p-Si wafer\ncan be converted into n-Si" + }, + { + "Chapter": "9", + "sentence_range": "3449-3452", + "Text": "5 1 p-n junction formation\nConsider a thin p-type silicon (p-Si) semiconductor wafer By adding\nprecisely a small quantity of pentavelent impurity, part of the p-Si wafer\ncan be converted into n-Si There are several processes by which a\nsemiconductor can be formed" + }, + { + "Chapter": "9", + "sentence_range": "3450-3453", + "Text": "1 p-n junction formation\nConsider a thin p-type silicon (p-Si) semiconductor wafer By adding\nprecisely a small quantity of pentavelent impurity, part of the p-Si wafer\ncan be converted into n-Si There are several processes by which a\nsemiconductor can be formed The wafer now contains p-region and\nn-region and a metallurgical junction between p-, and n- region" + }, + { + "Chapter": "9", + "sentence_range": "3451-3454", + "Text": "By adding\nprecisely a small quantity of pentavelent impurity, part of the p-Si wafer\ncan be converted into n-Si There are several processes by which a\nsemiconductor can be formed The wafer now contains p-region and\nn-region and a metallurgical junction between p-, and n- region Two important processes occur during the formation of a p-n junction:\ndiffusion and drift" + }, + { + "Chapter": "9", + "sentence_range": "3452-3455", + "Text": "There are several processes by which a\nsemiconductor can be formed The wafer now contains p-region and\nn-region and a metallurgical junction between p-, and n- region Two important processes occur during the formation of a p-n junction:\ndiffusion and drift We know that in an n-type semiconductor, the\nconcentration of electrons (number of electrons per unit volume) is more\ncompared to the concentration of holes" + }, + { + "Chapter": "9", + "sentence_range": "3453-3456", + "Text": "The wafer now contains p-region and\nn-region and a metallurgical junction between p-, and n- region Two important processes occur during the formation of a p-n junction:\ndiffusion and drift We know that in an n-type semiconductor, the\nconcentration of electrons (number of electrons per unit volume) is more\ncompared to the concentration of holes Similarly, in a p-type\nsemiconductor, the concentration of holes is more than the concentration\nof electrons" + }, + { + "Chapter": "9", + "sentence_range": "3454-3457", + "Text": "Two important processes occur during the formation of a p-n junction:\ndiffusion and drift We know that in an n-type semiconductor, the\nconcentration of electrons (number of electrons per unit volume) is more\ncompared to the concentration of holes Similarly, in a p-type\nsemiconductor, the concentration of holes is more than the concentration\nof electrons During the formation of p-n junction, and due to the\nconcentration gradient across p-, and n- sides, holes diffuse from p-side\nto n-side (p \u00ae n) and electrons diffuse from n-side to p-side (n \u00ae p)" + }, + { + "Chapter": "9", + "sentence_range": "3455-3458", + "Text": "We know that in an n-type semiconductor, the\nconcentration of electrons (number of electrons per unit volume) is more\ncompared to the concentration of holes Similarly, in a p-type\nsemiconductor, the concentration of holes is more than the concentration\nof electrons During the formation of p-n junction, and due to the\nconcentration gradient across p-, and n- sides, holes diffuse from p-side\nto n-side (p \u00ae n) and electrons diffuse from n-side to p-side (n \u00ae p) This\nmotion of charge carries gives rise to diffusion current across the junction" + }, + { + "Chapter": "9", + "sentence_range": "3456-3459", + "Text": "Similarly, in a p-type\nsemiconductor, the concentration of holes is more than the concentration\nof electrons During the formation of p-n junction, and due to the\nconcentration gradient across p-, and n- sides, holes diffuse from p-side\nto n-side (p \u00ae n) and electrons diffuse from n-side to p-side (n \u00ae p) This\nmotion of charge carries gives rise to diffusion current across the junction When an electron diffuses from n \u00ae p, it leaves behind an ionised\ndonor on n-side" + }, + { + "Chapter": "9", + "sentence_range": "3457-3460", + "Text": "During the formation of p-n junction, and due to the\nconcentration gradient across p-, and n- sides, holes diffuse from p-side\nto n-side (p \u00ae n) and electrons diffuse from n-side to p-side (n \u00ae p) This\nmotion of charge carries gives rise to diffusion current across the junction When an electron diffuses from n \u00ae p, it leaves behind an ionised\ndonor on n-side This ionised donor (positive charge) is immobile as it is\nbonded to the surrounding atoms" + }, + { + "Chapter": "9", + "sentence_range": "3458-3461", + "Text": "This\nmotion of charge carries gives rise to diffusion current across the junction When an electron diffuses from n \u00ae p, it leaves behind an ionised\ndonor on n-side This ionised donor (positive charge) is immobile as it is\nbonded to the surrounding atoms As the electrons continue to diffuse\nfrom n \u00ae p, a layer of positive charge (or positive space-charge region) on\nn-side of the junction is developed" + }, + { + "Chapter": "9", + "sentence_range": "3459-3462", + "Text": "When an electron diffuses from n \u00ae p, it leaves behind an ionised\ndonor on n-side This ionised donor (positive charge) is immobile as it is\nbonded to the surrounding atoms As the electrons continue to diffuse\nfrom n \u00ae p, a layer of positive charge (or positive space-charge region) on\nn-side of the junction is developed Similarly, when a hole diffuses from p \u00ae n due to the concentration\ngradient, it leaves behind an ionised acceptor (negative charge) which is\nimmobile" + }, + { + "Chapter": "9", + "sentence_range": "3460-3463", + "Text": "This ionised donor (positive charge) is immobile as it is\nbonded to the surrounding atoms As the electrons continue to diffuse\nfrom n \u00ae p, a layer of positive charge (or positive space-charge region) on\nn-side of the junction is developed Similarly, when a hole diffuses from p \u00ae n due to the concentration\ngradient, it leaves behind an ionised acceptor (negative charge) which is\nimmobile As the holes continue to diffuse, a layer of negative charge (or\nnegative space-charge region) on the p-side of the junction is developed" + }, + { + "Chapter": "9", + "sentence_range": "3461-3464", + "Text": "As the electrons continue to diffuse\nfrom n \u00ae p, a layer of positive charge (or positive space-charge region) on\nn-side of the junction is developed Similarly, when a hole diffuses from p \u00ae n due to the concentration\ngradient, it leaves behind an ionised acceptor (negative charge) which is\nimmobile As the holes continue to diffuse, a layer of negative charge (or\nnegative space-charge region) on the p-side of the junction is developed This space-charge region on either side of the junction together is known\nas depletion region as the electrons and holes taking\npart in the initial movement across the junction depleted\nthe region of its free charges (Fig" + }, + { + "Chapter": "9", + "sentence_range": "3462-3465", + "Text": "Similarly, when a hole diffuses from p \u00ae n due to the concentration\ngradient, it leaves behind an ionised acceptor (negative charge) which is\nimmobile As the holes continue to diffuse, a layer of negative charge (or\nnegative space-charge region) on the p-side of the junction is developed This space-charge region on either side of the junction together is known\nas depletion region as the electrons and holes taking\npart in the initial movement across the junction depleted\nthe region of its free charges (Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3463-3466", + "Text": "As the holes continue to diffuse, a layer of negative charge (or\nnegative space-charge region) on the p-side of the junction is developed This space-charge region on either side of the junction together is known\nas depletion region as the electrons and holes taking\npart in the initial movement across the junction depleted\nthe region of its free charges (Fig 14 10)" + }, + { + "Chapter": "9", + "sentence_range": "3464-3467", + "Text": "This space-charge region on either side of the junction together is known\nas depletion region as the electrons and holes taking\npart in the initial movement across the junction depleted\nthe region of its free charges (Fig 14 10) The thickness\nof depletion region is of the order of one-tenth of a\nmicrometre" + }, + { + "Chapter": "9", + "sentence_range": "3465-3468", + "Text": "14 10) The thickness\nof depletion region is of the order of one-tenth of a\nmicrometre Due to the positive space-charge region on\nn-side of the junction and negative space charge region\non p-side of the junction, an electric field directed from\npositive charge towards negative charge develops" + }, + { + "Chapter": "9", + "sentence_range": "3466-3469", + "Text": "10) The thickness\nof depletion region is of the order of one-tenth of a\nmicrometre Due to the positive space-charge region on\nn-side of the junction and negative space charge region\non p-side of the junction, an electric field directed from\npositive charge towards negative charge develops Due\nto this field, an electron on p-side of the junction moves\nto n-side and a hole on n-side of the junction moves to p-\nside" + }, + { + "Chapter": "9", + "sentence_range": "3467-3470", + "Text": "The thickness\nof depletion region is of the order of one-tenth of a\nmicrometre Due to the positive space-charge region on\nn-side of the junction and negative space charge region\non p-side of the junction, an electric field directed from\npositive charge towards negative charge develops Due\nto this field, an electron on p-side of the junction moves\nto n-side and a hole on n-side of the junction moves to p-\nside The motion of charge carriers due to the electric field\nis called drift" + }, + { + "Chapter": "9", + "sentence_range": "3468-3471", + "Text": "Due to the positive space-charge region on\nn-side of the junction and negative space charge region\non p-side of the junction, an electric field directed from\npositive charge towards negative charge develops Due\nto this field, an electron on p-side of the junction moves\nto n-side and a hole on n-side of the junction moves to p-\nside The motion of charge carriers due to the electric field\nis called drift Thus a drift current, which is opposite in\ndirection to the diffusion current (Fig" + }, + { + "Chapter": "9", + "sentence_range": "3469-3472", + "Text": "Due\nto this field, an electron on p-side of the junction moves\nto n-side and a hole on n-side of the junction moves to p-\nside The motion of charge carriers due to the electric field\nis called drift Thus a drift current, which is opposite in\ndirection to the diffusion current (Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3470-3473", + "Text": "The motion of charge carriers due to the electric field\nis called drift Thus a drift current, which is opposite in\ndirection to the diffusion current (Fig 14 10) starts" + }, + { + "Chapter": "9", + "sentence_range": "3471-3474", + "Text": "Thus a drift current, which is opposite in\ndirection to the diffusion current (Fig 14 10) starts FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3472-3475", + "Text": "14 10) starts FIGURE 14 10 p-n junction\nformation process" + }, + { + "Chapter": "9", + "sentence_range": "3473-3476", + "Text": "10) starts FIGURE 14 10 p-n junction\nformation process Formation and working of p-n junction diode\nhttp://hyperphysics" + }, + { + "Chapter": "9", + "sentence_range": "3474-3477", + "Text": "FIGURE 14 10 p-n junction\nformation process Formation and working of p-n junction diode\nhttp://hyperphysics phy-astr" + }, + { + "Chapter": "9", + "sentence_range": "3475-3478", + "Text": "10 p-n junction\nformation process Formation and working of p-n junction diode\nhttp://hyperphysics phy-astr gsu" + }, + { + "Chapter": "9", + "sentence_range": "3476-3479", + "Text": "Formation and working of p-n junction diode\nhttp://hyperphysics phy-astr gsu edu/hbase/solids/pnjun" + }, + { + "Chapter": "9", + "sentence_range": "3477-3480", + "Text": "phy-astr gsu edu/hbase/solids/pnjun html\nRationalised 2023-24\nPhysics\n334\n EXAMPLE 14" + }, + { + "Chapter": "9", + "sentence_range": "3478-3481", + "Text": "gsu edu/hbase/solids/pnjun html\nRationalised 2023-24\nPhysics\n334\n EXAMPLE 14 3\nInitially, diffusion current is large and drift current is small" + }, + { + "Chapter": "9", + "sentence_range": "3479-3482", + "Text": "edu/hbase/solids/pnjun html\nRationalised 2023-24\nPhysics\n334\n EXAMPLE 14 3\nInitially, diffusion current is large and drift current is small As the diffusion process continues, the space-charge regions\non either side of the junction extend, thus increasing the electric\nfield strength and hence drift current" + }, + { + "Chapter": "9", + "sentence_range": "3480-3483", + "Text": "html\nRationalised 2023-24\nPhysics\n334\n EXAMPLE 14 3\nInitially, diffusion current is large and drift current is small As the diffusion process continues, the space-charge regions\non either side of the junction extend, thus increasing the electric\nfield strength and hence drift current This process continues\nuntil the diffusion current equals the drift current" + }, + { + "Chapter": "9", + "sentence_range": "3481-3484", + "Text": "3\nInitially, diffusion current is large and drift current is small As the diffusion process continues, the space-charge regions\non either side of the junction extend, thus increasing the electric\nfield strength and hence drift current This process continues\nuntil the diffusion current equals the drift current Thus a p-n\njunction is formed" + }, + { + "Chapter": "9", + "sentence_range": "3482-3485", + "Text": "As the diffusion process continues, the space-charge regions\non either side of the junction extend, thus increasing the electric\nfield strength and hence drift current This process continues\nuntil the diffusion current equals the drift current Thus a p-n\njunction is formed In a p-n junction under equilibrium there\nis no net current" + }, + { + "Chapter": "9", + "sentence_range": "3483-3486", + "Text": "This process continues\nuntil the diffusion current equals the drift current Thus a p-n\njunction is formed In a p-n junction under equilibrium there\nis no net current The loss of electrons from the n-region and the gain of\nelectron by the p-region causes a difference of potential across\nthe junction of the two regions" + }, + { + "Chapter": "9", + "sentence_range": "3484-3487", + "Text": "Thus a p-n\njunction is formed In a p-n junction under equilibrium there\nis no net current The loss of electrons from the n-region and the gain of\nelectron by the p-region causes a difference of potential across\nthe junction of the two regions The polarity of this potential is\nsuch as to oppose further flow of carriers so that a condition of\nequilibrium exists" + }, + { + "Chapter": "9", + "sentence_range": "3485-3488", + "Text": "In a p-n junction under equilibrium there\nis no net current The loss of electrons from the n-region and the gain of\nelectron by the p-region causes a difference of potential across\nthe junction of the two regions The polarity of this potential is\nsuch as to oppose further flow of carriers so that a condition of\nequilibrium exists Figure 14" + }, + { + "Chapter": "9", + "sentence_range": "3486-3489", + "Text": "The loss of electrons from the n-region and the gain of\nelectron by the p-region causes a difference of potential across\nthe junction of the two regions The polarity of this potential is\nsuch as to oppose further flow of carriers so that a condition of\nequilibrium exists Figure 14 11 shows the p-n junction at\nequilibrium and the potential across the junction" + }, + { + "Chapter": "9", + "sentence_range": "3487-3490", + "Text": "The polarity of this potential is\nsuch as to oppose further flow of carriers so that a condition of\nequilibrium exists Figure 14 11 shows the p-n junction at\nequilibrium and the potential across the junction The\nn-material has lost electrons, and p material has acquired\nelectrons" + }, + { + "Chapter": "9", + "sentence_range": "3488-3491", + "Text": "Figure 14 11 shows the p-n junction at\nequilibrium and the potential across the junction The\nn-material has lost electrons, and p material has acquired\nelectrons The n material is thus positive relative to the p\nmaterial" + }, + { + "Chapter": "9", + "sentence_range": "3489-3492", + "Text": "11 shows the p-n junction at\nequilibrium and the potential across the junction The\nn-material has lost electrons, and p material has acquired\nelectrons The n material is thus positive relative to the p\nmaterial Since this potential tends to prevent the movement of\nelectron from the n region into the p region, it is often called a\nbarrier potential" + }, + { + "Chapter": "9", + "sentence_range": "3490-3493", + "Text": "The\nn-material has lost electrons, and p material has acquired\nelectrons The n material is thus positive relative to the p\nmaterial Since this potential tends to prevent the movement of\nelectron from the n region into the p region, it is often called a\nbarrier potential Example 14" + }, + { + "Chapter": "9", + "sentence_range": "3491-3494", + "Text": "The n material is thus positive relative to the p\nmaterial Since this potential tends to prevent the movement of\nelectron from the n region into the p region, it is often called a\nbarrier potential Example 14 3 Can we take one slab of p-type semiconductor and\nphysically join it to another n-type semiconductor to get p-n junction" + }, + { + "Chapter": "9", + "sentence_range": "3492-3495", + "Text": "Since this potential tends to prevent the movement of\nelectron from the n region into the p region, it is often called a\nbarrier potential Example 14 3 Can we take one slab of p-type semiconductor and\nphysically join it to another n-type semiconductor to get p-n junction Solution No" + }, + { + "Chapter": "9", + "sentence_range": "3493-3496", + "Text": "Example 14 3 Can we take one slab of p-type semiconductor and\nphysically join it to another n-type semiconductor to get p-n junction Solution No Any slab, howsoever flat, will have roughness much\nlarger than the inter-atomic crystal spacing (~2 to 3 \u00c5) and hence\ncontinuous contact at the atomic level will not be possible" + }, + { + "Chapter": "9", + "sentence_range": "3494-3497", + "Text": "3 Can we take one slab of p-type semiconductor and\nphysically join it to another n-type semiconductor to get p-n junction Solution No Any slab, howsoever flat, will have roughness much\nlarger than the inter-atomic crystal spacing (~2 to 3 \u00c5) and hence\ncontinuous contact at the atomic level will not be possible The junction\nwill behave as a discontinuity for the flowing charge carriers" + }, + { + "Chapter": "9", + "sentence_range": "3495-3498", + "Text": "Solution No Any slab, howsoever flat, will have roughness much\nlarger than the inter-atomic crystal spacing (~2 to 3 \u00c5) and hence\ncontinuous contact at the atomic level will not be possible The junction\nwill behave as a discontinuity for the flowing charge carriers 14" + }, + { + "Chapter": "9", + "sentence_range": "3496-3499", + "Text": "Any slab, howsoever flat, will have roughness much\nlarger than the inter-atomic crystal spacing (~2 to 3 \u00c5) and hence\ncontinuous contact at the atomic level will not be possible The junction\nwill behave as a discontinuity for the flowing charge carriers 14 6 SEMICONDUCTOR DIODE\nA semiconductor diode [Fig" + }, + { + "Chapter": "9", + "sentence_range": "3497-3500", + "Text": "The junction\nwill behave as a discontinuity for the flowing charge carriers 14 6 SEMICONDUCTOR DIODE\nA semiconductor diode [Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3498-3501", + "Text": "14 6 SEMICONDUCTOR DIODE\nA semiconductor diode [Fig 14 12(a)] is basically a p-n\njunction with metallic contacts provided at the ends for\nthe application of an external voltage" + }, + { + "Chapter": "9", + "sentence_range": "3499-3502", + "Text": "6 SEMICONDUCTOR DIODE\nA semiconductor diode [Fig 14 12(a)] is basically a p-n\njunction with metallic contacts provided at the ends for\nthe application of an external voltage It is a two terminal\ndevice" + }, + { + "Chapter": "9", + "sentence_range": "3500-3503", + "Text": "14 12(a)] is basically a p-n\njunction with metallic contacts provided at the ends for\nthe application of an external voltage It is a two terminal\ndevice A p-n junction diode is symbolically represented\nas shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3501-3504", + "Text": "12(a)] is basically a p-n\njunction with metallic contacts provided at the ends for\nthe application of an external voltage It is a two terminal\ndevice A p-n junction diode is symbolically represented\nas shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3502-3505", + "Text": "It is a two terminal\ndevice A p-n junction diode is symbolically represented\nas shown in Fig 14 12(b)" + }, + { + "Chapter": "9", + "sentence_range": "3503-3506", + "Text": "A p-n junction diode is symbolically represented\nas shown in Fig 14 12(b) The direction of arrow indicates the conventional\ndirection of current (when the diode is under forward\nbias)" + }, + { + "Chapter": "9", + "sentence_range": "3504-3507", + "Text": "14 12(b) The direction of arrow indicates the conventional\ndirection of current (when the diode is under forward\nbias) The equilibrium barrier potential can be altered\nby applying an external voltage V across the diode" + }, + { + "Chapter": "9", + "sentence_range": "3505-3508", + "Text": "12(b) The direction of arrow indicates the conventional\ndirection of current (when the diode is under forward\nbias) The equilibrium barrier potential can be altered\nby applying an external voltage V across the diode The\nsituation of p-n junction diode under equilibrium\n(without bias) is shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3506-3509", + "Text": "The direction of arrow indicates the conventional\ndirection of current (when the diode is under forward\nbias) The equilibrium barrier potential can be altered\nby applying an external voltage V across the diode The\nsituation of p-n junction diode under equilibrium\n(without bias) is shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3507-3510", + "Text": "The equilibrium barrier potential can be altered\nby applying an external voltage V across the diode The\nsituation of p-n junction diode under equilibrium\n(without bias) is shown in Fig 14 11(a) and (b)" + }, + { + "Chapter": "9", + "sentence_range": "3508-3511", + "Text": "The\nsituation of p-n junction diode under equilibrium\n(without bias) is shown in Fig 14 11(a) and (b) 14" + }, + { + "Chapter": "9", + "sentence_range": "3509-3512", + "Text": "14 11(a) and (b) 14 6" + }, + { + "Chapter": "9", + "sentence_range": "3510-3513", + "Text": "11(a) and (b) 14 6 1 p-n junction diode under forward bias\nWhen an external voltage V is applied across a semiconductor diode such\nthat p-side is connected to the positive terminal of the battery and n-side\nto the negative terminal [Fig" + }, + { + "Chapter": "9", + "sentence_range": "3511-3514", + "Text": "14 6 1 p-n junction diode under forward bias\nWhen an external voltage V is applied across a semiconductor diode such\nthat p-side is connected to the positive terminal of the battery and n-side\nto the negative terminal [Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3512-3515", + "Text": "6 1 p-n junction diode under forward bias\nWhen an external voltage V is applied across a semiconductor diode such\nthat p-side is connected to the positive terminal of the battery and n-side\nto the negative terminal [Fig 14 13(a)], it is said to be forward biased" + }, + { + "Chapter": "9", + "sentence_range": "3513-3516", + "Text": "1 p-n junction diode under forward bias\nWhen an external voltage V is applied across a semiconductor diode such\nthat p-side is connected to the positive terminal of the battery and n-side\nto the negative terminal [Fig 14 13(a)], it is said to be forward biased The applied voltage mostly drops across the depletion region and the\nvoltage drop across the p-side and n-side of the junction is negligible" + }, + { + "Chapter": "9", + "sentence_range": "3514-3517", + "Text": "14 13(a)], it is said to be forward biased The applied voltage mostly drops across the depletion region and the\nvoltage drop across the p-side and n-side of the junction is negligible (This is because the resistance of the depletion region \u2013 a region where\nthere are no charges \u2013 is very high compared to the resistance of n-side\nand p-side" + }, + { + "Chapter": "9", + "sentence_range": "3515-3518", + "Text": "13(a)], it is said to be forward biased The applied voltage mostly drops across the depletion region and the\nvoltage drop across the p-side and n-side of the junction is negligible (This is because the resistance of the depletion region \u2013 a region where\nthere are no charges \u2013 is very high compared to the resistance of n-side\nand p-side ) The direction of the applied voltage (V ) is opposite to the\nFIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3516-3519", + "Text": "The applied voltage mostly drops across the depletion region and the\nvoltage drop across the p-side and n-side of the junction is negligible (This is because the resistance of the depletion region \u2013 a region where\nthere are no charges \u2013 is very high compared to the resistance of n-side\nand p-side ) The direction of the applied voltage (V ) is opposite to the\nFIGURE 14 11 (a) Diode under\nequilibrium (V = 0), (b) Barrier\npotential under no bias" + }, + { + "Chapter": "9", + "sentence_range": "3517-3520", + "Text": "(This is because the resistance of the depletion region \u2013 a region where\nthere are no charges \u2013 is very high compared to the resistance of n-side\nand p-side ) The direction of the applied voltage (V ) is opposite to the\nFIGURE 14 11 (a) Diode under\nequilibrium (V = 0), (b) Barrier\npotential under no bias FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3518-3521", + "Text": ") The direction of the applied voltage (V ) is opposite to the\nFIGURE 14 11 (a) Diode under\nequilibrium (V = 0), (b) Barrier\npotential under no bias FIGURE 14 12 (a) Semiconductor diode,\n(b) Symbol for p-n junction diode" + }, + { + "Chapter": "9", + "sentence_range": "3519-3522", + "Text": "11 (a) Diode under\nequilibrium (V = 0), (b) Barrier\npotential under no bias FIGURE 14 12 (a) Semiconductor diode,\n(b) Symbol for p-n junction diode n\np\nRationalised 2023-24\n335\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nbuilt-in potential V0" + }, + { + "Chapter": "9", + "sentence_range": "3520-3523", + "Text": "FIGURE 14 12 (a) Semiconductor diode,\n(b) Symbol for p-n junction diode n\np\nRationalised 2023-24\n335\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nbuilt-in potential V0 As a result, the depletion layer width\ndecreases and the barrier height is reduced [Fig" + }, + { + "Chapter": "9", + "sentence_range": "3521-3524", + "Text": "12 (a) Semiconductor diode,\n(b) Symbol for p-n junction diode n\np\nRationalised 2023-24\n335\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nbuilt-in potential V0 As a result, the depletion layer width\ndecreases and the barrier height is reduced [Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3522-3525", + "Text": "n\np\nRationalised 2023-24\n335\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nbuilt-in potential V0 As a result, the depletion layer width\ndecreases and the barrier height is reduced [Fig 14 13(b)]" + }, + { + "Chapter": "9", + "sentence_range": "3523-3526", + "Text": "As a result, the depletion layer width\ndecreases and the barrier height is reduced [Fig 14 13(b)] The\neffective barrier height under forward bias is (V0 \u2013 V )" + }, + { + "Chapter": "9", + "sentence_range": "3524-3527", + "Text": "14 13(b)] The\neffective barrier height under forward bias is (V0 \u2013 V ) If the applied voltage is small, the barrier potential will be\nreduced only slightly below the equilibrium value, and only a\nsmall number of carriers in the material\u2014those that happen to\nbe in the uppermost energy levels\u2014will possess enough energy\nto cross the junction" + }, + { + "Chapter": "9", + "sentence_range": "3525-3528", + "Text": "13(b)] The\neffective barrier height under forward bias is (V0 \u2013 V ) If the applied voltage is small, the barrier potential will be\nreduced only slightly below the equilibrium value, and only a\nsmall number of carriers in the material\u2014those that happen to\nbe in the uppermost energy levels\u2014will possess enough energy\nto cross the junction So the current will be small" + }, + { + "Chapter": "9", + "sentence_range": "3526-3529", + "Text": "The\neffective barrier height under forward bias is (V0 \u2013 V ) If the applied voltage is small, the barrier potential will be\nreduced only slightly below the equilibrium value, and only a\nsmall number of carriers in the material\u2014those that happen to\nbe in the uppermost energy levels\u2014will possess enough energy\nto cross the junction So the current will be small If we increase\nthe applied voltage significantly, the barrier height will be reduced\nand more number of carriers will have the required energy" + }, + { + "Chapter": "9", + "sentence_range": "3527-3530", + "Text": "If the applied voltage is small, the barrier potential will be\nreduced only slightly below the equilibrium value, and only a\nsmall number of carriers in the material\u2014those that happen to\nbe in the uppermost energy levels\u2014will possess enough energy\nto cross the junction So the current will be small If we increase\nthe applied voltage significantly, the barrier height will be reduced\nand more number of carriers will have the required energy Thus\nthe current increases" + }, + { + "Chapter": "9", + "sentence_range": "3528-3531", + "Text": "So the current will be small If we increase\nthe applied voltage significantly, the barrier height will be reduced\nand more number of carriers will have the required energy Thus\nthe current increases Due to the applied voltage, electrons from n-side cross the\ndepletion region and reach p-side (where they are minority\ncarries)" + }, + { + "Chapter": "9", + "sentence_range": "3529-3532", + "Text": "If we increase\nthe applied voltage significantly, the barrier height will be reduced\nand more number of carriers will have the required energy Thus\nthe current increases Due to the applied voltage, electrons from n-side cross the\ndepletion region and reach p-side (where they are minority\ncarries) Similarly, holes from p-side cross the junction and reach\nthe n-side (where they are minority carries)" + }, + { + "Chapter": "9", + "sentence_range": "3530-3533", + "Text": "Thus\nthe current increases Due to the applied voltage, electrons from n-side cross the\ndepletion region and reach p-side (where they are minority\ncarries) Similarly, holes from p-side cross the junction and reach\nthe n-side (where they are minority carries) This process under\nforward bias is known as minority carrier injection" + }, + { + "Chapter": "9", + "sentence_range": "3531-3534", + "Text": "Due to the applied voltage, electrons from n-side cross the\ndepletion region and reach p-side (where they are minority\ncarries) Similarly, holes from p-side cross the junction and reach\nthe n-side (where they are minority carries) This process under\nforward bias is known as minority carrier injection At the\njunction boundary, on each side, the minority carrier\nconcentration increases significantly compared to the locations\nfar from the junction" + }, + { + "Chapter": "9", + "sentence_range": "3532-3535", + "Text": "Similarly, holes from p-side cross the junction and reach\nthe n-side (where they are minority carries) This process under\nforward bias is known as minority carrier injection At the\njunction boundary, on each side, the minority carrier\nconcentration increases significantly compared to the locations\nfar from the junction Due to this concentration gradient, the injected electrons on\np-side diffuse from the junction edge of p-side to the other end\nof p-side" + }, + { + "Chapter": "9", + "sentence_range": "3533-3536", + "Text": "This process under\nforward bias is known as minority carrier injection At the\njunction boundary, on each side, the minority carrier\nconcentration increases significantly compared to the locations\nfar from the junction Due to this concentration gradient, the injected electrons on\np-side diffuse from the junction edge of p-side to the other end\nof p-side Likewise, the injected holes on n-side diffuse from the\njunction edge of n-side to the other end of n-side\n(Fig" + }, + { + "Chapter": "9", + "sentence_range": "3534-3537", + "Text": "At the\njunction boundary, on each side, the minority carrier\nconcentration increases significantly compared to the locations\nfar from the junction Due to this concentration gradient, the injected electrons on\np-side diffuse from the junction edge of p-side to the other end\nof p-side Likewise, the injected holes on n-side diffuse from the\njunction edge of n-side to the other end of n-side\n(Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3535-3538", + "Text": "Due to this concentration gradient, the injected electrons on\np-side diffuse from the junction edge of p-side to the other end\nof p-side Likewise, the injected holes on n-side diffuse from the\njunction edge of n-side to the other end of n-side\n(Fig 14 14)" + }, + { + "Chapter": "9", + "sentence_range": "3536-3539", + "Text": "Likewise, the injected holes on n-side diffuse from the\njunction edge of n-side to the other end of n-side\n(Fig 14 14) This motion of charged carriers on either side\ngives rise to current" + }, + { + "Chapter": "9", + "sentence_range": "3537-3540", + "Text": "14 14) This motion of charged carriers on either side\ngives rise to current The total diode forward current is sum\nof hole diffusion current and conventional current due to\nelectron diffusion" + }, + { + "Chapter": "9", + "sentence_range": "3538-3541", + "Text": "14) This motion of charged carriers on either side\ngives rise to current The total diode forward current is sum\nof hole diffusion current and conventional current due to\nelectron diffusion The magnitude of this current is usually\nin mA" + }, + { + "Chapter": "9", + "sentence_range": "3539-3542", + "Text": "This motion of charged carriers on either side\ngives rise to current The total diode forward current is sum\nof hole diffusion current and conventional current due to\nelectron diffusion The magnitude of this current is usually\nin mA 14" + }, + { + "Chapter": "9", + "sentence_range": "3540-3543", + "Text": "The total diode forward current is sum\nof hole diffusion current and conventional current due to\nelectron diffusion The magnitude of this current is usually\nin mA 14 6" + }, + { + "Chapter": "9", + "sentence_range": "3541-3544", + "Text": "The magnitude of this current is usually\nin mA 14 6 2 p-n junction diode under reverse bias\nWhen an external voltage (V ) is applied across the diode such\nthat n-side is positive and p-side is negative, it is said to be\nreverse biased [Fig" + }, + { + "Chapter": "9", + "sentence_range": "3542-3545", + "Text": "14 6 2 p-n junction diode under reverse bias\nWhen an external voltage (V ) is applied across the diode such\nthat n-side is positive and p-side is negative, it is said to be\nreverse biased [Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3543-3546", + "Text": "6 2 p-n junction diode under reverse bias\nWhen an external voltage (V ) is applied across the diode such\nthat n-side is positive and p-side is negative, it is said to be\nreverse biased [Fig 14 15(a)]" + }, + { + "Chapter": "9", + "sentence_range": "3544-3547", + "Text": "2 p-n junction diode under reverse bias\nWhen an external voltage (V ) is applied across the diode such\nthat n-side is positive and p-side is negative, it is said to be\nreverse biased [Fig 14 15(a)] The applied voltage mostly\ndrops across the depletion region" + }, + { + "Chapter": "9", + "sentence_range": "3545-3548", + "Text": "14 15(a)] The applied voltage mostly\ndrops across the depletion region The direction of applied voltage is same\nas the direction of barrier potential" + }, + { + "Chapter": "9", + "sentence_range": "3546-3549", + "Text": "15(a)] The applied voltage mostly\ndrops across the depletion region The direction of applied voltage is same\nas the direction of barrier potential As a result, the barrier height increases\nand the depletion region widens due to the change in the electric field" + }, + { + "Chapter": "9", + "sentence_range": "3547-3550", + "Text": "The applied voltage mostly\ndrops across the depletion region The direction of applied voltage is same\nas the direction of barrier potential As a result, the barrier height increases\nand the depletion region widens due to the change in the electric field The effective barrier height under reverse bias is (V0 + V ), [Fig" + }, + { + "Chapter": "9", + "sentence_range": "3548-3551", + "Text": "The direction of applied voltage is same\nas the direction of barrier potential As a result, the barrier height increases\nand the depletion region widens due to the change in the electric field The effective barrier height under reverse bias is (V0 + V ), [Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3549-3552", + "Text": "As a result, the barrier height increases\nand the depletion region widens due to the change in the electric field The effective barrier height under reverse bias is (V0 + V ), [Fig 14 15(b)]" + }, + { + "Chapter": "9", + "sentence_range": "3550-3553", + "Text": "The effective barrier height under reverse bias is (V0 + V ), [Fig 14 15(b)] This suppresses the flow of electrons from n \u00ae p and holes from p \u00ae n" + }, + { + "Chapter": "9", + "sentence_range": "3551-3554", + "Text": "14 15(b)] This suppresses the flow of electrons from n \u00ae p and holes from p \u00ae n Thus, diffusion current, decreases enormously compared to the diode\nunder forward bias" + }, + { + "Chapter": "9", + "sentence_range": "3552-3555", + "Text": "15(b)] This suppresses the flow of electrons from n \u00ae p and holes from p \u00ae n Thus, diffusion current, decreases enormously compared to the diode\nunder forward bias The electric field direction of the junction is such that if electrons on\np-side or holes on n-side in their random motion come close to the\njunction, they will be swept to its majority zone" + }, + { + "Chapter": "9", + "sentence_range": "3553-3556", + "Text": "This suppresses the flow of electrons from n \u00ae p and holes from p \u00ae n Thus, diffusion current, decreases enormously compared to the diode\nunder forward bias The electric field direction of the junction is such that if electrons on\np-side or holes on n-side in their random motion come close to the\njunction, they will be swept to its majority zone This drift of carriers\ngives rise to current" + }, + { + "Chapter": "9", + "sentence_range": "3554-3557", + "Text": "Thus, diffusion current, decreases enormously compared to the diode\nunder forward bias The electric field direction of the junction is such that if electrons on\np-side or holes on n-side in their random motion come close to the\njunction, they will be swept to its majority zone This drift of carriers\ngives rise to current The drift current is of the order of a few mA" + }, + { + "Chapter": "9", + "sentence_range": "3555-3558", + "Text": "The electric field direction of the junction is such that if electrons on\np-side or holes on n-side in their random motion come close to the\njunction, they will be swept to its majority zone This drift of carriers\ngives rise to current The drift current is of the order of a few mA This is\nquite low because it is due to the motion of carriers from their minority\nside to their majority side across the junction" + }, + { + "Chapter": "9", + "sentence_range": "3556-3559", + "Text": "This drift of carriers\ngives rise to current The drift current is of the order of a few mA This is\nquite low because it is due to the motion of carriers from their minority\nside to their majority side across the junction The drift current is also\nthere under forward bias but it is negligible (mA) when compared with\ncurrent due to injected carriers which is usually in mA" + }, + { + "Chapter": "9", + "sentence_range": "3557-3560", + "Text": "The drift current is of the order of a few mA This is\nquite low because it is due to the motion of carriers from their minority\nside to their majority side across the junction The drift current is also\nthere under forward bias but it is negligible (mA) when compared with\ncurrent due to injected carriers which is usually in mA The diode reverse current is not very much dependent on the applied\nvoltage" + }, + { + "Chapter": "9", + "sentence_range": "3558-3561", + "Text": "This is\nquite low because it is due to the motion of carriers from their minority\nside to their majority side across the junction The drift current is also\nthere under forward bias but it is negligible (mA) when compared with\ncurrent due to injected carriers which is usually in mA The diode reverse current is not very much dependent on the applied\nvoltage Even a small voltage is sufficient to sweep the minority carriers\nfrom one side of the junction to the other side of the junction" + }, + { + "Chapter": "9", + "sentence_range": "3559-3562", + "Text": "The drift current is also\nthere under forward bias but it is negligible (mA) when compared with\ncurrent due to injected carriers which is usually in mA The diode reverse current is not very much dependent on the applied\nvoltage Even a small voltage is sufficient to sweep the minority carriers\nfrom one side of the junction to the other side of the junction The current\nFIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3560-3563", + "Text": "The diode reverse current is not very much dependent on the applied\nvoltage Even a small voltage is sufficient to sweep the minority carriers\nfrom one side of the junction to the other side of the junction The current\nFIGURE 14 13 (a) p-n\njunction diode under forward\nbias, (b) Barrier potential\n(1) without battery, (2) Low\nbattery voltage, and (3) High\nvoltage battery" + }, + { + "Chapter": "9", + "sentence_range": "3561-3564", + "Text": "Even a small voltage is sufficient to sweep the minority carriers\nfrom one side of the junction to the other side of the junction The current\nFIGURE 14 13 (a) p-n\njunction diode under forward\nbias, (b) Barrier potential\n(1) without battery, (2) Low\nbattery voltage, and (3) High\nvoltage battery FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3562-3565", + "Text": "The current\nFIGURE 14 13 (a) p-n\njunction diode under forward\nbias, (b) Barrier potential\n(1) without battery, (2) Low\nbattery voltage, and (3) High\nvoltage battery FIGURE 14 14 Forward bias\nminority carrier injection" + }, + { + "Chapter": "9", + "sentence_range": "3563-3566", + "Text": "13 (a) p-n\njunction diode under forward\nbias, (b) Barrier potential\n(1) without battery, (2) Low\nbattery voltage, and (3) High\nvoltage battery FIGURE 14 14 Forward bias\nminority carrier injection Rationalised 2023-24\nPhysics\n336\nis not limited by the magnitude of the applied voltage but is\nlimited due to the concentration of the minority carrier on either\nside of the junction" + }, + { + "Chapter": "9", + "sentence_range": "3564-3567", + "Text": "FIGURE 14 14 Forward bias\nminority carrier injection Rationalised 2023-24\nPhysics\n336\nis not limited by the magnitude of the applied voltage but is\nlimited due to the concentration of the minority carrier on either\nside of the junction The current under reverse bias is essentially voltage\nindependent upto a critical reverse bias voltage, known as\nbreakdown voltage (Vbr )" + }, + { + "Chapter": "9", + "sentence_range": "3565-3568", + "Text": "14 Forward bias\nminority carrier injection Rationalised 2023-24\nPhysics\n336\nis not limited by the magnitude of the applied voltage but is\nlimited due to the concentration of the minority carrier on either\nside of the junction The current under reverse bias is essentially voltage\nindependent upto a critical reverse bias voltage, known as\nbreakdown voltage (Vbr ) When V = Vbr, the diode reverse current\nincreases sharply" + }, + { + "Chapter": "9", + "sentence_range": "3566-3569", + "Text": "Rationalised 2023-24\nPhysics\n336\nis not limited by the magnitude of the applied voltage but is\nlimited due to the concentration of the minority carrier on either\nside of the junction The current under reverse bias is essentially voltage\nindependent upto a critical reverse bias voltage, known as\nbreakdown voltage (Vbr ) When V = Vbr, the diode reverse current\nincreases sharply Even a slight increase in the bias voltage causes\nlarge change in the current" + }, + { + "Chapter": "9", + "sentence_range": "3567-3570", + "Text": "The current under reverse bias is essentially voltage\nindependent upto a critical reverse bias voltage, known as\nbreakdown voltage (Vbr ) When V = Vbr, the diode reverse current\nincreases sharply Even a slight increase in the bias voltage causes\nlarge change in the current If the reverse current is not limited by\nan external circuit below the rated value (specified by the\nmanufacturer) the p-n junction will get destroyed" + }, + { + "Chapter": "9", + "sentence_range": "3568-3571", + "Text": "When V = Vbr, the diode reverse current\nincreases sharply Even a slight increase in the bias voltage causes\nlarge change in the current If the reverse current is not limited by\nan external circuit below the rated value (specified by the\nmanufacturer) the p-n junction will get destroyed Once it exceeds\nthe rated value, the diode gets destroyed due to overheating" + }, + { + "Chapter": "9", + "sentence_range": "3569-3572", + "Text": "Even a slight increase in the bias voltage causes\nlarge change in the current If the reverse current is not limited by\nan external circuit below the rated value (specified by the\nmanufacturer) the p-n junction will get destroyed Once it exceeds\nthe rated value, the diode gets destroyed due to overheating This\ncan happen even for the diode under forward bias, if the forward\ncurrent exceeds the rated value" + }, + { + "Chapter": "9", + "sentence_range": "3570-3573", + "Text": "If the reverse current is not limited by\nan external circuit below the rated value (specified by the\nmanufacturer) the p-n junction will get destroyed Once it exceeds\nthe rated value, the diode gets destroyed due to overheating This\ncan happen even for the diode under forward bias, if the forward\ncurrent exceeds the rated value The circuit arrangement for studying the V-I characteristics\nof a diode, (i" + }, + { + "Chapter": "9", + "sentence_range": "3571-3574", + "Text": "Once it exceeds\nthe rated value, the diode gets destroyed due to overheating This\ncan happen even for the diode under forward bias, if the forward\ncurrent exceeds the rated value The circuit arrangement for studying the V-I characteristics\nof a diode, (i e" + }, + { + "Chapter": "9", + "sentence_range": "3572-3575", + "Text": "This\ncan happen even for the diode under forward bias, if the forward\ncurrent exceeds the rated value The circuit arrangement for studying the V-I characteristics\nof a diode, (i e , the variation of current as a function of applied\nvoltage) are shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3573-3576", + "Text": "The circuit arrangement for studying the V-I characteristics\nof a diode, (i e , the variation of current as a function of applied\nvoltage) are shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3574-3577", + "Text": "e , the variation of current as a function of applied\nvoltage) are shown in Fig 14 16(a) and (b)" + }, + { + "Chapter": "9", + "sentence_range": "3575-3578", + "Text": ", the variation of current as a function of applied\nvoltage) are shown in Fig 14 16(a) and (b) The battery is connected\nto the diode through a potentiometer (or reheostat) so that the\napplied voltage to the diode can be changed" + }, + { + "Chapter": "9", + "sentence_range": "3576-3579", + "Text": "14 16(a) and (b) The battery is connected\nto the diode through a potentiometer (or reheostat) so that the\napplied voltage to the diode can be changed For different values\nof voltages, the value of the current is noted" + }, + { + "Chapter": "9", + "sentence_range": "3577-3580", + "Text": "16(a) and (b) The battery is connected\nto the diode through a potentiometer (or reheostat) so that the\napplied voltage to the diode can be changed For different values\nof voltages, the value of the current is noted A graph between V\nand I is obtained as in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3578-3581", + "Text": "The battery is connected\nto the diode through a potentiometer (or reheostat) so that the\napplied voltage to the diode can be changed For different values\nof voltages, the value of the current is noted A graph between V\nand I is obtained as in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3579-3582", + "Text": "For different values\nof voltages, the value of the current is noted A graph between V\nand I is obtained as in Fig 14 16(c)" + }, + { + "Chapter": "9", + "sentence_range": "3580-3583", + "Text": "A graph between V\nand I is obtained as in Fig 14 16(c) Note that in forward bias\nmeasurement, we use a milliammeter since the expected current is large\n(as explained in the earlier section) while a micrometer is used in reverse\nbias to measure the current" + }, + { + "Chapter": "9", + "sentence_range": "3581-3584", + "Text": "14 16(c) Note that in forward bias\nmeasurement, we use a milliammeter since the expected current is large\n(as explained in the earlier section) while a micrometer is used in reverse\nbias to measure the current You can see in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3582-3585", + "Text": "16(c) Note that in forward bias\nmeasurement, we use a milliammeter since the expected current is large\n(as explained in the earlier section) while a micrometer is used in reverse\nbias to measure the current You can see in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3583-3586", + "Text": "Note that in forward bias\nmeasurement, we use a milliammeter since the expected current is large\n(as explained in the earlier section) while a micrometer is used in reverse\nbias to measure the current You can see in Fig 14 16(c) that in forward\nFIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3584-3587", + "Text": "You can see in Fig 14 16(c) that in forward\nFIGURE 14 15 (a) Diode\nunder reverse bias,\n(b) Barrier potential under\nreverse bias" + }, + { + "Chapter": "9", + "sentence_range": "3585-3588", + "Text": "14 16(c) that in forward\nFIGURE 14 15 (a) Diode\nunder reverse bias,\n(b) Barrier potential under\nreverse bias FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3586-3589", + "Text": "16(c) that in forward\nFIGURE 14 15 (a) Diode\nunder reverse bias,\n(b) Barrier potential under\nreverse bias FIGURE 14 16 Experimental circuit arrangement for studying V-I characteristics of\na p-n junction diode (a) in forward bias, (b) in reverse bias" + }, + { + "Chapter": "9", + "sentence_range": "3587-3590", + "Text": "15 (a) Diode\nunder reverse bias,\n(b) Barrier potential under\nreverse bias FIGURE 14 16 Experimental circuit arrangement for studying V-I characteristics of\na p-n junction diode (a) in forward bias, (b) in reverse bias (c) Typical V-I\ncharacteristics of a silicon diode" + }, + { + "Chapter": "9", + "sentence_range": "3588-3591", + "Text": "FIGURE 14 16 Experimental circuit arrangement for studying V-I characteristics of\na p-n junction diode (a) in forward bias, (b) in reverse bias (c) Typical V-I\ncharacteristics of a silicon diode Rationalised 2023-24\n337\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n EXAMPLE 14" + }, + { + "Chapter": "9", + "sentence_range": "3589-3592", + "Text": "16 Experimental circuit arrangement for studying V-I characteristics of\na p-n junction diode (a) in forward bias, (b) in reverse bias (c) Typical V-I\ncharacteristics of a silicon diode Rationalised 2023-24\n337\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n EXAMPLE 14 4\nbias, the current first increases very slowly, almost negligibly, till the\nvoltage across the diode crosses a certain value" + }, + { + "Chapter": "9", + "sentence_range": "3590-3593", + "Text": "(c) Typical V-I\ncharacteristics of a silicon diode Rationalised 2023-24\n337\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n EXAMPLE 14 4\nbias, the current first increases very slowly, almost negligibly, till the\nvoltage across the diode crosses a certain value After the characteristic\nvoltage, the diode current increases significantly (exponentially), even for\na very small increase in the diode bias voltage" + }, + { + "Chapter": "9", + "sentence_range": "3591-3594", + "Text": "Rationalised 2023-24\n337\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\n EXAMPLE 14 4\nbias, the current first increases very slowly, almost negligibly, till the\nvoltage across the diode crosses a certain value After the characteristic\nvoltage, the diode current increases significantly (exponentially), even for\na very small increase in the diode bias voltage This voltage is called the\nthreshold voltage or cut-in voltage (~0" + }, + { + "Chapter": "9", + "sentence_range": "3592-3595", + "Text": "4\nbias, the current first increases very slowly, almost negligibly, till the\nvoltage across the diode crosses a certain value After the characteristic\nvoltage, the diode current increases significantly (exponentially), even for\na very small increase in the diode bias voltage This voltage is called the\nthreshold voltage or cut-in voltage (~0 2V for germanium diode and\n~0" + }, + { + "Chapter": "9", + "sentence_range": "3593-3596", + "Text": "After the characteristic\nvoltage, the diode current increases significantly (exponentially), even for\na very small increase in the diode bias voltage This voltage is called the\nthreshold voltage or cut-in voltage (~0 2V for germanium diode and\n~0 7 V for silicon diode)" + }, + { + "Chapter": "9", + "sentence_range": "3594-3597", + "Text": "This voltage is called the\nthreshold voltage or cut-in voltage (~0 2V for germanium diode and\n~0 7 V for silicon diode) For the diode in reverse bias, the current is very small (~mA) and almost\nremains constant with change in bias" + }, + { + "Chapter": "9", + "sentence_range": "3595-3598", + "Text": "2V for germanium diode and\n~0 7 V for silicon diode) For the diode in reverse bias, the current is very small (~mA) and almost\nremains constant with change in bias It is called reverse saturation\ncurrent" + }, + { + "Chapter": "9", + "sentence_range": "3596-3599", + "Text": "7 V for silicon diode) For the diode in reverse bias, the current is very small (~mA) and almost\nremains constant with change in bias It is called reverse saturation\ncurrent However, for special cases, at very high reverse bias (break down\nvoltage), the current suddenly increases" + }, + { + "Chapter": "9", + "sentence_range": "3597-3600", + "Text": "For the diode in reverse bias, the current is very small (~mA) and almost\nremains constant with change in bias It is called reverse saturation\ncurrent However, for special cases, at very high reverse bias (break down\nvoltage), the current suddenly increases This special action of the diode\nis discussed later in Section 14" + }, + { + "Chapter": "9", + "sentence_range": "3598-3601", + "Text": "It is called reverse saturation\ncurrent However, for special cases, at very high reverse bias (break down\nvoltage), the current suddenly increases This special action of the diode\nis discussed later in Section 14 8" + }, + { + "Chapter": "9", + "sentence_range": "3599-3602", + "Text": "However, for special cases, at very high reverse bias (break down\nvoltage), the current suddenly increases This special action of the diode\nis discussed later in Section 14 8 The general purpose diode are not\nused beyond the reverse saturation current region" + }, + { + "Chapter": "9", + "sentence_range": "3600-3603", + "Text": "This special action of the diode\nis discussed later in Section 14 8 The general purpose diode are not\nused beyond the reverse saturation current region The above discussion shows that the p-n junction diode primerly\nallows the flow of current only in one direction (forward bias)" + }, + { + "Chapter": "9", + "sentence_range": "3601-3604", + "Text": "8 The general purpose diode are not\nused beyond the reverse saturation current region The above discussion shows that the p-n junction diode primerly\nallows the flow of current only in one direction (forward bias) The forward\nbias resistance is low as compared to the reverse bias resistance" + }, + { + "Chapter": "9", + "sentence_range": "3602-3605", + "Text": "The general purpose diode are not\nused beyond the reverse saturation current region The above discussion shows that the p-n junction diode primerly\nallows the flow of current only in one direction (forward bias) The forward\nbias resistance is low as compared to the reverse bias resistance This\nproperty is used for rectification of ac voltages as discussed in the next\nsection" + }, + { + "Chapter": "9", + "sentence_range": "3603-3606", + "Text": "The above discussion shows that the p-n junction diode primerly\nallows the flow of current only in one direction (forward bias) The forward\nbias resistance is low as compared to the reverse bias resistance This\nproperty is used for rectification of ac voltages as discussed in the next\nsection For diodes, we define a quantity called dynamic resistance as\nthe ratio of small change in voltage DV to a small change in current DI:\nd\nV\nr\nI\n\u2206\n= \u2206\n(14" + }, + { + "Chapter": "9", + "sentence_range": "3604-3607", + "Text": "The forward\nbias resistance is low as compared to the reverse bias resistance This\nproperty is used for rectification of ac voltages as discussed in the next\nsection For diodes, we define a quantity called dynamic resistance as\nthe ratio of small change in voltage DV to a small change in current DI:\nd\nV\nr\nI\n\u2206\n= \u2206\n(14 6)\nExample 14" + }, + { + "Chapter": "9", + "sentence_range": "3605-3608", + "Text": "This\nproperty is used for rectification of ac voltages as discussed in the next\nsection For diodes, we define a quantity called dynamic resistance as\nthe ratio of small change in voltage DV to a small change in current DI:\nd\nV\nr\nI\n\u2206\n= \u2206\n(14 6)\nExample 14 4 The V-I characteristic of a silicon diode is shown in\nthe Fig" + }, + { + "Chapter": "9", + "sentence_range": "3606-3609", + "Text": "For diodes, we define a quantity called dynamic resistance as\nthe ratio of small change in voltage DV to a small change in current DI:\nd\nV\nr\nI\n\u2206\n= \u2206\n(14 6)\nExample 14 4 The V-I characteristic of a silicon diode is shown in\nthe Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3607-3610", + "Text": "6)\nExample 14 4 The V-I characteristic of a silicon diode is shown in\nthe Fig 14 17" + }, + { + "Chapter": "9", + "sentence_range": "3608-3611", + "Text": "4 The V-I characteristic of a silicon diode is shown in\nthe Fig 14 17 Calculate the resistance of the diode at (a) ID = 15 mA\nand (b) VD = \u201310 V" + }, + { + "Chapter": "9", + "sentence_range": "3609-3612", + "Text": "14 17 Calculate the resistance of the diode at (a) ID = 15 mA\nand (b) VD = \u201310 V FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3610-3613", + "Text": "17 Calculate the resistance of the diode at (a) ID = 15 mA\nand (b) VD = \u201310 V FIGURE 14 17\nSolution Considering the diode characteristics as a straight line\nbetween I = 10 mA to I = 20 mA passing through the origin, we can\ncalculate the resistance using Ohm\u2019s law" + }, + { + "Chapter": "9", + "sentence_range": "3611-3614", + "Text": "Calculate the resistance of the diode at (a) ID = 15 mA\nand (b) VD = \u201310 V FIGURE 14 17\nSolution Considering the diode characteristics as a straight line\nbetween I = 10 mA to I = 20 mA passing through the origin, we can\ncalculate the resistance using Ohm\u2019s law (a) From the curve, at I = 20 mA, V = 0" + }, + { + "Chapter": "9", + "sentence_range": "3612-3615", + "Text": "FIGURE 14 17\nSolution Considering the diode characteristics as a straight line\nbetween I = 10 mA to I = 20 mA passing through the origin, we can\ncalculate the resistance using Ohm\u2019s law (a) From the curve, at I = 20 mA, V = 0 8 V; I = 10 mA, V = 0" + }, + { + "Chapter": "9", + "sentence_range": "3613-3616", + "Text": "17\nSolution Considering the diode characteristics as a straight line\nbetween I = 10 mA to I = 20 mA passing through the origin, we can\ncalculate the resistance using Ohm\u2019s law (a) From the curve, at I = 20 mA, V = 0 8 V; I = 10 mA, V = 0 7 V\nrfb = DV/DI = 0" + }, + { + "Chapter": "9", + "sentence_range": "3614-3617", + "Text": "(a) From the curve, at I = 20 mA, V = 0 8 V; I = 10 mA, V = 0 7 V\nrfb = DV/DI = 0 1V/10 mA = 10 W\n(b) From the curve at V = \u201310 V, I = \u20131 mA,\nTherefore,\nrrb = 10 V/1mA= 1" + }, + { + "Chapter": "9", + "sentence_range": "3615-3618", + "Text": "8 V; I = 10 mA, V = 0 7 V\nrfb = DV/DI = 0 1V/10 mA = 10 W\n(b) From the curve at V = \u201310 V, I = \u20131 mA,\nTherefore,\nrrb = 10 V/1mA= 1 0 \u00d7 107 W\nRationalised 2023-24\nPhysics\n338\n14" + }, + { + "Chapter": "9", + "sentence_range": "3616-3619", + "Text": "7 V\nrfb = DV/DI = 0 1V/10 mA = 10 W\n(b) From the curve at V = \u201310 V, I = \u20131 mA,\nTherefore,\nrrb = 10 V/1mA= 1 0 \u00d7 107 W\nRationalised 2023-24\nPhysics\n338\n14 7 APPLICATION OF JUNCTION DIODE AS A RECTIFIER\nFrom the V-I characteristic of a junction diode we see that it allows current\nto pass only when it is forward biased" + }, + { + "Chapter": "9", + "sentence_range": "3617-3620", + "Text": "1V/10 mA = 10 W\n(b) From the curve at V = \u201310 V, I = \u20131 mA,\nTherefore,\nrrb = 10 V/1mA= 1 0 \u00d7 107 W\nRationalised 2023-24\nPhysics\n338\n14 7 APPLICATION OF JUNCTION DIODE AS A RECTIFIER\nFrom the V-I characteristic of a junction diode we see that it allows current\nto pass only when it is forward biased So if an alternating voltage is\napplied across a diode the current flows only in that part of the cycle\nwhen the diode is forward biased" + }, + { + "Chapter": "9", + "sentence_range": "3618-3621", + "Text": "0 \u00d7 107 W\nRationalised 2023-24\nPhysics\n338\n14 7 APPLICATION OF JUNCTION DIODE AS A RECTIFIER\nFrom the V-I characteristic of a junction diode we see that it allows current\nto pass only when it is forward biased So if an alternating voltage is\napplied across a diode the current flows only in that part of the cycle\nwhen the diode is forward biased This property\nis used to rectify alternating voltages and the\ncircuit used for this purpose is called a rectifier" + }, + { + "Chapter": "9", + "sentence_range": "3619-3622", + "Text": "7 APPLICATION OF JUNCTION DIODE AS A RECTIFIER\nFrom the V-I characteristic of a junction diode we see that it allows current\nto pass only when it is forward biased So if an alternating voltage is\napplied across a diode the current flows only in that part of the cycle\nwhen the diode is forward biased This property\nis used to rectify alternating voltages and the\ncircuit used for this purpose is called a rectifier If an alternating voltage is applied across a\ndiode in series with a load, a pulsating voltage will\nappear across the load only during the half cycles\nof the ac input during which the diode is forward\nbiased" + }, + { + "Chapter": "9", + "sentence_range": "3620-3623", + "Text": "So if an alternating voltage is\napplied across a diode the current flows only in that part of the cycle\nwhen the diode is forward biased This property\nis used to rectify alternating voltages and the\ncircuit used for this purpose is called a rectifier If an alternating voltage is applied across a\ndiode in series with a load, a pulsating voltage will\nappear across the load only during the half cycles\nof the ac input during which the diode is forward\nbiased Such rectifier circuit, as shown in\nFig" + }, + { + "Chapter": "9", + "sentence_range": "3621-3624", + "Text": "This property\nis used to rectify alternating voltages and the\ncircuit used for this purpose is called a rectifier If an alternating voltage is applied across a\ndiode in series with a load, a pulsating voltage will\nappear across the load only during the half cycles\nof the ac input during which the diode is forward\nbiased Such rectifier circuit, as shown in\nFig 14" + }, + { + "Chapter": "9", + "sentence_range": "3622-3625", + "Text": "If an alternating voltage is applied across a\ndiode in series with a load, a pulsating voltage will\nappear across the load only during the half cycles\nof the ac input during which the diode is forward\nbiased Such rectifier circuit, as shown in\nFig 14 18, is called a half-wave rectifier" + }, + { + "Chapter": "9", + "sentence_range": "3623-3626", + "Text": "Such rectifier circuit, as shown in\nFig 14 18, is called a half-wave rectifier The\nsecondary of a transformer supplies the desired\nac voltage across terminals A and B" + }, + { + "Chapter": "9", + "sentence_range": "3624-3627", + "Text": "14 18, is called a half-wave rectifier The\nsecondary of a transformer supplies the desired\nac voltage across terminals A and B When the\nvoltage at A is positive, the diode is forward biased\nand it conducts" + }, + { + "Chapter": "9", + "sentence_range": "3625-3628", + "Text": "18, is called a half-wave rectifier The\nsecondary of a transformer supplies the desired\nac voltage across terminals A and B When the\nvoltage at A is positive, the diode is forward biased\nand it conducts When A is negative, the diode is\nreverse-biased and it does not conduct" + }, + { + "Chapter": "9", + "sentence_range": "3626-3629", + "Text": "The\nsecondary of a transformer supplies the desired\nac voltage across terminals A and B When the\nvoltage at A is positive, the diode is forward biased\nand it conducts When A is negative, the diode is\nreverse-biased and it does not conduct The reverse\nsaturation current of a diode is negligible and can\nbe considered equal to zero for practical purposes" + }, + { + "Chapter": "9", + "sentence_range": "3627-3630", + "Text": "When the\nvoltage at A is positive, the diode is forward biased\nand it conducts When A is negative, the diode is\nreverse-biased and it does not conduct The reverse\nsaturation current of a diode is negligible and can\nbe considered equal to zero for practical purposes (The reverse breakdown voltage of the diode must\nbe sufficiently higher than the peak ac voltage at\nthe secondary of the transformer to protect the\ndiode from reverse breakdown" + }, + { + "Chapter": "9", + "sentence_range": "3628-3631", + "Text": "When A is negative, the diode is\nreverse-biased and it does not conduct The reverse\nsaturation current of a diode is negligible and can\nbe considered equal to zero for practical purposes (The reverse breakdown voltage of the diode must\nbe sufficiently higher than the peak ac voltage at\nthe secondary of the transformer to protect the\ndiode from reverse breakdown )\nTherefore, in the positive half-cycle of ac there\nis a current through the load resistor RL and we\nget an output voltage, as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3629-3632", + "Text": "The reverse\nsaturation current of a diode is negligible and can\nbe considered equal to zero for practical purposes (The reverse breakdown voltage of the diode must\nbe sufficiently higher than the peak ac voltage at\nthe secondary of the transformer to protect the\ndiode from reverse breakdown )\nTherefore, in the positive half-cycle of ac there\nis a current through the load resistor RL and we\nget an output voltage, as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3630-3633", + "Text": "(The reverse breakdown voltage of the diode must\nbe sufficiently higher than the peak ac voltage at\nthe secondary of the transformer to protect the\ndiode from reverse breakdown )\nTherefore, in the positive half-cycle of ac there\nis a current through the load resistor RL and we\nget an output voltage, as shown in Fig 14 18(b),\nwhereas there is no current in the negative half-\ncycle" + }, + { + "Chapter": "9", + "sentence_range": "3631-3634", + "Text": ")\nTherefore, in the positive half-cycle of ac there\nis a current through the load resistor RL and we\nget an output voltage, as shown in Fig 14 18(b),\nwhereas there is no current in the negative half-\ncycle In the next positive half-cycle, again we get\nthe output voltage" + }, + { + "Chapter": "9", + "sentence_range": "3632-3635", + "Text": "14 18(b),\nwhereas there is no current in the negative half-\ncycle In the next positive half-cycle, again we get\nthe output voltage Thus, the output voltage, though still varying, is\nrestricted to only one direction and is said to be rectified" + }, + { + "Chapter": "9", + "sentence_range": "3633-3636", + "Text": "18(b),\nwhereas there is no current in the negative half-\ncycle In the next positive half-cycle, again we get\nthe output voltage Thus, the output voltage, though still varying, is\nrestricted to only one direction and is said to be rectified Since the\nrectified output of this circuit is only for half of the input ac wave it is\ncalled as half-wave rectifier" + }, + { + "Chapter": "9", + "sentence_range": "3634-3637", + "Text": "In the next positive half-cycle, again we get\nthe output voltage Thus, the output voltage, though still varying, is\nrestricted to only one direction and is said to be rectified Since the\nrectified output of this circuit is only for half of the input ac wave it is\ncalled as half-wave rectifier The circuit using two diodes, shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3635-3638", + "Text": "Thus, the output voltage, though still varying, is\nrestricted to only one direction and is said to be rectified Since the\nrectified output of this circuit is only for half of the input ac wave it is\ncalled as half-wave rectifier The circuit using two diodes, shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3636-3639", + "Text": "Since the\nrectified output of this circuit is only for half of the input ac wave it is\ncalled as half-wave rectifier The circuit using two diodes, shown in Fig 14 19(a), gives output\nrectified voltage corresponding to both the positive as well as negative\nhalf of the ac cycle" + }, + { + "Chapter": "9", + "sentence_range": "3637-3640", + "Text": "The circuit using two diodes, shown in Fig 14 19(a), gives output\nrectified voltage corresponding to both the positive as well as negative\nhalf of the ac cycle Hence, it is known as full-wave rectifier" + }, + { + "Chapter": "9", + "sentence_range": "3638-3641", + "Text": "14 19(a), gives output\nrectified voltage corresponding to both the positive as well as negative\nhalf of the ac cycle Hence, it is known as full-wave rectifier Here the\np-side of the two diodes are connected to the ends of the secondary of the\ntransformer" + }, + { + "Chapter": "9", + "sentence_range": "3639-3642", + "Text": "19(a), gives output\nrectified voltage corresponding to both the positive as well as negative\nhalf of the ac cycle Hence, it is known as full-wave rectifier Here the\np-side of the two diodes are connected to the ends of the secondary of the\ntransformer The n-side of the diodes are connected together and the\noutput is taken between this common point of diodes and the midpoint\nof the secondary of the transformer" + }, + { + "Chapter": "9", + "sentence_range": "3640-3643", + "Text": "Hence, it is known as full-wave rectifier Here the\np-side of the two diodes are connected to the ends of the secondary of the\ntransformer The n-side of the diodes are connected together and the\noutput is taken between this common point of diodes and the midpoint\nof the secondary of the transformer So for a full-wave rectifier the\nsecondary of the transformer is provided with a centre tapping and so it\nis called centre-tap transformer" + }, + { + "Chapter": "9", + "sentence_range": "3641-3644", + "Text": "Here the\np-side of the two diodes are connected to the ends of the secondary of the\ntransformer The n-side of the diodes are connected together and the\noutput is taken between this common point of diodes and the midpoint\nof the secondary of the transformer So for a full-wave rectifier the\nsecondary of the transformer is provided with a centre tapping and so it\nis called centre-tap transformer As can be seen from Fig" + }, + { + "Chapter": "9", + "sentence_range": "3642-3645", + "Text": "The n-side of the diodes are connected together and the\noutput is taken between this common point of diodes and the midpoint\nof the secondary of the transformer So for a full-wave rectifier the\nsecondary of the transformer is provided with a centre tapping and so it\nis called centre-tap transformer As can be seen from Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3643-3646", + "Text": "So for a full-wave rectifier the\nsecondary of the transformer is provided with a centre tapping and so it\nis called centre-tap transformer As can be seen from Fig 14 19(c) the\nvoltage rectified by each diode is only half the total secondary voltage" + }, + { + "Chapter": "9", + "sentence_range": "3644-3647", + "Text": "As can be seen from Fig 14 19(c) the\nvoltage rectified by each diode is only half the total secondary voltage Each diode rectifies only for half the cycle, but the two do so for alternate\ncycles" + }, + { + "Chapter": "9", + "sentence_range": "3645-3648", + "Text": "14 19(c) the\nvoltage rectified by each diode is only half the total secondary voltage Each diode rectifies only for half the cycle, but the two do so for alternate\ncycles Thus, the output between their common terminals and the centre-\ntap of the transformer becomes a full-wave rectifier output" + }, + { + "Chapter": "9", + "sentence_range": "3646-3649", + "Text": "19(c) the\nvoltage rectified by each diode is only half the total secondary voltage Each diode rectifies only for half the cycle, but the two do so for alternate\ncycles Thus, the output between their common terminals and the centre-\ntap of the transformer becomes a full-wave rectifier output (Note that\nthere is another circuit of full wave rectifier which does not need a centre-\ntap transformer but needs four diodes" + }, + { + "Chapter": "9", + "sentence_range": "3647-3650", + "Text": "Each diode rectifies only for half the cycle, but the two do so for alternate\ncycles Thus, the output between their common terminals and the centre-\ntap of the transformer becomes a full-wave rectifier output (Note that\nthere is another circuit of full wave rectifier which does not need a centre-\ntap transformer but needs four diodes ) Suppose the input voltage to A\nFIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3648-3651", + "Text": "Thus, the output between their common terminals and the centre-\ntap of the transformer becomes a full-wave rectifier output (Note that\nthere is another circuit of full wave rectifier which does not need a centre-\ntap transformer but needs four diodes ) Suppose the input voltage to A\nFIGURE 14 18 (a) Half-wave rectifier\ncircuit, (b) Input ac voltage and output\nvoltage waveforms from the rectifier circuit" + }, + { + "Chapter": "9", + "sentence_range": "3649-3652", + "Text": "(Note that\nthere is another circuit of full wave rectifier which does not need a centre-\ntap transformer but needs four diodes ) Suppose the input voltage to A\nFIGURE 14 18 (a) Half-wave rectifier\ncircuit, (b) Input ac voltage and output\nvoltage waveforms from the rectifier circuit Rationalised 2023-24\n339\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nwith respect to the centre tap at any instant\nis positive" + }, + { + "Chapter": "9", + "sentence_range": "3650-3653", + "Text": ") Suppose the input voltage to A\nFIGURE 14 18 (a) Half-wave rectifier\ncircuit, (b) Input ac voltage and output\nvoltage waveforms from the rectifier circuit Rationalised 2023-24\n339\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nwith respect to the centre tap at any instant\nis positive It is clear that, at that instant,\nvoltage at B being out of phase will be\nnegative as shown in Fig" + }, + { + "Chapter": "9", + "sentence_range": "3651-3654", + "Text": "18 (a) Half-wave rectifier\ncircuit, (b) Input ac voltage and output\nvoltage waveforms from the rectifier circuit Rationalised 2023-24\n339\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nwith respect to the centre tap at any instant\nis positive It is clear that, at that instant,\nvoltage at B being out of phase will be\nnegative as shown in Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3652-3655", + "Text": "Rationalised 2023-24\n339\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nwith respect to the centre tap at any instant\nis positive It is clear that, at that instant,\nvoltage at B being out of phase will be\nnegative as shown in Fig 14 19(b)" + }, + { + "Chapter": "9", + "sentence_range": "3653-3656", + "Text": "It is clear that, at that instant,\nvoltage at B being out of phase will be\nnegative as shown in Fig 14 19(b) So, diode\nD1 gets forward biased and conducts (while\nD2 being reverse biased is not conducting)" + }, + { + "Chapter": "9", + "sentence_range": "3654-3657", + "Text": "14 19(b) So, diode\nD1 gets forward biased and conducts (while\nD2 being reverse biased is not conducting) Hence, during this positive half cycle we get\nan output current (and a output voltage\nacross the load resistor RL) as shown in\nFig" + }, + { + "Chapter": "9", + "sentence_range": "3655-3658", + "Text": "19(b) So, diode\nD1 gets forward biased and conducts (while\nD2 being reverse biased is not conducting) Hence, during this positive half cycle we get\nan output current (and a output voltage\nacross the load resistor RL) as shown in\nFig 14" + }, + { + "Chapter": "9", + "sentence_range": "3656-3659", + "Text": "So, diode\nD1 gets forward biased and conducts (while\nD2 being reverse biased is not conducting) Hence, during this positive half cycle we get\nan output current (and a output voltage\nacross the load resistor RL) as shown in\nFig 14 19(c)" + }, + { + "Chapter": "9", + "sentence_range": "3657-3660", + "Text": "Hence, during this positive half cycle we get\nan output current (and a output voltage\nacross the load resistor RL) as shown in\nFig 14 19(c) In the course of the ac cycle\nwhen the voltage at A becomes negative with\nrespect to centre tap, the voltage at B would\nbe positive" + }, + { + "Chapter": "9", + "sentence_range": "3658-3661", + "Text": "14 19(c) In the course of the ac cycle\nwhen the voltage at A becomes negative with\nrespect to centre tap, the voltage at B would\nbe positive In this part of the cycle diode\nD1 would not conduct but diode D2 would,\ngiving an output current and output\nvoltage (across RL) during the negative half\ncycle of the input ac" + }, + { + "Chapter": "9", + "sentence_range": "3659-3662", + "Text": "19(c) In the course of the ac cycle\nwhen the voltage at A becomes negative with\nrespect to centre tap, the voltage at B would\nbe positive In this part of the cycle diode\nD1 would not conduct but diode D2 would,\ngiving an output current and output\nvoltage (across RL) during the negative half\ncycle of the input ac Thus, we get output\nvoltage during both the positive as well as\nthe negative half of the cycle" + }, + { + "Chapter": "9", + "sentence_range": "3660-3663", + "Text": "In the course of the ac cycle\nwhen the voltage at A becomes negative with\nrespect to centre tap, the voltage at B would\nbe positive In this part of the cycle diode\nD1 would not conduct but diode D2 would,\ngiving an output current and output\nvoltage (across RL) during the negative half\ncycle of the input ac Thus, we get output\nvoltage during both the positive as well as\nthe negative half of the cycle Obviously,\nthis is a more efficient circuit for getting\nrectified voltage or current than the half-\nwave rectifier" + }, + { + "Chapter": "9", + "sentence_range": "3661-3664", + "Text": "In this part of the cycle diode\nD1 would not conduct but diode D2 would,\ngiving an output current and output\nvoltage (across RL) during the negative half\ncycle of the input ac Thus, we get output\nvoltage during both the positive as well as\nthe negative half of the cycle Obviously,\nthis is a more efficient circuit for getting\nrectified voltage or current than the half-\nwave rectifier The rectified voltage is in the form of\npulses of the shape of half sinusoids" + }, + { + "Chapter": "9", + "sentence_range": "3662-3665", + "Text": "Thus, we get output\nvoltage during both the positive as well as\nthe negative half of the cycle Obviously,\nthis is a more efficient circuit for getting\nrectified voltage or current than the half-\nwave rectifier The rectified voltage is in the form of\npulses of the shape of half sinusoids Though it is unidirectional it does not have\na steady value" + }, + { + "Chapter": "9", + "sentence_range": "3663-3666", + "Text": "Obviously,\nthis is a more efficient circuit for getting\nrectified voltage or current than the half-\nwave rectifier The rectified voltage is in the form of\npulses of the shape of half sinusoids Though it is unidirectional it does not have\na steady value To get steady dc output\nfrom the pulsating voltage normally a\ncapacitor is connected across the output\nterminals (parallel to the load RL)" + }, + { + "Chapter": "9", + "sentence_range": "3664-3667", + "Text": "The rectified voltage is in the form of\npulses of the shape of half sinusoids Though it is unidirectional it does not have\na steady value To get steady dc output\nfrom the pulsating voltage normally a\ncapacitor is connected across the output\nterminals (parallel to the load RL) One can\nalso use an inductor in series with RL for\nthe same purpose" + }, + { + "Chapter": "9", + "sentence_range": "3665-3668", + "Text": "Though it is unidirectional it does not have\na steady value To get steady dc output\nfrom the pulsating voltage normally a\ncapacitor is connected across the output\nterminals (parallel to the load RL) One can\nalso use an inductor in series with RL for\nthe same purpose Since these additional\ncircuits appear to filter out the ac ripple\nand give a pure dc voltage, so they are\ncalled filters" + }, + { + "Chapter": "9", + "sentence_range": "3666-3669", + "Text": "To get steady dc output\nfrom the pulsating voltage normally a\ncapacitor is connected across the output\nterminals (parallel to the load RL) One can\nalso use an inductor in series with RL for\nthe same purpose Since these additional\ncircuits appear to filter out the ac ripple\nand give a pure dc voltage, so they are\ncalled filters Now we shall discuss the role of\ncapacitor in filtering" + }, + { + "Chapter": "9", + "sentence_range": "3667-3670", + "Text": "One can\nalso use an inductor in series with RL for\nthe same purpose Since these additional\ncircuits appear to filter out the ac ripple\nand give a pure dc voltage, so they are\ncalled filters Now we shall discuss the role of\ncapacitor in filtering When the voltage\nacross the capacitor is rising, it gets\ncharged" + }, + { + "Chapter": "9", + "sentence_range": "3668-3671", + "Text": "Since these additional\ncircuits appear to filter out the ac ripple\nand give a pure dc voltage, so they are\ncalled filters Now we shall discuss the role of\ncapacitor in filtering When the voltage\nacross the capacitor is rising, it gets\ncharged If there is no external load, it remains charged to the peak voltage\nof the rectified output" + }, + { + "Chapter": "9", + "sentence_range": "3669-3672", + "Text": "Now we shall discuss the role of\ncapacitor in filtering When the voltage\nacross the capacitor is rising, it gets\ncharged If there is no external load, it remains charged to the peak voltage\nof the rectified output When there is a load, it gets discharged through\nthe load and the voltage across it begins to fall" + }, + { + "Chapter": "9", + "sentence_range": "3670-3673", + "Text": "When the voltage\nacross the capacitor is rising, it gets\ncharged If there is no external load, it remains charged to the peak voltage\nof the rectified output When there is a load, it gets discharged through\nthe load and the voltage across it begins to fall In the next half-cycle of\nrectified output it again gets charged to the peak value (Fig" + }, + { + "Chapter": "9", + "sentence_range": "3671-3674", + "Text": "If there is no external load, it remains charged to the peak voltage\nof the rectified output When there is a load, it gets discharged through\nthe load and the voltage across it begins to fall In the next half-cycle of\nrectified output it again gets charged to the peak value (Fig 14" + }, + { + "Chapter": "9", + "sentence_range": "3672-3675", + "Text": "When there is a load, it gets discharged through\nthe load and the voltage across it begins to fall In the next half-cycle of\nrectified output it again gets charged to the peak value (Fig 14 20)" + }, + { + "Chapter": "9", + "sentence_range": "3673-3676", + "Text": "In the next half-cycle of\nrectified output it again gets charged to the peak value (Fig 14 20) The\nrate of fall of the voltage across the capacitor depends inversely upon the\nproduct of capacitance C and the effective resistance RL used in the circuit\nand is called the time constant" + }, + { + "Chapter": "9", + "sentence_range": "3674-3677", + "Text": "14 20) The\nrate of fall of the voltage across the capacitor depends inversely upon the\nproduct of capacitance C and the effective resistance RL used in the circuit\nand is called the time constant To make the time constant large value of\nC should be large" + }, + { + "Chapter": "9", + "sentence_range": "3675-3678", + "Text": "20) The\nrate of fall of the voltage across the capacitor depends inversely upon the\nproduct of capacitance C and the effective resistance RL used in the circuit\nand is called the time constant To make the time constant large value of\nC should be large So capacitor input filters use large capacitors" + }, + { + "Chapter": "9", + "sentence_range": "3676-3679", + "Text": "The\nrate of fall of the voltage across the capacitor depends inversely upon the\nproduct of capacitance C and the effective resistance RL used in the circuit\nand is called the time constant To make the time constant large value of\nC should be large So capacitor input filters use large capacitors The\noutput voltage obtained by using capacitor input filter is nearer to the\npeak voltage of the rectified voltage" + }, + { + "Chapter": "9", + "sentence_range": "3677-3680", + "Text": "To make the time constant large value of\nC should be large So capacitor input filters use large capacitors The\noutput voltage obtained by using capacitor input filter is nearer to the\npeak voltage of the rectified voltage This type of filter is most widely\nused in power supplies" + }, + { + "Chapter": "9", + "sentence_range": "3678-3681", + "Text": "So capacitor input filters use large capacitors The\noutput voltage obtained by using capacitor input filter is nearer to the\npeak voltage of the rectified voltage This type of filter is most widely\nused in power supplies FIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3679-3682", + "Text": "The\noutput voltage obtained by using capacitor input filter is nearer to the\npeak voltage of the rectified voltage This type of filter is most widely\nused in power supplies FIGURE 14 19 (a) A Full-wave rectifier\ncircuit; (b) Input wave forms given to the\ndiode D1 at A and to the diode D2 at B;\n(c) Output waveform across the\nload RL connected in the full-wave\nrectifier circuit" + }, + { + "Chapter": "9", + "sentence_range": "3680-3683", + "Text": "This type of filter is most widely\nused in power supplies FIGURE 14 19 (a) A Full-wave rectifier\ncircuit; (b) Input wave forms given to the\ndiode D1 at A and to the diode D2 at B;\n(c) Output waveform across the\nload RL connected in the full-wave\nrectifier circuit Rationalised 2023-24\nPhysics\n340\nFIGURE 14" + }, + { + "Chapter": "9", + "sentence_range": "3681-3684", + "Text": "FIGURE 14 19 (a) A Full-wave rectifier\ncircuit; (b) Input wave forms given to the\ndiode D1 at A and to the diode D2 at B;\n(c) Output waveform across the\nload RL connected in the full-wave\nrectifier circuit Rationalised 2023-24\nPhysics\n340\nFIGURE 14 20 (a) A full-wave rectifier with capacitor filter, (b) Input and output\nvoltage of rectifier in (a)" + }, + { + "Chapter": "9", + "sentence_range": "3682-3685", + "Text": "19 (a) A Full-wave rectifier\ncircuit; (b) Input wave forms given to the\ndiode D1 at A and to the diode D2 at B;\n(c) Output waveform across the\nload RL connected in the full-wave\nrectifier circuit Rationalised 2023-24\nPhysics\n340\nFIGURE 14 20 (a) A full-wave rectifier with capacitor filter, (b) Input and output\nvoltage of rectifier in (a) SUMMARY\n1" + }, + { + "Chapter": "9", + "sentence_range": "3683-3686", + "Text": "Rationalised 2023-24\nPhysics\n340\nFIGURE 14 20 (a) A full-wave rectifier with capacitor filter, (b) Input and output\nvoltage of rectifier in (a) SUMMARY\n1 Semiconductors are the basic materials used in the present solid state\nelectronic devices like diode, transistor, ICs, etc" + }, + { + "Chapter": "9", + "sentence_range": "3684-3687", + "Text": "20 (a) A full-wave rectifier with capacitor filter, (b) Input and output\nvoltage of rectifier in (a) SUMMARY\n1 Semiconductors are the basic materials used in the present solid state\nelectronic devices like diode, transistor, ICs, etc 2" + }, + { + "Chapter": "9", + "sentence_range": "3685-3688", + "Text": "SUMMARY\n1 Semiconductors are the basic materials used in the present solid state\nelectronic devices like diode, transistor, ICs, etc 2 Lattice structure and the atomic structure of constituent elements\ndecide whether a particular material will be insulator, metal or\nsemiconductor" + }, + { + "Chapter": "9", + "sentence_range": "3686-3689", + "Text": "Semiconductors are the basic materials used in the present solid state\nelectronic devices like diode, transistor, ICs, etc 2 Lattice structure and the atomic structure of constituent elements\ndecide whether a particular material will be insulator, metal or\nsemiconductor 3" + }, + { + "Chapter": "9", + "sentence_range": "3687-3690", + "Text": "2 Lattice structure and the atomic structure of constituent elements\ndecide whether a particular material will be insulator, metal or\nsemiconductor 3 Metals have low resistivity (10\u20132 to 10\u20138 Wm), insulators have very high\nresistivity (>108 W m\u20131), while semiconductors have intermediate values\nof resistivity" + }, + { + "Chapter": "9", + "sentence_range": "3688-3691", + "Text": "Lattice structure and the atomic structure of constituent elements\ndecide whether a particular material will be insulator, metal or\nsemiconductor 3 Metals have low resistivity (10\u20132 to 10\u20138 Wm), insulators have very high\nresistivity (>108 W m\u20131), while semiconductors have intermediate values\nof resistivity 4" + }, + { + "Chapter": "9", + "sentence_range": "3689-3692", + "Text": "3 Metals have low resistivity (10\u20132 to 10\u20138 Wm), insulators have very high\nresistivity (>108 W m\u20131), while semiconductors have intermediate values\nof resistivity 4 Semiconductors are elemental (Si, Ge) as well as compound (GaAs,\nCdS, etc" + }, + { + "Chapter": "9", + "sentence_range": "3690-3693", + "Text": "Metals have low resistivity (10\u20132 to 10\u20138 Wm), insulators have very high\nresistivity (>108 W m\u20131), while semiconductors have intermediate values\nof resistivity 4 Semiconductors are elemental (Si, Ge) as well as compound (GaAs,\nCdS, etc )" + }, + { + "Chapter": "9", + "sentence_range": "3691-3694", + "Text": "4 Semiconductors are elemental (Si, Ge) as well as compound (GaAs,\nCdS, etc ) 5" + }, + { + "Chapter": "9", + "sentence_range": "3692-3695", + "Text": "Semiconductors are elemental (Si, Ge) as well as compound (GaAs,\nCdS, etc ) 5 Pure semiconductors are called \u2018intrinsic semiconductors\u2019" + }, + { + "Chapter": "9", + "sentence_range": "3693-3696", + "Text": ") 5 Pure semiconductors are called \u2018intrinsic semiconductors\u2019 The presence\nof charge carriers (electrons and holes) is an \u2018intrinsic\u2019 property of the\nmaterial and these are obtained as a result of thermal excitation" + }, + { + "Chapter": "9", + "sentence_range": "3694-3697", + "Text": "5 Pure semiconductors are called \u2018intrinsic semiconductors\u2019 The presence\nof charge carriers (electrons and holes) is an \u2018intrinsic\u2019 property of the\nmaterial and these are obtained as a result of thermal excitation The\nnumber of electrons (ne) is equal to the number of holes (nh ) in intrinsic\nconductors" + }, + { + "Chapter": "9", + "sentence_range": "3695-3698", + "Text": "Pure semiconductors are called \u2018intrinsic semiconductors\u2019 The presence\nof charge carriers (electrons and holes) is an \u2018intrinsic\u2019 property of the\nmaterial and these are obtained as a result of thermal excitation The\nnumber of electrons (ne) is equal to the number of holes (nh ) in intrinsic\nconductors Holes are essentially electron vacancies with an effective\npositive charge" + }, + { + "Chapter": "9", + "sentence_range": "3696-3699", + "Text": "The presence\nof charge carriers (electrons and holes) is an \u2018intrinsic\u2019 property of the\nmaterial and these are obtained as a result of thermal excitation The\nnumber of electrons (ne) is equal to the number of holes (nh ) in intrinsic\nconductors Holes are essentially electron vacancies with an effective\npositive charge 6" + }, + { + "Chapter": "9", + "sentence_range": "3697-3700", + "Text": "The\nnumber of electrons (ne) is equal to the number of holes (nh ) in intrinsic\nconductors Holes are essentially electron vacancies with an effective\npositive charge 6 The number of charge carriers can be changed by \u2018doping\u2019 of a suitable\nimpurity in pure semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3698-3701", + "Text": "Holes are essentially electron vacancies with an effective\npositive charge 6 The number of charge carriers can be changed by \u2018doping\u2019 of a suitable\nimpurity in pure semiconductors Such semiconductors are known as\nextrinsic semiconductors" + }, + { + "Chapter": "9", + "sentence_range": "3699-3702", + "Text": "6 The number of charge carriers can be changed by \u2018doping\u2019 of a suitable\nimpurity in pure semiconductors Such semiconductors are known as\nextrinsic semiconductors These are of two types (n-type and p-type)" + }, + { + "Chapter": "9", + "sentence_range": "3700-3703", + "Text": "The number of charge carriers can be changed by \u2018doping\u2019 of a suitable\nimpurity in pure semiconductors Such semiconductors are known as\nextrinsic semiconductors These are of two types (n-type and p-type) 7" + }, + { + "Chapter": "9", + "sentence_range": "3701-3704", + "Text": "Such semiconductors are known as\nextrinsic semiconductors These are of two types (n-type and p-type) 7 In n-type semiconductors, ne >> nh while in p-type semiconductors nh >> ne" + }, + { + "Chapter": "9", + "sentence_range": "3702-3705", + "Text": "These are of two types (n-type and p-type) 7 In n-type semiconductors, ne >> nh while in p-type semiconductors nh >> ne 8" + }, + { + "Chapter": "9", + "sentence_range": "3703-3706", + "Text": "7 In n-type semiconductors, ne >> nh while in p-type semiconductors nh >> ne 8 n-type semiconducting Si or Ge is obtained by doping with pentavalent\natoms (donors) like As, Sb, P, etc" + }, + { + "Chapter": "9", + "sentence_range": "3704-3707", + "Text": "In n-type semiconductors, ne >> nh while in p-type semiconductors nh >> ne 8 n-type semiconducting Si or Ge is obtained by doping with pentavalent\natoms (donors) like As, Sb, P, etc , while p-type Si or Ge can be obtained\nby doping with trivalent atom (acceptors) like B, Al, In etc" + }, + { + "Chapter": "9", + "sentence_range": "3705-3708", + "Text": "8 n-type semiconducting Si or Ge is obtained by doping with pentavalent\natoms (donors) like As, Sb, P, etc , while p-type Si or Ge can be obtained\nby doping with trivalent atom (acceptors) like B, Al, In etc 9" + }, + { + "Chapter": "9", + "sentence_range": "3706-3709", + "Text": "n-type semiconducting Si or Ge is obtained by doping with pentavalent\natoms (donors) like As, Sb, P, etc , while p-type Si or Ge can be obtained\nby doping with trivalent atom (acceptors) like B, Al, In etc 9 nenh = ni\n2 in all cases" + }, + { + "Chapter": "9", + "sentence_range": "3707-3710", + "Text": ", while p-type Si or Ge can be obtained\nby doping with trivalent atom (acceptors) like B, Al, In etc 9 nenh = ni\n2 in all cases Further, the material possesses an overall charge\nneutrality" + }, + { + "Chapter": "9", + "sentence_range": "3708-3711", + "Text": "9 nenh = ni\n2 in all cases Further, the material possesses an overall charge\nneutrality 10" + }, + { + "Chapter": "9", + "sentence_range": "3709-3712", + "Text": "nenh = ni\n2 in all cases Further, the material possesses an overall charge\nneutrality 10 There are two distinct band of energies (called valence band and\nconduction band) in which the electrons in a material lie" + }, + { + "Chapter": "9", + "sentence_range": "3710-3713", + "Text": "Further, the material possesses an overall charge\nneutrality 10 There are two distinct band of energies (called valence band and\nconduction band) in which the electrons in a material lie Valence\nband energies are low as compared to conduction band energies" + }, + { + "Chapter": "9", + "sentence_range": "3711-3714", + "Text": "10 There are two distinct band of energies (called valence band and\nconduction band) in which the electrons in a material lie Valence\nband energies are low as compared to conduction band energies All\nenergy levels in the valence band are filled while energy levels in the\nconduction band may be fully empty or partially filled" + }, + { + "Chapter": "9", + "sentence_range": "3712-3715", + "Text": "There are two distinct band of energies (called valence band and\nconduction band) in which the electrons in a material lie Valence\nband energies are low as compared to conduction band energies All\nenergy levels in the valence band are filled while energy levels in the\nconduction band may be fully empty or partially filled The electrons in\nthe conduction band are free to move in a solid and are responsible for\nthe conductivity" + }, + { + "Chapter": "9", + "sentence_range": "3713-3716", + "Text": "Valence\nband energies are low as compared to conduction band energies All\nenergy levels in the valence band are filled while energy levels in the\nconduction band may be fully empty or partially filled The electrons in\nthe conduction band are free to move in a solid and are responsible for\nthe conductivity The extent of conductivity depends upon the energy\ngap (Eg) between the top of valence band (EV ) and the bottom of the\nconduction band EC" + }, + { + "Chapter": "9", + "sentence_range": "3714-3717", + "Text": "All\nenergy levels in the valence band are filled while energy levels in the\nconduction band may be fully empty or partially filled The electrons in\nthe conduction band are free to move in a solid and are responsible for\nthe conductivity The extent of conductivity depends upon the energy\ngap (Eg) between the top of valence band (EV ) and the bottom of the\nconduction band EC The electrons from valence band can be excited by\nRationalised 2023-24\n341\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nheat, light or electrical energy to the conduction band and thus, produce\na change in the current flowing in a semiconductor" + }, + { + "Chapter": "9", + "sentence_range": "3715-3718", + "Text": "The electrons in\nthe conduction band are free to move in a solid and are responsible for\nthe conductivity The extent of conductivity depends upon the energy\ngap (Eg) between the top of valence band (EV ) and the bottom of the\nconduction band EC The electrons from valence band can be excited by\nRationalised 2023-24\n341\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nheat, light or electrical energy to the conduction band and thus, produce\na change in the current flowing in a semiconductor 11" + }, + { + "Chapter": "9", + "sentence_range": "3716-3719", + "Text": "The extent of conductivity depends upon the energy\ngap (Eg) between the top of valence band (EV ) and the bottom of the\nconduction band EC The electrons from valence band can be excited by\nRationalised 2023-24\n341\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nheat, light or electrical energy to the conduction band and thus, produce\na change in the current flowing in a semiconductor 11 For insulators Eg > 3 eV, for semiconductors Eg is 0" + }, + { + "Chapter": "9", + "sentence_range": "3717-3720", + "Text": "The electrons from valence band can be excited by\nRationalised 2023-24\n341\nSemiconductor Electronics:\nMaterials, Devices and\nSimple Circuits\nheat, light or electrical energy to the conduction band and thus, produce\na change in the current flowing in a semiconductor 11 For insulators Eg > 3 eV, for semiconductors Eg is 0 2 eV to 3 eV, while\nfor metals Eg \u00bb 0" + }, + { + "Chapter": "9", + "sentence_range": "3718-3721", + "Text": "11 For insulators Eg > 3 eV, for semiconductors Eg is 0 2 eV to 3 eV, while\nfor metals Eg \u00bb 0 12" + }, + { + "Chapter": "9", + "sentence_range": "3719-3722", + "Text": "For insulators Eg > 3 eV, for semiconductors Eg is 0 2 eV to 3 eV, while\nfor metals Eg \u00bb 0 12 p-n junction is the \u2018key\u2019 to all semiconductor devices" + }, + { + "Chapter": "9", + "sentence_range": "3720-3723", + "Text": "2 eV to 3 eV, while\nfor metals Eg \u00bb 0 12 p-n junction is the \u2018key\u2019 to all semiconductor devices When such a\njunction is made, a \u2018depletion layer\u2019 is formed consisting of immobile\nion-cores devoid of their electrons or holes" + }, + { + "Chapter": "9", + "sentence_range": "3721-3724", + "Text": "12 p-n junction is the \u2018key\u2019 to all semiconductor devices When such a\njunction is made, a \u2018depletion layer\u2019 is formed consisting of immobile\nion-cores devoid of their electrons or holes This is responsible for a\njunction potential barrier" + }, + { + "Chapter": "9", + "sentence_range": "3722-3725", + "Text": "p-n junction is the \u2018key\u2019 to all semiconductor devices When such a\njunction is made, a \u2018depletion layer\u2019 is formed consisting of immobile\nion-cores devoid of their electrons or holes This is responsible for a\njunction potential barrier 13" + }, + { + "Chapter": "9", + "sentence_range": "3723-3726", + "Text": "When such a\njunction is made, a \u2018depletion layer\u2019 is formed consisting of immobile\nion-cores devoid of their electrons or holes This is responsible for a\njunction potential barrier 13 By changing the external applied voltage, junction barriers can be\nchanged" + }, + { + "Chapter": "9", + "sentence_range": "3724-3727", + "Text": "This is responsible for a\njunction potential barrier 13 By changing the external applied voltage, junction barriers can be\nchanged In forward bias (n-side is connected to negative terminal of the\nbattery and p-side is connected to the positive), the barrier is decreased\nwhile the barrier increases in reverse bias" + }, + { + "Chapter": "9", + "sentence_range": "3725-3728", + "Text": "13 By changing the external applied voltage, junction barriers can be\nchanged In forward bias (n-side is connected to negative terminal of the\nbattery and p-side is connected to the positive), the barrier is decreased\nwhile the barrier increases in reverse bias Hence, forward bias current\nis more (mA) while it is very small (mA) in a p-n junction diode" + }, + { + "Chapter": "9", + "sentence_range": "3726-3729", + "Text": "By changing the external applied voltage, junction barriers can be\nchanged In forward bias (n-side is connected to negative terminal of the\nbattery and p-side is connected to the positive), the barrier is decreased\nwhile the barrier increases in reverse bias Hence, forward bias current\nis more (mA) while it is very small (mA) in a p-n junction diode 14" + }, + { + "Chapter": "9", + "sentence_range": "3727-3730", + "Text": "In forward bias (n-side is connected to negative terminal of the\nbattery and p-side is connected to the positive), the barrier is decreased\nwhile the barrier increases in reverse bias Hence, forward bias current\nis more (mA) while it is very small (mA) in a p-n junction diode 14 Diodes can be used for rectifying an ac voltage (restricting the ac voltage\nto one direction)" + }, + { + "Chapter": "9", + "sentence_range": "3728-3731", + "Text": "Hence, forward bias current\nis more (mA) while it is very small (mA) in a p-n junction diode 14 Diodes can be used for rectifying an ac voltage (restricting the ac voltage\nto one direction) With the help of a capacitor or a suitable filter, a dc\nvoltage can be obtained" + }, + { + "Chapter": "9", + "sentence_range": "3729-3732", + "Text": "14 Diodes can be used for rectifying an ac voltage (restricting the ac voltage\nto one direction) With the help of a capacitor or a suitable filter, a dc\nvoltage can be obtained POINTS TO PONDER\n1" + }, + { + "Chapter": "9", + "sentence_range": "3730-3733", + "Text": "Diodes can be used for rectifying an ac voltage (restricting the ac voltage\nto one direction) With the help of a capacitor or a suitable filter, a dc\nvoltage can be obtained POINTS TO PONDER\n1 The energy bands (EC or EV) in the semiconductors are space delocalised\nwhich means that these are not located in any specific place inside the\nsolid" + }, + { + "Chapter": "9", + "sentence_range": "3731-3734", + "Text": "With the help of a capacitor or a suitable filter, a dc\nvoltage can be obtained POINTS TO PONDER\n1 The energy bands (EC or EV) in the semiconductors are space delocalised\nwhich means that these are not located in any specific place inside the\nsolid The energies are the overall averages" + }, + { + "Chapter": "9", + "sentence_range": "3732-3735", + "Text": "POINTS TO PONDER\n1 The energy bands (EC or EV) in the semiconductors are space delocalised\nwhich means that these are not located in any specific place inside the\nsolid The energies are the overall averages When you see a picture in\nwhich EC or EV are drawn as straight lines, then they should be\nrespectively taken simply as the bottom of conduction band energy levels\nand top of valence band energy levels" + }, + { + "Chapter": "9", + "sentence_range": "3733-3736", + "Text": "The energy bands (EC or EV) in the semiconductors are space delocalised\nwhich means that these are not located in any specific place inside the\nsolid The energies are the overall averages When you see a picture in\nwhich EC or EV are drawn as straight lines, then they should be\nrespectively taken simply as the bottom of conduction band energy levels\nand top of valence band energy levels 2" + }, + { + "Chapter": "9", + "sentence_range": "3734-3737", + "Text": "The energies are the overall averages When you see a picture in\nwhich EC or EV are drawn as straight lines, then they should be\nrespectively taken simply as the bottom of conduction band energy levels\nand top of valence band energy levels 2 In elemental semiconductors (Si or Ge), the n-type or p-type\nsemiconductors are obtained by introducing \u2018dopants\u2019 as defects" + }, + { + "Chapter": "9", + "sentence_range": "3735-3738", + "Text": "When you see a picture in\nwhich EC or EV are drawn as straight lines, then they should be\nrespectively taken simply as the bottom of conduction band energy levels\nand top of valence band energy levels 2 In elemental semiconductors (Si or Ge), the n-type or p-type\nsemiconductors are obtained by introducing \u2018dopants\u2019 as defects In\ncompound semiconductors, the change in relative stoichiometric ratio\ncan also change the type of semiconductor" + }, + { + "Chapter": "9", + "sentence_range": "3736-3739", + "Text": "2 In elemental semiconductors (Si or Ge), the n-type or p-type\nsemiconductors are obtained by introducing \u2018dopants\u2019 as defects In\ncompound semiconductors, the change in relative stoichiometric ratio\ncan also change the type of semiconductor For example, in ideal GaAs\nthe ratio of Ga:As is 1:1 but in Ga-rich or As-rich GaAs it could\nrespectively be Ga1" + }, + { + "Chapter": "9", + "sentence_range": "3737-3740", + "Text": "In elemental semiconductors (Si or Ge), the n-type or p-type\nsemiconductors are obtained by introducing \u2018dopants\u2019 as defects In\ncompound semiconductors, the change in relative stoichiometric ratio\ncan also change the type of semiconductor For example, in ideal GaAs\nthe ratio of Ga:As is 1:1 but in Ga-rich or As-rich GaAs it could\nrespectively be Ga1 1 As0" + }, + { + "Chapter": "9", + "sentence_range": "3738-3741", + "Text": "In\ncompound semiconductors, the change in relative stoichiometric ratio\ncan also change the type of semiconductor For example, in ideal GaAs\nthe ratio of Ga:As is 1:1 but in Ga-rich or As-rich GaAs it could\nrespectively be Ga1 1 As0 9 or Ga0" + }, + { + "Chapter": "9", + "sentence_range": "3739-3742", + "Text": "For example, in ideal GaAs\nthe ratio of Ga:As is 1:1 but in Ga-rich or As-rich GaAs it could\nrespectively be Ga1 1 As0 9 or Ga0 9 As1" + }, + { + "Chapter": "9", + "sentence_range": "3740-3743", + "Text": "1 As0 9 or Ga0 9 As1 1" + }, + { + "Chapter": "9", + "sentence_range": "3741-3744", + "Text": "9 or Ga0 9 As1 1 In general, the presence of\ndefects control the properties of semiconductors in many ways" + }, + { + "Chapter": "9", + "sentence_range": "3742-3745", + "Text": "9 As1 1 In general, the presence of\ndefects control the properties of semiconductors in many ways EXERCISES\n14" + }, + { + "Chapter": "9", + "sentence_range": "3743-3746", + "Text": "1 In general, the presence of\ndefects control the properties of semiconductors in many ways EXERCISES\n14 1\nIn an n-type silicon, which of the following statement is true:\n(a) Electrons are majority carriers and trivalent atoms are the\ndopants" + }, + { + "Chapter": "9", + "sentence_range": "3744-3747", + "Text": "In general, the presence of\ndefects control the properties of semiconductors in many ways EXERCISES\n14 1\nIn an n-type silicon, which of the following statement is true:\n(a) Electrons are majority carriers and trivalent atoms are the\ndopants (b) Electrons are minority carriers and pentavalent atoms are the\ndopants" + }, + { + "Chapter": "9", + "sentence_range": "3745-3748", + "Text": "EXERCISES\n14 1\nIn an n-type silicon, which of the following statement is true:\n(a) Electrons are majority carriers and trivalent atoms are the\ndopants (b) Electrons are minority carriers and pentavalent atoms are the\ndopants (c) Holes are minority carriers and pentavalent atoms are the\ndopants" + }, + { + "Chapter": "9", + "sentence_range": "3746-3749", + "Text": "1\nIn an n-type silicon, which of the following statement is true:\n(a) Electrons are majority carriers and trivalent atoms are the\ndopants (b) Electrons are minority carriers and pentavalent atoms are the\ndopants (c) Holes are minority carriers and pentavalent atoms are the\ndopants (d) Holes are majority carriers and trivalent atoms are the dopants" + }, + { + "Chapter": "9", + "sentence_range": "3747-3750", + "Text": "(b) Electrons are minority carriers and pentavalent atoms are the\ndopants (c) Holes are minority carriers and pentavalent atoms are the\ndopants (d) Holes are majority carriers and trivalent atoms are the dopants 14" + }, + { + "Chapter": "9", + "sentence_range": "3748-3751", + "Text": "(c) Holes are minority carriers and pentavalent atoms are the\ndopants (d) Holes are majority carriers and trivalent atoms are the dopants 14 2\nWhich of the statements given in Exercise 14" + }, + { + "Chapter": "9", + "sentence_range": "3749-3752", + "Text": "(d) Holes are majority carriers and trivalent atoms are the dopants 14 2\nWhich of the statements given in Exercise 14 1 is true for p-type\nsemiconductos" + }, + { + "Chapter": "9", + "sentence_range": "3750-3753", + "Text": "14 2\nWhich of the statements given in Exercise 14 1 is true for p-type\nsemiconductos 14" + }, + { + "Chapter": "9", + "sentence_range": "3751-3754", + "Text": "2\nWhich of the statements given in Exercise 14 1 is true for p-type\nsemiconductos 14 3\nCarbon, silicon and germanium have four valence electrons each" + }, + { + "Chapter": "9", + "sentence_range": "3752-3755", + "Text": "1 is true for p-type\nsemiconductos 14 3\nCarbon, silicon and germanium have four valence electrons each These are characterised by valence and conduction bands separated\nRationalised 2023-24\nPhysics\n342\nby energy band gap respectively equal to (Eg)C, (Eg)Si and (Eg)Ge" + }, + { + "Chapter": "9", + "sentence_range": "3753-3756", + "Text": "14 3\nCarbon, silicon and germanium have four valence electrons each These are characterised by valence and conduction bands separated\nRationalised 2023-24\nPhysics\n342\nby energy band gap respectively equal to (Eg)C, (Eg)Si and (Eg)Ge Which\nof the following statements is true" + }, + { + "Chapter": "9", + "sentence_range": "3754-3757", + "Text": "3\nCarbon, silicon and germanium have four valence electrons each These are characterised by valence and conduction bands separated\nRationalised 2023-24\nPhysics\n342\nby energy band gap respectively equal to (Eg)C, (Eg)Si and (Eg)Ge Which\nof the following statements is true (a) (Eg)Si < (Eg)Ge < (Eg)C\n(b) (Eg)C < (Eg)Ge > (Eg)Si\n(c) (Eg)C > (Eg)Si > (Eg)Ge\n(d) (Eg)C = (Eg)Si = (Eg)Ge\n14" + }, + { + "Chapter": "9", + "sentence_range": "3755-3758", + "Text": "These are characterised by valence and conduction bands separated\nRationalised 2023-24\nPhysics\n342\nby energy band gap respectively equal to (Eg)C, (Eg)Si and (Eg)Ge Which\nof the following statements is true (a) (Eg)Si < (Eg)Ge < (Eg)C\n(b) (Eg)C < (Eg)Ge > (Eg)Si\n(c) (Eg)C > (Eg)Si > (Eg)Ge\n(d) (Eg)C = (Eg)Si = (Eg)Ge\n14 4\nIn an unbiased p-n junction, holes diffuse from the p-region to\nn-region because\n(a) free electrons in the n-region attract them" + }, + { + "Chapter": "9", + "sentence_range": "3756-3759", + "Text": "Which\nof the following statements is true (a) (Eg)Si < (Eg)Ge < (Eg)C\n(b) (Eg)C < (Eg)Ge > (Eg)Si\n(c) (Eg)C > (Eg)Si > (Eg)Ge\n(d) (Eg)C = (Eg)Si = (Eg)Ge\n14 4\nIn an unbiased p-n junction, holes diffuse from the p-region to\nn-region because\n(a) free electrons in the n-region attract them (b) they move across the junction by the potential difference" + }, + { + "Chapter": "9", + "sentence_range": "3757-3760", + "Text": "(a) (Eg)Si < (Eg)Ge < (Eg)C\n(b) (Eg)C < (Eg)Ge > (Eg)Si\n(c) (Eg)C > (Eg)Si > (Eg)Ge\n(d) (Eg)C = (Eg)Si = (Eg)Ge\n14 4\nIn an unbiased p-n junction, holes diffuse from the p-region to\nn-region because\n(a) free electrons in the n-region attract them (b) they move across the junction by the potential difference (c) hole concentration in p-region is more as compared to n-region" + }, + { + "Chapter": "9", + "sentence_range": "3758-3761", + "Text": "4\nIn an unbiased p-n junction, holes diffuse from the p-region to\nn-region because\n(a) free electrons in the n-region attract them (b) they move across the junction by the potential difference (c) hole concentration in p-region is more as compared to n-region (d) All the above" + }, + { + "Chapter": "9", + "sentence_range": "3759-3762", + "Text": "(b) they move across the junction by the potential difference (c) hole concentration in p-region is more as compared to n-region (d) All the above 14" + }, + { + "Chapter": "9", + "sentence_range": "3760-3763", + "Text": "(c) hole concentration in p-region is more as compared to n-region (d) All the above 14 5\nWhen a forward bias is applied to a p-n junction, it\n(a) raises the potential barrier" + }, + { + "Chapter": "9", + "sentence_range": "3761-3764", + "Text": "(d) All the above 14 5\nWhen a forward bias is applied to a p-n junction, it\n(a) raises the potential barrier (b) reduces the majority carrier current to zero" + }, + { + "Chapter": "9", + "sentence_range": "3762-3765", + "Text": "14 5\nWhen a forward bias is applied to a p-n junction, it\n(a) raises the potential barrier (b) reduces the majority carrier current to zero (c) lowers the potential barrier" + }, + { + "Chapter": "9", + "sentence_range": "3763-3766", + "Text": "5\nWhen a forward bias is applied to a p-n junction, it\n(a) raises the potential barrier (b) reduces the majority carrier current to zero (c) lowers the potential barrier (d) None of the above" + }, + { + "Chapter": "9", + "sentence_range": "3764-3767", + "Text": "(b) reduces the majority carrier current to zero (c) lowers the potential barrier (d) None of the above 14" + }, + { + "Chapter": "9", + "sentence_range": "3765-3768", + "Text": "(c) lowers the potential barrier (d) None of the above 14 6\nIn half-wave rectification, what is the output frequency if the input\nfrequency is 50 Hz" + }, + { + "Chapter": "9", + "sentence_range": "3766-3769", + "Text": "(d) None of the above 14 6\nIn half-wave rectification, what is the output frequency if the input\nfrequency is 50 Hz What is the output frequency of a full-wave rectifier\nfor the same input frequency" + }, + { + "Chapter": "9", + "sentence_range": "3767-3770", + "Text": "14 6\nIn half-wave rectification, what is the output frequency if the input\nfrequency is 50 Hz What is the output frequency of a full-wave rectifier\nfor the same input frequency Rationalised 2023-24\nNotes\nRationalised 2023-24\n344\nPhysics\n APPENDICES\nAPPENDIX A 1\nTHE GREEK ALPHABET\nAPPENDIX A 2\nCOMMON SI PREFIXES AND SYMBOLS FOR MULTIPLES AND SUB-MULTIPLES\nRationalised 2023-24\n345\nAnswers\nAppendices\nAPPENDIX A 3\nSOME IMPORTANT CONSTANTS\nOTHER USEFUL CONSTANTS\nRationalised 2023-24\n346\nPhysics\nANSWERS\nCHAPTER 9\n9" + }, + { + "Chapter": "9", + "sentence_range": "3768-3771", + "Text": "6\nIn half-wave rectification, what is the output frequency if the input\nfrequency is 50 Hz What is the output frequency of a full-wave rectifier\nfor the same input frequency Rationalised 2023-24\nNotes\nRationalised 2023-24\n344\nPhysics\n APPENDICES\nAPPENDIX A 1\nTHE GREEK ALPHABET\nAPPENDIX A 2\nCOMMON SI PREFIXES AND SYMBOLS FOR MULTIPLES AND SUB-MULTIPLES\nRationalised 2023-24\n345\nAnswers\nAppendices\nAPPENDIX A 3\nSOME IMPORTANT CONSTANTS\nOTHER USEFUL CONSTANTS\nRationalised 2023-24\n346\nPhysics\nANSWERS\nCHAPTER 9\n9 1\nv = \u201354 cm" + }, + { + "Chapter": "9", + "sentence_range": "3769-3772", + "Text": "What is the output frequency of a full-wave rectifier\nfor the same input frequency Rationalised 2023-24\nNotes\nRationalised 2023-24\n344\nPhysics\n APPENDICES\nAPPENDIX A 1\nTHE GREEK ALPHABET\nAPPENDIX A 2\nCOMMON SI PREFIXES AND SYMBOLS FOR MULTIPLES AND SUB-MULTIPLES\nRationalised 2023-24\n345\nAnswers\nAppendices\nAPPENDIX A 3\nSOME IMPORTANT CONSTANTS\nOTHER USEFUL CONSTANTS\nRationalised 2023-24\n346\nPhysics\nANSWERS\nCHAPTER 9\n9 1\nv = \u201354 cm The image is real, inverted and magnified" + }, + { + "Chapter": "9", + "sentence_range": "3770-3773", + "Text": "Rationalised 2023-24\nNotes\nRationalised 2023-24\n344\nPhysics\n APPENDICES\nAPPENDIX A 1\nTHE GREEK ALPHABET\nAPPENDIX A 2\nCOMMON SI PREFIXES AND SYMBOLS FOR MULTIPLES AND SUB-MULTIPLES\nRationalised 2023-24\n345\nAnswers\nAppendices\nAPPENDIX A 3\nSOME IMPORTANT CONSTANTS\nOTHER USEFUL CONSTANTS\nRationalised 2023-24\n346\nPhysics\nANSWERS\nCHAPTER 9\n9 1\nv = \u201354 cm The image is real, inverted and magnified The size of the\nimage is 5" + }, + { + "Chapter": "9", + "sentence_range": "3771-3774", + "Text": "1\nv = \u201354 cm The image is real, inverted and magnified The size of the\nimage is 5 0 cm" + }, + { + "Chapter": "9", + "sentence_range": "3772-3775", + "Text": "The image is real, inverted and magnified The size of the\nimage is 5 0 cm As u \u00ae f, v \u00ae \u00a5; for u < f, image is virtual" + }, + { + "Chapter": "9", + "sentence_range": "3773-3776", + "Text": "The size of the\nimage is 5 0 cm As u \u00ae f, v \u00ae \u00a5; for u < f, image is virtual 9" + }, + { + "Chapter": "9", + "sentence_range": "3774-3777", + "Text": "0 cm As u \u00ae f, v \u00ae \u00a5; for u < f, image is virtual 9 2\nv = 6" + }, + { + "Chapter": "9", + "sentence_range": "3775-3778", + "Text": "As u \u00ae f, v \u00ae \u00a5; for u < f, image is virtual 9 2\nv = 6 7 cm" + }, + { + "Chapter": "9", + "sentence_range": "3776-3779", + "Text": "9 2\nv = 6 7 cm Magnification = 5/9, i" + }, + { + "Chapter": "9", + "sentence_range": "3777-3780", + "Text": "2\nv = 6 7 cm Magnification = 5/9, i e" + }, + { + "Chapter": "9", + "sentence_range": "3778-3781", + "Text": "7 cm Magnification = 5/9, i e , the size of the image is 2" + }, + { + "Chapter": "9", + "sentence_range": "3779-3782", + "Text": "Magnification = 5/9, i e , the size of the image is 2 5 cm" + }, + { + "Chapter": "9", + "sentence_range": "3780-3783", + "Text": "e , the size of the image is 2 5 cm As\nu \u00ae \u00a5; v \u00ae f (but never beyond) while m \u00ae 0" + }, + { + "Chapter": "9", + "sentence_range": "3781-3784", + "Text": ", the size of the image is 2 5 cm As\nu \u00ae \u00a5; v \u00ae f (but never beyond) while m \u00ae 0 9" + }, + { + "Chapter": "9", + "sentence_range": "3782-3785", + "Text": "5 cm As\nu \u00ae \u00a5; v \u00ae f (but never beyond) while m \u00ae 0 9 3\n1" + }, + { + "Chapter": "9", + "sentence_range": "3783-3786", + "Text": "As\nu \u00ae \u00a5; v \u00ae f (but never beyond) while m \u00ae 0 9 3\n1 33; 1" + }, + { + "Chapter": "9", + "sentence_range": "3784-3787", + "Text": "9 3\n1 33; 1 7 cm\n9" + }, + { + "Chapter": "9", + "sentence_range": "3785-3788", + "Text": "3\n1 33; 1 7 cm\n9 4\nnga = 1" + }, + { + "Chapter": "9", + "sentence_range": "3786-3789", + "Text": "33; 1 7 cm\n9 4\nnga = 1 51; nwa = 1" + }, + { + "Chapter": "9", + "sentence_range": "3787-3790", + "Text": "7 cm\n9 4\nnga = 1 51; nwa = 1 32; ngw = 1" + }, + { + "Chapter": "9", + "sentence_range": "3788-3791", + "Text": "4\nnga = 1 51; nwa = 1 32; ngw = 1 144; which gives sin r = 0" + }, + { + "Chapter": "9", + "sentence_range": "3789-3792", + "Text": "51; nwa = 1 32; ngw = 1 144; which gives sin r = 0 6181 i" + }, + { + "Chapter": "9", + "sentence_range": "3790-3793", + "Text": "32; ngw = 1 144; which gives sin r = 0 6181 i e" + }, + { + "Chapter": "9", + "sentence_range": "3791-3794", + "Text": "144; which gives sin r = 0 6181 i e ,\nr ~ 38\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "3792-3795", + "Text": "6181 i e ,\nr ~ 38\u00b0 9" + }, + { + "Chapter": "9", + "sentence_range": "3793-3796", + "Text": "e ,\nr ~ 38\u00b0 9 5\nr = 0" + }, + { + "Chapter": "9", + "sentence_range": "3794-3797", + "Text": ",\nr ~ 38\u00b0 9 5\nr = 0 8 \u00d7 tan ic and sin\n1/1" + }, + { + "Chapter": "9", + "sentence_range": "3795-3798", + "Text": "9 5\nr = 0 8 \u00d7 tan ic and sin\n1/1 33\n0" + }, + { + "Chapter": "9", + "sentence_range": "3796-3799", + "Text": "5\nr = 0 8 \u00d7 tan ic and sin\n1/1 33\n0 75\nci\n=\n\u2245\n, where r is the radius (in m)\nof the largest circle from which light comes out and ic is the critical\nangle for water-air interface, Area = 2" + }, + { + "Chapter": "9", + "sentence_range": "3797-3800", + "Text": "8 \u00d7 tan ic and sin\n1/1 33\n0 75\nci\n=\n\u2245\n, where r is the radius (in m)\nof the largest circle from which light comes out and ic is the critical\nangle for water-air interface, Area = 2 6 m2\n9" + }, + { + "Chapter": "9", + "sentence_range": "3798-3801", + "Text": "33\n0 75\nci\n=\n\u2245\n, where r is the radius (in m)\nof the largest circle from which light comes out and ic is the critical\nangle for water-air interface, Area = 2 6 m2\n9 6\nn \u2245 1" + }, + { + "Chapter": "9", + "sentence_range": "3799-3802", + "Text": "75\nci\n=\n\u2245\n, where r is the radius (in m)\nof the largest circle from which light comes out and ic is the critical\nangle for water-air interface, Area = 2 6 m2\n9 6\nn \u2245 1 53 and Dm for prism in water \u2245 10\u00b0\n9" + }, + { + "Chapter": "9", + "sentence_range": "3800-3803", + "Text": "6 m2\n9 6\nn \u2245 1 53 and Dm for prism in water \u2245 10\u00b0\n9 7\nR = 22 cm\n9" + }, + { + "Chapter": "9", + "sentence_range": "3801-3804", + "Text": "6\nn \u2245 1 53 and Dm for prism in water \u2245 10\u00b0\n9 7\nR = 22 cm\n9 8\nHere the object is virtual and the image is real" + }, + { + "Chapter": "9", + "sentence_range": "3802-3805", + "Text": "53 and Dm for prism in water \u2245 10\u00b0\n9 7\nR = 22 cm\n9 8\nHere the object is virtual and the image is real u = +12 cm (object on\nright; virtual)\n(a)\nf = +20 cm" + }, + { + "Chapter": "9", + "sentence_range": "3803-3806", + "Text": "7\nR = 22 cm\n9 8\nHere the object is virtual and the image is real u = +12 cm (object on\nright; virtual)\n(a)\nf = +20 cm Image is real and at 7" + }, + { + "Chapter": "9", + "sentence_range": "3804-3807", + "Text": "8\nHere the object is virtual and the image is real u = +12 cm (object on\nright; virtual)\n(a)\nf = +20 cm Image is real and at 7 5 cm from the lens on its right\nside" + }, + { + "Chapter": "9", + "sentence_range": "3805-3808", + "Text": "u = +12 cm (object on\nright; virtual)\n(a)\nf = +20 cm Image is real and at 7 5 cm from the lens on its right\nside (b)\nf = \u201316 cm" + }, + { + "Chapter": "9", + "sentence_range": "3806-3809", + "Text": "Image is real and at 7 5 cm from the lens on its right\nside (b)\nf = \u201316 cm Image is real and at 48 cm from the lens on its right side" + }, + { + "Chapter": "9", + "sentence_range": "3807-3810", + "Text": "5 cm from the lens on its right\nside (b)\nf = \u201316 cm Image is real and at 48 cm from the lens on its right side 9" + }, + { + "Chapter": "9", + "sentence_range": "3808-3811", + "Text": "(b)\nf = \u201316 cm Image is real and at 48 cm from the lens on its right side 9 9\nv = 8" + }, + { + "Chapter": "9", + "sentence_range": "3809-3812", + "Text": "Image is real and at 48 cm from the lens on its right side 9 9\nv = 8 4 cm, image is erect and virtual" + }, + { + "Chapter": "9", + "sentence_range": "3810-3813", + "Text": "9 9\nv = 8 4 cm, image is erect and virtual It is diminished to a size\n1" + }, + { + "Chapter": "9", + "sentence_range": "3811-3814", + "Text": "9\nv = 8 4 cm, image is erect and virtual It is diminished to a size\n1 8 cm" + }, + { + "Chapter": "9", + "sentence_range": "3812-3815", + "Text": "4 cm, image is erect and virtual It is diminished to a size\n1 8 cm As u \u00ae \u00a5, v \u00ae f (but never beyond f while m \u00ae 0)" + }, + { + "Chapter": "9", + "sentence_range": "3813-3816", + "Text": "It is diminished to a size\n1 8 cm As u \u00ae \u00a5, v \u00ae f (but never beyond f while m \u00ae 0) Note that when the object is placed at the focus of the concave lens\n(21 cm), the image is located at 10" + }, + { + "Chapter": "9", + "sentence_range": "3814-3817", + "Text": "8 cm As u \u00ae \u00a5, v \u00ae f (but never beyond f while m \u00ae 0) Note that when the object is placed at the focus of the concave lens\n(21 cm), the image is located at 10 5 cm (not at infinity as one might\nwrongly think)" + }, + { + "Chapter": "9", + "sentence_range": "3815-3818", + "Text": "As u \u00ae \u00a5, v \u00ae f (but never beyond f while m \u00ae 0) Note that when the object is placed at the focus of the concave lens\n(21 cm), the image is located at 10 5 cm (not at infinity as one might\nwrongly think) 9" + }, + { + "Chapter": "9", + "sentence_range": "3816-3819", + "Text": "Note that when the object is placed at the focus of the concave lens\n(21 cm), the image is located at 10 5 cm (not at infinity as one might\nwrongly think) 9 10\nA diverging lens of focal length 60 cm\n9" + }, + { + "Chapter": "9", + "sentence_range": "3817-3820", + "Text": "5 cm (not at infinity as one might\nwrongly think) 9 10\nA diverging lens of focal length 60 cm\n9 11\n(a)\nve = \u201325 cm and fe = 6" + }, + { + "Chapter": "9", + "sentence_range": "3818-3821", + "Text": "9 10\nA diverging lens of focal length 60 cm\n9 11\n(a)\nve = \u201325 cm and fe = 6 25 cm give ue = \u20135 cm; vO = (15 \u2013 5) cm =\n10 cm,\nfO = uO = \u2013 2" + }, + { + "Chapter": "9", + "sentence_range": "3819-3822", + "Text": "10\nA diverging lens of focal length 60 cm\n9 11\n(a)\nve = \u201325 cm and fe = 6 25 cm give ue = \u20135 cm; vO = (15 \u2013 5) cm =\n10 cm,\nfO = uO = \u2013 2 5 cm; Magnifying power = 20\n(b)\nuO = \u2013 2" + }, + { + "Chapter": "9", + "sentence_range": "3820-3823", + "Text": "11\n(a)\nve = \u201325 cm and fe = 6 25 cm give ue = \u20135 cm; vO = (15 \u2013 5) cm =\n10 cm,\nfO = uO = \u2013 2 5 cm; Magnifying power = 20\n(b)\nuO = \u2013 2 59 cm" + }, + { + "Chapter": "9", + "sentence_range": "3821-3824", + "Text": "25 cm give ue = \u20135 cm; vO = (15 \u2013 5) cm =\n10 cm,\nfO = uO = \u2013 2 5 cm; Magnifying power = 20\n(b)\nuO = \u2013 2 59 cm Magnifying power = 13" + }, + { + "Chapter": "9", + "sentence_range": "3822-3825", + "Text": "5 cm; Magnifying power = 20\n(b)\nuO = \u2013 2 59 cm Magnifying power = 13 5" + }, + { + "Chapter": "9", + "sentence_range": "3823-3826", + "Text": "59 cm Magnifying power = 13 5 9" + }, + { + "Chapter": "9", + "sentence_range": "3824-3827", + "Text": "Magnifying power = 13 5 9 12\nAngular magnification of the eye-piece for image at 25 cm\n\uf03d\n\uf02b\n\uf03d\n25\n2 5\n1\n11" + }, + { + "Chapter": "9", + "sentence_range": "3825-3828", + "Text": "5 9 12\nAngular magnification of the eye-piece for image at 25 cm\n\uf03d\n\uf02b\n\uf03d\n25\n2 5\n1\n11 ; |\n|" + }, + { + "Chapter": "9", + "sentence_range": "3826-3829", + "Text": "9 12\nAngular magnification of the eye-piece for image at 25 cm\n\uf03d\n\uf02b\n\uf03d\n25\n2 5\n1\n11 ; |\n| 25 cm\n2 27cm\n11\nue\n=\n=\n; vO = 7" + }, + { + "Chapter": "9", + "sentence_range": "3827-3830", + "Text": "12\nAngular magnification of the eye-piece for image at 25 cm\n\uf03d\n\uf02b\n\uf03d\n25\n2 5\n1\n11 ; |\n| 25 cm\n2 27cm\n11\nue\n=\n=\n; vO = 7 2 cm\nSeparation = 9" + }, + { + "Chapter": "9", + "sentence_range": "3828-3831", + "Text": "; |\n| 25 cm\n2 27cm\n11\nue\n=\n=\n; vO = 7 2 cm\nSeparation = 9 47 cm; Magnifying power = 88\n9" + }, + { + "Chapter": "9", + "sentence_range": "3829-3832", + "Text": "25 cm\n2 27cm\n11\nue\n=\n=\n; vO = 7 2 cm\nSeparation = 9 47 cm; Magnifying power = 88\n9 13\n24; 150 cm\n9" + }, + { + "Chapter": "9", + "sentence_range": "3830-3833", + "Text": "2 cm\nSeparation = 9 47 cm; Magnifying power = 88\n9 13\n24; 150 cm\n9 14\n(a)\nAngular magnification = 1500\n(b)\nDiameter of the image = 13" + }, + { + "Chapter": "9", + "sentence_range": "3831-3834", + "Text": "47 cm; Magnifying power = 88\n9 13\n24; 150 cm\n9 14\n(a)\nAngular magnification = 1500\n(b)\nDiameter of the image = 13 7 cm" + }, + { + "Chapter": "9", + "sentence_range": "3832-3835", + "Text": "13\n24; 150 cm\n9 14\n(a)\nAngular magnification = 1500\n(b)\nDiameter of the image = 13 7 cm Rationalised 2023-24\n347\nAnswers\n9" + }, + { + "Chapter": "9", + "sentence_range": "3833-3836", + "Text": "14\n(a)\nAngular magnification = 1500\n(b)\nDiameter of the image = 13 7 cm Rationalised 2023-24\n347\nAnswers\n9 15\nApply mirror equation and the condition:\n(a)\nf < 0 (concave mirror); u < 0 (object on left)\n(b)\nf > 0; u < 0\n(c)\nf > 0 (convex mirror) and u < 0\n(d)\nf < 0 (concave mirror); f < u < 0\nto deduce the desired result" + }, + { + "Chapter": "9", + "sentence_range": "3834-3837", + "Text": "7 cm Rationalised 2023-24\n347\nAnswers\n9 15\nApply mirror equation and the condition:\n(a)\nf < 0 (concave mirror); u < 0 (object on left)\n(b)\nf > 0; u < 0\n(c)\nf > 0 (convex mirror) and u < 0\n(d)\nf < 0 (concave mirror); f < u < 0\nto deduce the desired result 9" + }, + { + "Chapter": "9", + "sentence_range": "3835-3838", + "Text": "Rationalised 2023-24\n347\nAnswers\n9 15\nApply mirror equation and the condition:\n(a)\nf < 0 (concave mirror); u < 0 (object on left)\n(b)\nf > 0; u < 0\n(c)\nf > 0 (convex mirror) and u < 0\n(d)\nf < 0 (concave mirror); f < u < 0\nto deduce the desired result 9 16\nThe pin appears raised by 5" + }, + { + "Chapter": "9", + "sentence_range": "3836-3839", + "Text": "15\nApply mirror equation and the condition:\n(a)\nf < 0 (concave mirror); u < 0 (object on left)\n(b)\nf > 0; u < 0\n(c)\nf > 0 (convex mirror) and u < 0\n(d)\nf < 0 (concave mirror); f < u < 0\nto deduce the desired result 9 16\nThe pin appears raised by 5 0 cm" + }, + { + "Chapter": "9", + "sentence_range": "3837-3840", + "Text": "9 16\nThe pin appears raised by 5 0 cm It can be seen with an explicit ray\ndiagram that the answer is independent of the location of the slab\n(for small angles of incidence)" + }, + { + "Chapter": "9", + "sentence_range": "3838-3841", + "Text": "16\nThe pin appears raised by 5 0 cm It can be seen with an explicit ray\ndiagram that the answer is independent of the location of the slab\n(for small angles of incidence) 9" + }, + { + "Chapter": "9", + "sentence_range": "3839-3842", + "Text": "0 cm It can be seen with an explicit ray\ndiagram that the answer is independent of the location of the slab\n(for small angles of incidence) 9 17\n(a)\nsin i\u00a2c = 1" + }, + { + "Chapter": "9", + "sentence_range": "3840-3843", + "Text": "It can be seen with an explicit ray\ndiagram that the answer is independent of the location of the slab\n(for small angles of incidence) 9 17\n(a)\nsin i\u00a2c = 1 44/1" + }, + { + "Chapter": "9", + "sentence_range": "3841-3844", + "Text": "9 17\n(a)\nsin i\u00a2c = 1 44/1 68 which gives i\u00a2c = 59\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "3842-3845", + "Text": "17\n(a)\nsin i\u00a2c = 1 44/1 68 which gives i\u00a2c = 59\u00b0 Total internal reflection\ntakes place when i > 59\u00b0 or when r < rmax = 31\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "3843-3846", + "Text": "44/1 68 which gives i\u00a2c = 59\u00b0 Total internal reflection\ntakes place when i > 59\u00b0 or when r < rmax = 31\u00b0 Now,\n(sin\n/sin\n)" + }, + { + "Chapter": "9", + "sentence_range": "3844-3847", + "Text": "68 which gives i\u00a2c = 59\u00b0 Total internal reflection\ntakes place when i > 59\u00b0 or when r < rmax = 31\u00b0 Now,\n(sin\n/sin\n) max\nmax\ni\nr\n= 1 68 , which gives imax ~ 60\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "3845-3848", + "Text": "Total internal reflection\ntakes place when i > 59\u00b0 or when r < rmax = 31\u00b0 Now,\n(sin\n/sin\n) max\nmax\ni\nr\n= 1 68 , which gives imax ~ 60\u00b0 Thus, all\nincident rays of angles in the range 0 < i < 60\u00b0 will suffer total\ninternal reflections in the pipe" + }, + { + "Chapter": "9", + "sentence_range": "3846-3849", + "Text": "Now,\n(sin\n/sin\n) max\nmax\ni\nr\n= 1 68 , which gives imax ~ 60\u00b0 Thus, all\nincident rays of angles in the range 0 < i < 60\u00b0 will suffer total\ninternal reflections in the pipe (If the length of the pipe is\nfinite, which it is in practice, there will be a lower limit on i\ndetermined by the ratio of the diameter to the length of the\npipe" + }, + { + "Chapter": "9", + "sentence_range": "3847-3850", + "Text": "max\nmax\ni\nr\n= 1 68 , which gives imax ~ 60\u00b0 Thus, all\nincident rays of angles in the range 0 < i < 60\u00b0 will suffer total\ninternal reflections in the pipe (If the length of the pipe is\nfinite, which it is in practice, there will be a lower limit on i\ndetermined by the ratio of the diameter to the length of the\npipe )\n(b)\nIf there is no outer coating, i\u00a2c = sin\u20131(1/1" + }, + { + "Chapter": "9", + "sentence_range": "3848-3851", + "Text": "Thus, all\nincident rays of angles in the range 0 < i < 60\u00b0 will suffer total\ninternal reflections in the pipe (If the length of the pipe is\nfinite, which it is in practice, there will be a lower limit on i\ndetermined by the ratio of the diameter to the length of the\npipe )\n(b)\nIf there is no outer coating, i\u00a2c = sin\u20131(1/1 68) = 36" + }, + { + "Chapter": "9", + "sentence_range": "3849-3852", + "Text": "(If the length of the pipe is\nfinite, which it is in practice, there will be a lower limit on i\ndetermined by the ratio of the diameter to the length of the\npipe )\n(b)\nIf there is no outer coating, i\u00a2c = sin\u20131(1/1 68) = 36 5\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "3850-3853", + "Text": ")\n(b)\nIf there is no outer coating, i\u00a2c = sin\u20131(1/1 68) = 36 5\u00b0 Now,\ni = 90\u00b0 will have r = 36" + }, + { + "Chapter": "9", + "sentence_range": "3851-3854", + "Text": "68) = 36 5\u00b0 Now,\ni = 90\u00b0 will have r = 36 5\u00b0 and i\u00a2 = 53" + }, + { + "Chapter": "9", + "sentence_range": "3852-3855", + "Text": "5\u00b0 Now,\ni = 90\u00b0 will have r = 36 5\u00b0 and i\u00a2 = 53 5\u00b0 which is greater than\ni\u00a2c" + }, + { + "Chapter": "9", + "sentence_range": "3853-3856", + "Text": "Now,\ni = 90\u00b0 will have r = 36 5\u00b0 and i\u00a2 = 53 5\u00b0 which is greater than\ni\u00a2c Thus, all incident rays (in the range 53" + }, + { + "Chapter": "9", + "sentence_range": "3854-3857", + "Text": "5\u00b0 and i\u00a2 = 53 5\u00b0 which is greater than\ni\u00a2c Thus, all incident rays (in the range 53 5\u00b0 < i < 90\u00b0) will\nsuffer total internal reflections" + }, + { + "Chapter": "9", + "sentence_range": "3855-3858", + "Text": "5\u00b0 which is greater than\ni\u00a2c Thus, all incident rays (in the range 53 5\u00b0 < i < 90\u00b0) will\nsuffer total internal reflections 9" + }, + { + "Chapter": "9", + "sentence_range": "3856-3859", + "Text": "Thus, all incident rays (in the range 53 5\u00b0 < i < 90\u00b0) will\nsuffer total internal reflections 9 18\nFor fixed distance s between object and screen, the lens equation\ndoes not give a real solution for u or v if f is greater than s/4" + }, + { + "Chapter": "9", + "sentence_range": "3857-3860", + "Text": "5\u00b0 < i < 90\u00b0) will\nsuffer total internal reflections 9 18\nFor fixed distance s between object and screen, the lens equation\ndoes not give a real solution for u or v if f is greater than s/4 Therefore, fmax = 0" + }, + { + "Chapter": "9", + "sentence_range": "3858-3861", + "Text": "9 18\nFor fixed distance s between object and screen, the lens equation\ndoes not give a real solution for u or v if f is greater than s/4 Therefore, fmax = 0 75 m" + }, + { + "Chapter": "9", + "sentence_range": "3859-3862", + "Text": "18\nFor fixed distance s between object and screen, the lens equation\ndoes not give a real solution for u or v if f is greater than s/4 Therefore, fmax = 0 75 m 9" + }, + { + "Chapter": "9", + "sentence_range": "3860-3863", + "Text": "Therefore, fmax = 0 75 m 9 19\n21" + }, + { + "Chapter": "9", + "sentence_range": "3861-3864", + "Text": "75 m 9 19\n21 4 cm\n9" + }, + { + "Chapter": "9", + "sentence_range": "3862-3865", + "Text": "9 19\n21 4 cm\n9 20\n(a)\n(i) Let a parallel beam be the incident from the left on the convex\nlens first" + }, + { + "Chapter": "9", + "sentence_range": "3863-3866", + "Text": "19\n21 4 cm\n9 20\n(a)\n(i) Let a parallel beam be the incident from the left on the convex\nlens first f1 = 30 cm and u1 = \u2013 \uf0a5, give v1 = + 30 cm" + }, + { + "Chapter": "9", + "sentence_range": "3864-3867", + "Text": "4 cm\n9 20\n(a)\n(i) Let a parallel beam be the incident from the left on the convex\nlens first f1 = 30 cm and u1 = \u2013 \uf0a5, give v1 = + 30 cm This image becomes\na virtual object for the second lens" + }, + { + "Chapter": "9", + "sentence_range": "3865-3868", + "Text": "20\n(a)\n(i) Let a parallel beam be the incident from the left on the convex\nlens first f1 = 30 cm and u1 = \u2013 \uf0a5, give v1 = + 30 cm This image becomes\na virtual object for the second lens f2 = \u201320 cm, u 2 = + (30 \u2013 8) cm = + 22 cm which gives,\nv2 = \u2013 220 cm" + }, + { + "Chapter": "9", + "sentence_range": "3866-3869", + "Text": "f1 = 30 cm and u1 = \u2013 \uf0a5, give v1 = + 30 cm This image becomes\na virtual object for the second lens f2 = \u201320 cm, u 2 = + (30 \u2013 8) cm = + 22 cm which gives,\nv2 = \u2013 220 cm The parallel incident beam appears to diverge\nfrom a point 216 cm from the centre of the two-lens system" + }, + { + "Chapter": "9", + "sentence_range": "3867-3870", + "Text": "This image becomes\na virtual object for the second lens f2 = \u201320 cm, u 2 = + (30 \u2013 8) cm = + 22 cm which gives,\nv2 = \u2013 220 cm The parallel incident beam appears to diverge\nfrom a point 216 cm from the centre of the two-lens system (ii) Let the parallel beam be incident from the left on the concave\nlens first: f1 = \u2013 20 cm, u1 = \u2013 \u00a5, give v1 = \u2013 20 cm" + }, + { + "Chapter": "9", + "sentence_range": "3868-3871", + "Text": "f2 = \u201320 cm, u 2 = + (30 \u2013 8) cm = + 22 cm which gives,\nv2 = \u2013 220 cm The parallel incident beam appears to diverge\nfrom a point 216 cm from the centre of the two-lens system (ii) Let the parallel beam be incident from the left on the concave\nlens first: f1 = \u2013 20 cm, u1 = \u2013 \u00a5, give v1 = \u2013 20 cm This image\nbecomes a real object for the second lens: f2 = + 30 cm, u2 =\n\u2013 (20 + 8) cm = \u2013 28 cm which gives, v2 = \u2013 420 cm" + }, + { + "Chapter": "9", + "sentence_range": "3869-3872", + "Text": "The parallel incident beam appears to diverge\nfrom a point 216 cm from the centre of the two-lens system (ii) Let the parallel beam be incident from the left on the concave\nlens first: f1 = \u2013 20 cm, u1 = \u2013 \u00a5, give v1 = \u2013 20 cm This image\nbecomes a real object for the second lens: f2 = + 30 cm, u2 =\n\u2013 (20 + 8) cm = \u2013 28 cm which gives, v2 = \u2013 420 cm The parallel\nincident beam appears to diverge from a point 416 cm on the\nleft of the centre of the two-lens system" + }, + { + "Chapter": "9", + "sentence_range": "3870-3873", + "Text": "(ii) Let the parallel beam be incident from the left on the concave\nlens first: f1 = \u2013 20 cm, u1 = \u2013 \u00a5, give v1 = \u2013 20 cm This image\nbecomes a real object for the second lens: f2 = + 30 cm, u2 =\n\u2013 (20 + 8) cm = \u2013 28 cm which gives, v2 = \u2013 420 cm The parallel\nincident beam appears to diverge from a point 416 cm on the\nleft of the centre of the two-lens system Clearly, the answer depends on which side of the lens system\nthe parallel beam is incident" + }, + { + "Chapter": "9", + "sentence_range": "3871-3874", + "Text": "This image\nbecomes a real object for the second lens: f2 = + 30 cm, u2 =\n\u2013 (20 + 8) cm = \u2013 28 cm which gives, v2 = \u2013 420 cm The parallel\nincident beam appears to diverge from a point 416 cm on the\nleft of the centre of the two-lens system Clearly, the answer depends on which side of the lens system\nthe parallel beam is incident Further we do not have a simple lens\nequation true for all u (and v) in terms of a definite constant of the\nsystem (the constant being determined by f1 and f2, and the separation\nbetween the lenses)" + }, + { + "Chapter": "9", + "sentence_range": "3872-3875", + "Text": "The parallel\nincident beam appears to diverge from a point 416 cm on the\nleft of the centre of the two-lens system Clearly, the answer depends on which side of the lens system\nthe parallel beam is incident Further we do not have a simple lens\nequation true for all u (and v) in terms of a definite constant of the\nsystem (the constant being determined by f1 and f2, and the separation\nbetween the lenses) The notion of effective focal length, therefore,\ndoes not seem to be meaningful for this system" + }, + { + "Chapter": "9", + "sentence_range": "3873-3876", + "Text": "Clearly, the answer depends on which side of the lens system\nthe parallel beam is incident Further we do not have a simple lens\nequation true for all u (and v) in terms of a definite constant of the\nsystem (the constant being determined by f1 and f2, and the separation\nbetween the lenses) The notion of effective focal length, therefore,\ndoes not seem to be meaningful for this system (b)\nu1 = \u2013 40 cm, f1 = 30 cm, gives v1= 120 cm" + }, + { + "Chapter": "9", + "sentence_range": "3874-3877", + "Text": "Further we do not have a simple lens\nequation true for all u (and v) in terms of a definite constant of the\nsystem (the constant being determined by f1 and f2, and the separation\nbetween the lenses) The notion of effective focal length, therefore,\ndoes not seem to be meaningful for this system (b)\nu1 = \u2013 40 cm, f1 = 30 cm, gives v1= 120 cm Magnitude of magnification due to the first (convex) lens is 3" + }, + { + "Chapter": "9", + "sentence_range": "3875-3878", + "Text": "The notion of effective focal length, therefore,\ndoes not seem to be meaningful for this system (b)\nu1 = \u2013 40 cm, f1 = 30 cm, gives v1= 120 cm Magnitude of magnification due to the first (convex) lens is 3 u 2 = + (120 \u2013 8) cm = +112 cm (object virtual);\nf2 = \u2013 20 cm which gives v2\n112\n9220\n= \u2212\n\u00d7\ncm\nMagnitude of magnification due to the second (concave)\nRationalised 2023-24\n348\nPhysics\nlens = 20/92" + }, + { + "Chapter": "9", + "sentence_range": "3876-3879", + "Text": "(b)\nu1 = \u2013 40 cm, f1 = 30 cm, gives v1= 120 cm Magnitude of magnification due to the first (convex) lens is 3 u 2 = + (120 \u2013 8) cm = +112 cm (object virtual);\nf2 = \u2013 20 cm which gives v2\n112\n9220\n= \u2212\n\u00d7\ncm\nMagnitude of magnification due to the second (concave)\nRationalised 2023-24\n348\nPhysics\nlens = 20/92 Net magnitude of magnification = 0" + }, + { + "Chapter": "9", + "sentence_range": "3877-3880", + "Text": "Magnitude of magnification due to the first (convex) lens is 3 u 2 = + (120 \u2013 8) cm = +112 cm (object virtual);\nf2 = \u2013 20 cm which gives v2\n112\n9220\n= \u2212\n\u00d7\ncm\nMagnitude of magnification due to the second (concave)\nRationalised 2023-24\n348\nPhysics\nlens = 20/92 Net magnitude of magnification = 0 652\nSize of the image = 0" + }, + { + "Chapter": "9", + "sentence_range": "3878-3881", + "Text": "u 2 = + (120 \u2013 8) cm = +112 cm (object virtual);\nf2 = \u2013 20 cm which gives v2\n112\n9220\n= \u2212\n\u00d7\ncm\nMagnitude of magnification due to the second (concave)\nRationalised 2023-24\n348\nPhysics\nlens = 20/92 Net magnitude of magnification = 0 652\nSize of the image = 0 98 cm\n9" + }, + { + "Chapter": "9", + "sentence_range": "3879-3882", + "Text": "Net magnitude of magnification = 0 652\nSize of the image = 0 98 cm\n9 21\nIf the refracted ray in the prism is incident on the second face at the\ncritical angle ic, the angle of refraction r at the first face is (60\u00b0\u2013ic)" + }, + { + "Chapter": "9", + "sentence_range": "3880-3883", + "Text": "652\nSize of the image = 0 98 cm\n9 21\nIf the refracted ray in the prism is incident on the second face at the\ncritical angle ic, the angle of refraction r at the first face is (60\u00b0\u2013ic) Now, ic = sin\u20131 (1/1" + }, + { + "Chapter": "9", + "sentence_range": "3881-3884", + "Text": "98 cm\n9 21\nIf the refracted ray in the prism is incident on the second face at the\ncritical angle ic, the angle of refraction r at the first face is (60\u00b0\u2013ic) Now, ic = sin\u20131 (1/1 524) ~ 41\u00b0\nTherefore, r = 19\u00b0\nsin i = 0" + }, + { + "Chapter": "9", + "sentence_range": "3882-3885", + "Text": "21\nIf the refracted ray in the prism is incident on the second face at the\ncritical angle ic, the angle of refraction r at the first face is (60\u00b0\u2013ic) Now, ic = sin\u20131 (1/1 524) ~ 41\u00b0\nTherefore, r = 19\u00b0\nsin i = 0 4962; i ~ 30\u00b0\n9" + }, + { + "Chapter": "9", + "sentence_range": "3883-3886", + "Text": "Now, ic = sin\u20131 (1/1 524) ~ 41\u00b0\nTherefore, r = 19\u00b0\nsin i = 0 4962; i ~ 30\u00b0\n9 22\n(a)\n1\n91\n1\n10\nv\n+\n=\ni" + }, + { + "Chapter": "9", + "sentence_range": "3884-3887", + "Text": "524) ~ 41\u00b0\nTherefore, r = 19\u00b0\nsin i = 0 4962; i ~ 30\u00b0\n9 22\n(a)\n1\n91\n1\n10\nv\n+\n=\ni e" + }, + { + "Chapter": "9", + "sentence_range": "3885-3888", + "Text": "4962; i ~ 30\u00b0\n9 22\n(a)\n1\n91\n1\n10\nv\n+\n=\ni e ,\nv = \u2013 90 cm,\nMagnitude of magnification = 90/9 = 10" + }, + { + "Chapter": "9", + "sentence_range": "3886-3889", + "Text": "22\n(a)\n1\n91\n1\n10\nv\n+\n=\ni e ,\nv = \u2013 90 cm,\nMagnitude of magnification = 90/9 = 10 Each square in the virtual image has an area 10 \u00d7 10 \u00d7 1 mm2\n= 100 mm2 = 1 cm2\n(b)\nMagnifying power = 25/9 = 2" + }, + { + "Chapter": "9", + "sentence_range": "3887-3890", + "Text": "e ,\nv = \u2013 90 cm,\nMagnitude of magnification = 90/9 = 10 Each square in the virtual image has an area 10 \u00d7 10 \u00d7 1 mm2\n= 100 mm2 = 1 cm2\n(b)\nMagnifying power = 25/9 = 2 8\n(c)\nNo, magnification of an image by a lens and angular magnification\n(or magnifying power) of an optical instrument are two separate\nthings" + }, + { + "Chapter": "9", + "sentence_range": "3888-3891", + "Text": ",\nv = \u2013 90 cm,\nMagnitude of magnification = 90/9 = 10 Each square in the virtual image has an area 10 \u00d7 10 \u00d7 1 mm2\n= 100 mm2 = 1 cm2\n(b)\nMagnifying power = 25/9 = 2 8\n(c)\nNo, magnification of an image by a lens and angular magnification\n(or magnifying power) of an optical instrument are two separate\nthings The latter is the ratio of the angular size of the object\n(which is equal to the angular size of the image even if the image\nis magnified) to the angular size of the object if placed at the near\npoint (25 cm)" + }, + { + "Chapter": "9", + "sentence_range": "3889-3892", + "Text": "Each square in the virtual image has an area 10 \u00d7 10 \u00d7 1 mm2\n= 100 mm2 = 1 cm2\n(b)\nMagnifying power = 25/9 = 2 8\n(c)\nNo, magnification of an image by a lens and angular magnification\n(or magnifying power) of an optical instrument are two separate\nthings The latter is the ratio of the angular size of the object\n(which is equal to the angular size of the image even if the image\nis magnified) to the angular size of the object if placed at the near\npoint (25 cm) Thus, magnification magnitude is |(v/u)| and\nmagnifying power is (25/ |u|)" + }, + { + "Chapter": "9", + "sentence_range": "3890-3893", + "Text": "8\n(c)\nNo, magnification of an image by a lens and angular magnification\n(or magnifying power) of an optical instrument are two separate\nthings The latter is the ratio of the angular size of the object\n(which is equal to the angular size of the image even if the image\nis magnified) to the angular size of the object if placed at the near\npoint (25 cm) Thus, magnification magnitude is |(v/u)| and\nmagnifying power is (25/ |u|) Only when the image is located at\nthe near point |v| = 25 cm, are the two quantities equal" + }, + { + "Chapter": "9", + "sentence_range": "3891-3894", + "Text": "The latter is the ratio of the angular size of the object\n(which is equal to the angular size of the image even if the image\nis magnified) to the angular size of the object if placed at the near\npoint (25 cm) Thus, magnification magnitude is |(v/u)| and\nmagnifying power is (25/ |u|) Only when the image is located at\nthe near point |v| = 25 cm, are the two quantities equal 9" + }, + { + "Chapter": "9", + "sentence_range": "3892-3895", + "Text": "Thus, magnification magnitude is |(v/u)| and\nmagnifying power is (25/ |u|) Only when the image is located at\nthe near point |v| = 25 cm, are the two quantities equal 9 23\n(a)\nMaximum magnifying power is obtained when the image is at\nthe near point (25 cm)\nu = \u2013 7" + }, + { + "Chapter": "9", + "sentence_range": "3893-3896", + "Text": "Only when the image is located at\nthe near point |v| = 25 cm, are the two quantities equal 9 23\n(a)\nMaximum magnifying power is obtained when the image is at\nthe near point (25 cm)\nu = \u2013 7 14 cm" + }, + { + "Chapter": "9", + "sentence_range": "3894-3897", + "Text": "9 23\n(a)\nMaximum magnifying power is obtained when the image is at\nthe near point (25 cm)\nu = \u2013 7 14 cm (b)\nMagnitude of magnification = (25/ |u|) = 3" + }, + { + "Chapter": "9", + "sentence_range": "3895-3898", + "Text": "23\n(a)\nMaximum magnifying power is obtained when the image is at\nthe near point (25 cm)\nu = \u2013 7 14 cm (b)\nMagnitude of magnification = (25/ |u|) = 3 5" + }, + { + "Chapter": "9", + "sentence_range": "3896-3899", + "Text": "14 cm (b)\nMagnitude of magnification = (25/ |u|) = 3 5 (c)\nMagnifying power = 3" + }, + { + "Chapter": "9", + "sentence_range": "3897-3900", + "Text": "(b)\nMagnitude of magnification = (25/ |u|) = 3 5 (c)\nMagnifying power = 3 5\nYes, the magnifying power (when the image is produced at 25 cm)\nis equal to the magnitude of magnification" + }, + { + "Chapter": "9", + "sentence_range": "3898-3901", + "Text": "5 (c)\nMagnifying power = 3 5\nYes, the magnifying power (when the image is produced at 25 cm)\nis equal to the magnitude of magnification 9" + }, + { + "Chapter": "9", + "sentence_range": "3899-3902", + "Text": "(c)\nMagnifying power = 3 5\nYes, the magnifying power (when the image is produced at 25 cm)\nis equal to the magnitude of magnification 9 24\nMagnification = \n(" + }, + { + "Chapter": "9", + "sentence_range": "3900-3903", + "Text": "5\nYes, the magnifying power (when the image is produced at 25 cm)\nis equal to the magnitude of magnification 9 24\nMagnification = \n( 6 25/ )\n1 = 2" + }, + { + "Chapter": "9", + "sentence_range": "3901-3904", + "Text": "9 24\nMagnification = \n( 6 25/ )\n1 = 2 5\n v = +2" + }, + { + "Chapter": "9", + "sentence_range": "3902-3905", + "Text": "24\nMagnification = \n( 6 25/ )\n1 = 2 5\n v = +2 5u\n \uf02b\n\uf02d\n\uf03d\n1\n2 5\n1\n1\n10" + }, + { + "Chapter": "9", + "sentence_range": "3903-3906", + "Text": "6 25/ )\n1 = 2 5\n v = +2 5u\n \uf02b\n\uf02d\n\uf03d\n1\n2 5\n1\n1\n10 u\nu\ni" + }, + { + "Chapter": "9", + "sentence_range": "3904-3907", + "Text": "5\n v = +2 5u\n \uf02b\n\uf02d\n\uf03d\n1\n2 5\n1\n1\n10 u\nu\ni e" + }, + { + "Chapter": "9", + "sentence_range": "3905-3908", + "Text": "5u\n \uf02b\n\uf02d\n\uf03d\n1\n2 5\n1\n1\n10 u\nu\ni e ,u = \u2013 6 cm\n|v| = 15 cm\nThe virtual image is closer than the normal near point (25 cm) and\ncannot be seen by the eye distinctly" + }, + { + "Chapter": "9", + "sentence_range": "3906-3909", + "Text": "u\nu\ni e ,u = \u2013 6 cm\n|v| = 15 cm\nThe virtual image is closer than the normal near point (25 cm) and\ncannot be seen by the eye distinctly 9" + }, + { + "Chapter": "9", + "sentence_range": "3907-3910", + "Text": "e ,u = \u2013 6 cm\n|v| = 15 cm\nThe virtual image is closer than the normal near point (25 cm) and\ncannot be seen by the eye distinctly 9 25\n(a)\nEven though the absolute image size is bigger than the object\nsize, the angular size of the image is equal to the angular size of\nthe object" + }, + { + "Chapter": "9", + "sentence_range": "3908-3911", + "Text": ",u = \u2013 6 cm\n|v| = 15 cm\nThe virtual image is closer than the normal near point (25 cm) and\ncannot be seen by the eye distinctly 9 25\n(a)\nEven though the absolute image size is bigger than the object\nsize, the angular size of the image is equal to the angular size of\nthe object The magnifier helps in the following way: without it\nobject would be placed no closer than 25 cm; with it the object\ncan be placed much closer" + }, + { + "Chapter": "9", + "sentence_range": "3909-3912", + "Text": "9 25\n(a)\nEven though the absolute image size is bigger than the object\nsize, the angular size of the image is equal to the angular size of\nthe object The magnifier helps in the following way: without it\nobject would be placed no closer than 25 cm; with it the object\ncan be placed much closer The closer object has larger angular\nsize than the same object at 25 cm" + }, + { + "Chapter": "9", + "sentence_range": "3910-3913", + "Text": "25\n(a)\nEven though the absolute image size is bigger than the object\nsize, the angular size of the image is equal to the angular size of\nthe object The magnifier helps in the following way: without it\nobject would be placed no closer than 25 cm; with it the object\ncan be placed much closer The closer object has larger angular\nsize than the same object at 25 cm It is in this sense that angular\nmagnification is achieved" + }, + { + "Chapter": "9", + "sentence_range": "3911-3914", + "Text": "The magnifier helps in the following way: without it\nobject would be placed no closer than 25 cm; with it the object\ncan be placed much closer The closer object has larger angular\nsize than the same object at 25 cm It is in this sense that angular\nmagnification is achieved (b)\nYes, it decreases a little because the angle subtended at the eye\nis then slightly less than the angle subtended at the lens" + }, + { + "Chapter": "9", + "sentence_range": "3912-3915", + "Text": "The closer object has larger angular\nsize than the same object at 25 cm It is in this sense that angular\nmagnification is achieved (b)\nYes, it decreases a little because the angle subtended at the eye\nis then slightly less than the angle subtended at the lens The\nRationalised 2023-24\n349\nAnswers\neffect is negligible if the image is at a very large distance away" + }, + { + "Chapter": "9", + "sentence_range": "3913-3916", + "Text": "It is in this sense that angular\nmagnification is achieved (b)\nYes, it decreases a little because the angle subtended at the eye\nis then slightly less than the angle subtended at the lens The\nRationalised 2023-24\n349\nAnswers\neffect is negligible if the image is at a very large distance away [Note: When the eye is separated from the lens, the angles\nsubtended at the eye by the first object and its image are not\nequal" + }, + { + "Chapter": "9", + "sentence_range": "3914-3917", + "Text": "(b)\nYes, it decreases a little because the angle subtended at the eye\nis then slightly less than the angle subtended at the lens The\nRationalised 2023-24\n349\nAnswers\neffect is negligible if the image is at a very large distance away [Note: When the eye is separated from the lens, the angles\nsubtended at the eye by the first object and its image are not\nequal ]\n(c)\nFirst, grinding lens of very small focal length is not easy" + }, + { + "Chapter": "9", + "sentence_range": "3915-3918", + "Text": "The\nRationalised 2023-24\n349\nAnswers\neffect is negligible if the image is at a very large distance away [Note: When the eye is separated from the lens, the angles\nsubtended at the eye by the first object and its image are not\nequal ]\n(c)\nFirst, grinding lens of very small focal length is not easy More\nimportant, if you decrease focal length, aberrations (both spherical\nand chromatic) become more pronounced" + }, + { + "Chapter": "9", + "sentence_range": "3916-3919", + "Text": "[Note: When the eye is separated from the lens, the angles\nsubtended at the eye by the first object and its image are not\nequal ]\n(c)\nFirst, grinding lens of very small focal length is not easy More\nimportant, if you decrease focal length, aberrations (both spherical\nand chromatic) become more pronounced So, in practice, you\ncannot get a magnifying power of more than 3 or so with a simple\nconvex lens" + }, + { + "Chapter": "9", + "sentence_range": "3917-3920", + "Text": "]\n(c)\nFirst, grinding lens of very small focal length is not easy More\nimportant, if you decrease focal length, aberrations (both spherical\nand chromatic) become more pronounced So, in practice, you\ncannot get a magnifying power of more than 3 or so with a simple\nconvex lens However, using an aberration corrected lens system,\none can increase this limit by a factor of 10 or so" + }, + { + "Chapter": "9", + "sentence_range": "3918-3921", + "Text": "More\nimportant, if you decrease focal length, aberrations (both spherical\nand chromatic) become more pronounced So, in practice, you\ncannot get a magnifying power of more than 3 or so with a simple\nconvex lens However, using an aberration corrected lens system,\none can increase this limit by a factor of 10 or so (d)\nAngular magnification of eye-piece is [(25/fe) + 1] ( fe in cm) which\nincreases if fe is smaller" + }, + { + "Chapter": "9", + "sentence_range": "3919-3922", + "Text": "So, in practice, you\ncannot get a magnifying power of more than 3 or so with a simple\nconvex lens However, using an aberration corrected lens system,\none can increase this limit by a factor of 10 or so (d)\nAngular magnification of eye-piece is [(25/fe) + 1] ( fe in cm) which\nincreases if fe is smaller Further, magnification of the objective\nis given by \nO\nO\nO\nO\n1\n|\n|\n(|\n|/\n)\n1\nv\nu\nu\nf\n=\n\u2212\nwhich is large when \n|O\nu|\n is slightly greater than fO" + }, + { + "Chapter": "9", + "sentence_range": "3920-3923", + "Text": "However, using an aberration corrected lens system,\none can increase this limit by a factor of 10 or so (d)\nAngular magnification of eye-piece is [(25/fe) + 1] ( fe in cm) which\nincreases if fe is smaller Further, magnification of the objective\nis given by \nO\nO\nO\nO\n1\n|\n|\n(|\n|/\n)\n1\nv\nu\nu\nf\n=\n\u2212\nwhich is large when \n|O\nu|\n is slightly greater than fO The micro-\nscope is used for viewing very close object" + }, + { + "Chapter": "9", + "sentence_range": "3921-3924", + "Text": "(d)\nAngular magnification of eye-piece is [(25/fe) + 1] ( fe in cm) which\nincreases if fe is smaller Further, magnification of the objective\nis given by \nO\nO\nO\nO\n1\n|\n|\n(|\n|/\n)\n1\nv\nu\nu\nf\n=\n\u2212\nwhich is large when \n|O\nu|\n is slightly greater than fO The micro-\nscope is used for viewing very close object So \n|O\nu|\n is small, and\nso is fO" + }, + { + "Chapter": "9", + "sentence_range": "3922-3925", + "Text": "Further, magnification of the objective\nis given by \nO\nO\nO\nO\n1\n|\n|\n(|\n|/\n)\n1\nv\nu\nu\nf\n=\n\u2212\nwhich is large when \n|O\nu|\n is slightly greater than fO The micro-\nscope is used for viewing very close object So \n|O\nu|\n is small, and\nso is fO (e)\nThe image of the objective in the eye-piece is known as \u2018eye-ring\u2019" + }, + { + "Chapter": "9", + "sentence_range": "3923-3926", + "Text": "The micro-\nscope is used for viewing very close object So \n|O\nu|\n is small, and\nso is fO (e)\nThe image of the objective in the eye-piece is known as \u2018eye-ring\u2019 All the rays from the object refracted by objective go through the\neye-ring" + }, + { + "Chapter": "9", + "sentence_range": "3924-3927", + "Text": "So \n|O\nu|\n is small, and\nso is fO (e)\nThe image of the objective in the eye-piece is known as \u2018eye-ring\u2019 All the rays from the object refracted by objective go through the\neye-ring Therefore, it is an ideal position for our eyes for viewing" + }, + { + "Chapter": "9", + "sentence_range": "3925-3928", + "Text": "(e)\nThe image of the objective in the eye-piece is known as \u2018eye-ring\u2019 All the rays from the object refracted by objective go through the\neye-ring Therefore, it is an ideal position for our eyes for viewing If we place our eyes too close to the eye-piece, we shall not collect\nmuch of the light and also reduce our field of view" + }, + { + "Chapter": "9", + "sentence_range": "3926-3929", + "Text": "All the rays from the object refracted by objective go through the\neye-ring Therefore, it is an ideal position for our eyes for viewing If we place our eyes too close to the eye-piece, we shall not collect\nmuch of the light and also reduce our field of view If we position\nour eyes on the eye-ring and the area of the pupil of our eye is\ngreater or equal to the area of the eye-ring, our eyes will collect\nall the light refracted by the objective" + }, + { + "Chapter": "9", + "sentence_range": "3927-3930", + "Text": "Therefore, it is an ideal position for our eyes for viewing If we place our eyes too close to the eye-piece, we shall not collect\nmuch of the light and also reduce our field of view If we position\nour eyes on the eye-ring and the area of the pupil of our eye is\ngreater or equal to the area of the eye-ring, our eyes will collect\nall the light refracted by the objective The precise location of\nthe eye-ring naturally depends on the separation between the\nobjective and the eye-piece" + }, + { + "Chapter": "9", + "sentence_range": "3928-3931", + "Text": "If we place our eyes too close to the eye-piece, we shall not collect\nmuch of the light and also reduce our field of view If we position\nour eyes on the eye-ring and the area of the pupil of our eye is\ngreater or equal to the area of the eye-ring, our eyes will collect\nall the light refracted by the objective The precise location of\nthe eye-ring naturally depends on the separation between the\nobjective and the eye-piece When you view through a microscope\nby placing your eyes on one end,the ideal distance between the\neyes and eye-piece is usually built-in the design of the\ninstrument" + }, + { + "Chapter": "9", + "sentence_range": "3929-3932", + "Text": "If we position\nour eyes on the eye-ring and the area of the pupil of our eye is\ngreater or equal to the area of the eye-ring, our eyes will collect\nall the light refracted by the objective The precise location of\nthe eye-ring naturally depends on the separation between the\nobjective and the eye-piece When you view through a microscope\nby placing your eyes on one end,the ideal distance between the\neyes and eye-piece is usually built-in the design of the\ninstrument 9" + }, + { + "Chapter": "9", + "sentence_range": "3930-3933", + "Text": "The precise location of\nthe eye-ring naturally depends on the separation between the\nobjective and the eye-piece When you view through a microscope\nby placing your eyes on one end,the ideal distance between the\neyes and eye-piece is usually built-in the design of the\ninstrument 9 26\nAssume microscope in normal use i" + }, + { + "Chapter": "9", + "sentence_range": "3931-3934", + "Text": "When you view through a microscope\nby placing your eyes on one end,the ideal distance between the\neyes and eye-piece is usually built-in the design of the\ninstrument 9 26\nAssume microscope in normal use i e" + }, + { + "Chapter": "9", + "sentence_range": "3932-3935", + "Text": "9 26\nAssume microscope in normal use i e , image at 25 cm" + }, + { + "Chapter": "9", + "sentence_range": "3933-3936", + "Text": "26\nAssume microscope in normal use i e , image at 25 cm Angular\nmagnification of the eye-piece\n= 25\n5\n1\n6\n\uf02b\n\uf03d\nMagnification of the objective\n= 30\n6\n5\n\uf03d\nO\nO\n1\n1\n1\n5\n1" + }, + { + "Chapter": "9", + "sentence_range": "3934-3937", + "Text": "e , image at 25 cm Angular\nmagnification of the eye-piece\n= 25\n5\n1\n6\n\uf02b\n\uf03d\nMagnification of the objective\n= 30\n6\n5\n\uf03d\nO\nO\n1\n1\n1\n5\n1 25\nu\n\u2212u\n=\nwhich gives uO= \u20131" + }, + { + "Chapter": "9", + "sentence_range": "3935-3938", + "Text": ", image at 25 cm Angular\nmagnification of the eye-piece\n= 25\n5\n1\n6\n\uf02b\n\uf03d\nMagnification of the objective\n= 30\n6\n5\n\uf03d\nO\nO\n1\n1\n1\n5\n1 25\nu\n\u2212u\n=\nwhich gives uO= \u20131 5 cm; v0= 7" + }, + { + "Chapter": "9", + "sentence_range": "3936-3939", + "Text": "Angular\nmagnification of the eye-piece\n= 25\n5\n1\n6\n\uf02b\n\uf03d\nMagnification of the objective\n= 30\n6\n5\n\uf03d\nO\nO\n1\n1\n1\n5\n1 25\nu\n\u2212u\n=\nwhich gives uO= \u20131 5 cm; v0= 7 5 cm" + }, + { + "Chapter": "9", + "sentence_range": "3937-3940", + "Text": "25\nu\n\u2212u\n=\nwhich gives uO= \u20131 5 cm; v0= 7 5 cm |\n|\nue \uf03d (25/6) cm = 4" + }, + { + "Chapter": "9", + "sentence_range": "3938-3941", + "Text": "5 cm; v0= 7 5 cm |\n|\nue \uf03d (25/6) cm = 4 17 cm" + }, + { + "Chapter": "9", + "sentence_range": "3939-3942", + "Text": "5 cm |\n|\nue \uf03d (25/6) cm = 4 17 cm The\nseparation between the objective and the eye-piece should be (7" + }, + { + "Chapter": "9", + "sentence_range": "3940-3943", + "Text": "|\n|\nue \uf03d (25/6) cm = 4 17 cm The\nseparation between the objective and the eye-piece should be (7 5 +\n4" + }, + { + "Chapter": "9", + "sentence_range": "3941-3944", + "Text": "17 cm The\nseparation between the objective and the eye-piece should be (7 5 +\n4 17) cm = 11" + }, + { + "Chapter": "9", + "sentence_range": "3942-3945", + "Text": "The\nseparation between the objective and the eye-piece should be (7 5 +\n4 17) cm = 11 67 cm" + }, + { + "Chapter": "9", + "sentence_range": "3943-3946", + "Text": "5 +\n4 17) cm = 11 67 cm Further the object should be placed 1" + }, + { + "Chapter": "9", + "sentence_range": "3944-3947", + "Text": "17) cm = 11 67 cm Further the object should be placed 1 5 cm from\nthe objective to obtain the desired magnification" + }, + { + "Chapter": "9", + "sentence_range": "3945-3948", + "Text": "67 cm Further the object should be placed 1 5 cm from\nthe objective to obtain the desired magnification 9" + }, + { + "Chapter": "9", + "sentence_range": "3946-3949", + "Text": "Further the object should be placed 1 5 cm from\nthe objective to obtain the desired magnification 9 27\n(a)\nm = ( fO/fe) = 28\n(b)\nm = f\nf\nf\ne\nO\nO\n1\n\uf8f0\uf8ef\uf8ee+25\n\uf8f9\n\uf8fb\uf8fa = 33" + }, + { + "Chapter": "9", + "sentence_range": "3947-3950", + "Text": "5 cm from\nthe objective to obtain the desired magnification 9 27\n(a)\nm = ( fO/fe) = 28\n(b)\nm = f\nf\nf\ne\nO\nO\n1\n\uf8f0\uf8ef\uf8ee+25\n\uf8f9\n\uf8fb\uf8fa = 33 6\nRationalised 2023-24\n350\nPhysics\n9" + }, + { + "Chapter": "9", + "sentence_range": "3948-3951", + "Text": "9 27\n(a)\nm = ( fO/fe) = 28\n(b)\nm = f\nf\nf\ne\nO\nO\n1\n\uf8f0\uf8ef\uf8ee+25\n\uf8f9\n\uf8fb\uf8fa = 33 6\nRationalised 2023-24\n350\nPhysics\n9 28\n(a)\nfO + fe = 145 cm\n(b)\nAngle subtended by the tower = (100/3000) = (1/30) rad" + }, + { + "Chapter": "9", + "sentence_range": "3949-3952", + "Text": "27\n(a)\nm = ( fO/fe) = 28\n(b)\nm = f\nf\nf\ne\nO\nO\n1\n\uf8f0\uf8ef\uf8ee+25\n\uf8f9\n\uf8fb\uf8fa = 33 6\nRationalised 2023-24\n350\nPhysics\n9 28\n(a)\nfO + fe = 145 cm\n(b)\nAngle subtended by the tower = (100/3000) = (1/30) rad Angle subtended by the image produced by the objective\n= \nO\n140\nh\nh\nf\n=\nEquating the two, h = 4" + }, + { + "Chapter": "9", + "sentence_range": "3950-3953", + "Text": "6\nRationalised 2023-24\n350\nPhysics\n9 28\n(a)\nfO + fe = 145 cm\n(b)\nAngle subtended by the tower = (100/3000) = (1/30) rad Angle subtended by the image produced by the objective\n= \nO\n140\nh\nh\nf\n=\nEquating the two, h = 4 7 cm" + }, + { + "Chapter": "9", + "sentence_range": "3951-3954", + "Text": "28\n(a)\nfO + fe = 145 cm\n(b)\nAngle subtended by the tower = (100/3000) = (1/30) rad Angle subtended by the image produced by the objective\n= \nO\n140\nh\nh\nf\n=\nEquating the two, h = 4 7 cm (c)\nMagnification (magnitude) of the eye-piece = 6" + }, + { + "Chapter": "9", + "sentence_range": "3952-3955", + "Text": "Angle subtended by the image produced by the objective\n= \nO\n140\nh\nh\nf\n=\nEquating the two, h = 4 7 cm (c)\nMagnification (magnitude) of the eye-piece = 6 Height of the\nfinal image (magnitude) = 28 cm" + }, + { + "Chapter": "9", + "sentence_range": "3953-3956", + "Text": "7 cm (c)\nMagnification (magnitude) of the eye-piece = 6 Height of the\nfinal image (magnitude) = 28 cm 9" + }, + { + "Chapter": "9", + "sentence_range": "3954-3957", + "Text": "(c)\nMagnification (magnitude) of the eye-piece = 6 Height of the\nfinal image (magnitude) = 28 cm 9 29\nThe image formed by the larger (concave) mirror acts as virtual object\nfor the smaller (convex) mirror" + }, + { + "Chapter": "9", + "sentence_range": "3955-3958", + "Text": "Height of the\nfinal image (magnitude) = 28 cm 9 29\nThe image formed by the larger (concave) mirror acts as virtual object\nfor the smaller (convex) mirror Parallel rays coming from the object\nat infinity will focus at a distance of 110 mm from the larger mirror" + }, + { + "Chapter": "9", + "sentence_range": "3956-3959", + "Text": "9 29\nThe image formed by the larger (concave) mirror acts as virtual object\nfor the smaller (convex) mirror Parallel rays coming from the object\nat infinity will focus at a distance of 110 mm from the larger mirror The distance of virtual object for the smaller mirror = (110 \u201320) =\n90 mm" + }, + { + "Chapter": "9", + "sentence_range": "3957-3960", + "Text": "29\nThe image formed by the larger (concave) mirror acts as virtual object\nfor the smaller (convex) mirror Parallel rays coming from the object\nat infinity will focus at a distance of 110 mm from the larger mirror The distance of virtual object for the smaller mirror = (110 \u201320) =\n90 mm The focal length of smaller mirror is 70 mm" + }, + { + "Chapter": "9", + "sentence_range": "3958-3961", + "Text": "Parallel rays coming from the object\nat infinity will focus at a distance of 110 mm from the larger mirror The distance of virtual object for the smaller mirror = (110 \u201320) =\n90 mm The focal length of smaller mirror is 70 mm Using the mirror\nformula, image is formed at 315 mm from the smaller mirror" + }, + { + "Chapter": "9", + "sentence_range": "3959-3962", + "Text": "The distance of virtual object for the smaller mirror = (110 \u201320) =\n90 mm The focal length of smaller mirror is 70 mm Using the mirror\nformula, image is formed at 315 mm from the smaller mirror 9" + }, + { + "Chapter": "9", + "sentence_range": "3960-3963", + "Text": "The focal length of smaller mirror is 70 mm Using the mirror\nformula, image is formed at 315 mm from the smaller mirror 9 30\nThe reflected rays get deflected by twice the angle of rotation of the\nmirror" + }, + { + "Chapter": "9", + "sentence_range": "3961-3964", + "Text": "Using the mirror\nformula, image is formed at 315 mm from the smaller mirror 9 30\nThe reflected rays get deflected by twice the angle of rotation of the\nmirror Therefore, d/1" + }, + { + "Chapter": "9", + "sentence_range": "3962-3965", + "Text": "9 30\nThe reflected rays get deflected by twice the angle of rotation of the\nmirror Therefore, d/1 5 = tan 7\u00b0" + }, + { + "Chapter": "9", + "sentence_range": "3963-3966", + "Text": "30\nThe reflected rays get deflected by twice the angle of rotation of the\nmirror Therefore, d/1 5 = tan 7\u00b0 Hence d = 18" + }, + { + "Chapter": "9", + "sentence_range": "3964-3967", + "Text": "Therefore, d/1 5 = tan 7\u00b0 Hence d = 18 4 cm" + }, + { + "Chapter": "9", + "sentence_range": "3965-3968", + "Text": "5 = tan 7\u00b0 Hence d = 18 4 cm 9" + }, + { + "Chapter": "9", + "sentence_range": "3966-3969", + "Text": "Hence d = 18 4 cm 9 31\nn = 1" + }, + { + "Chapter": "9", + "sentence_range": "3967-3970", + "Text": "4 cm 9 31\nn = 1 33\nCHAPTER 10\n10" + }, + { + "Chapter": "9", + "sentence_range": "3968-3971", + "Text": "9 31\nn = 1 33\nCHAPTER 10\n10 1\n(a)\nReflected light: (wavelength, frequency, speed same as incident\nlight)\nl = 589 nm, n = 5" + }, + { + "Chapter": "9", + "sentence_range": "3969-3972", + "Text": "31\nn = 1 33\nCHAPTER 10\n10 1\n(a)\nReflected light: (wavelength, frequency, speed same as incident\nlight)\nl = 589 nm, n = 5 09 \u00b4 1014 Hz, c = 3" + }, + { + "Chapter": "9", + "sentence_range": "3970-3973", + "Text": "33\nCHAPTER 10\n10 1\n(a)\nReflected light: (wavelength, frequency, speed same as incident\nlight)\nl = 589 nm, n = 5 09 \u00b4 1014 Hz, c = 3 00 \u00b4 108 m s\u20131\n(b)\nRefracted light: (frequency same as the incident frequency)\nn = 5" + }, + { + "Chapter": "9", + "sentence_range": "3971-3974", + "Text": "1\n(a)\nReflected light: (wavelength, frequency, speed same as incident\nlight)\nl = 589 nm, n = 5 09 \u00b4 1014 Hz, c = 3 00 \u00b4 108 m s\u20131\n(b)\nRefracted light: (frequency same as the incident frequency)\nn = 5 09 \u00b4 1014Hz\nv = (c/n) = 2" + }, + { + "Chapter": "9", + "sentence_range": "3972-3975", + "Text": "09 \u00b4 1014 Hz, c = 3 00 \u00b4 108 m s\u20131\n(b)\nRefracted light: (frequency same as the incident frequency)\nn = 5 09 \u00b4 1014Hz\nv = (c/n) = 2 26 \u00d7 108 m s\u20131, l = (v/n) = 444 nm\n10" + }, + { + "Chapter": "9", + "sentence_range": "3973-3976", + "Text": "00 \u00b4 108 m s\u20131\n(b)\nRefracted light: (frequency same as the incident frequency)\nn = 5 09 \u00b4 1014Hz\nv = (c/n) = 2 26 \u00d7 108 m s\u20131, l = (v/n) = 444 nm\n10 2\n(a)\nSpherical\n(b)\nPlane\n(c)\nPlane (a small area on the surface of a large sphere is nearly\nplanar)" + }, + { + "Chapter": "9", + "sentence_range": "3974-3977", + "Text": "09 \u00b4 1014Hz\nv = (c/n) = 2 26 \u00d7 108 m s\u20131, l = (v/n) = 444 nm\n10 2\n(a)\nSpherical\n(b)\nPlane\n(c)\nPlane (a small area on the surface of a large sphere is nearly\nplanar) 10" + }, + { + "Chapter": "9", + "sentence_range": "3975-3978", + "Text": "26 \u00d7 108 m s\u20131, l = (v/n) = 444 nm\n10 2\n(a)\nSpherical\n(b)\nPlane\n(c)\nPlane (a small area on the surface of a large sphere is nearly\nplanar) 10 3\n(a)\n2" + }, + { + "Chapter": "9", + "sentence_range": "3976-3979", + "Text": "2\n(a)\nSpherical\n(b)\nPlane\n(c)\nPlane (a small area on the surface of a large sphere is nearly\nplanar) 10 3\n(a)\n2 0 \u00d7 108 m s\u20131\n(b)\nNo" + }, + { + "Chapter": "9", + "sentence_range": "3977-3980", + "Text": "10 3\n(a)\n2 0 \u00d7 108 m s\u20131\n(b)\nNo The refractive index, and hence the speed of light in a\nmedium, depends on wavelength" + }, + { + "Chapter": "9", + "sentence_range": "3978-3981", + "Text": "3\n(a)\n2 0 \u00d7 108 m s\u20131\n(b)\nNo The refractive index, and hence the speed of light in a\nmedium, depends on wavelength [When no particular\nwavelength or colour of light is specified, we may take the given\nrefractive index to refer to yellow colour" + }, + { + "Chapter": "9", + "sentence_range": "3979-3982", + "Text": "0 \u00d7 108 m s\u20131\n(b)\nNo The refractive index, and hence the speed of light in a\nmedium, depends on wavelength [When no particular\nwavelength or colour of light is specified, we may take the given\nrefractive index to refer to yellow colour ] Now we know violet\ncolour deviates more than red in a glass prism, i" + }, + { + "Chapter": "9", + "sentence_range": "3980-3983", + "Text": "The refractive index, and hence the speed of light in a\nmedium, depends on wavelength [When no particular\nwavelength or colour of light is specified, we may take the given\nrefractive index to refer to yellow colour ] Now we know violet\ncolour deviates more than red in a glass prism, i e" + }, + { + "Chapter": "9", + "sentence_range": "3981-3984", + "Text": "[When no particular\nwavelength or colour of light is specified, we may take the given\nrefractive index to refer to yellow colour ] Now we know violet\ncolour deviates more than red in a glass prism, i e nv > nr" + }, + { + "Chapter": "9", + "sentence_range": "3982-3985", + "Text": "] Now we know violet\ncolour deviates more than red in a glass prism, i e nv > nr Therefore, the violet component of white light travels slower than\nthe red component" + }, + { + "Chapter": "9", + "sentence_range": "3983-3986", + "Text": "e nv > nr Therefore, the violet component of white light travels slower than\nthe red component 10" + }, + { + "Chapter": "9", + "sentence_range": "3984-3987", + "Text": "nv > nr Therefore, the violet component of white light travels slower than\nthe red component 10 4\n\uf06c \uf03d\n\uf0b4\n\uf0b4\n\uf0b4\n\uf0b4\n1 2 10\n0 28 10\n4 14" + }, + { + "Chapter": "9", + "sentence_range": "3985-3988", + "Text": "Therefore, the violet component of white light travels slower than\nthe red component 10 4\n\uf06c \uf03d\n\uf0b4\n\uf0b4\n\uf0b4\n\uf0b4\n1 2 10\n0 28 10\n4 14 \u2013 2\n\u2013 3\n m = 600 nm\n10" + }, + { + "Chapter": "9", + "sentence_range": "3986-3989", + "Text": "10 4\n\uf06c \uf03d\n\uf0b4\n\uf0b4\n\uf0b4\n\uf0b4\n1 2 10\n0 28 10\n4 14 \u2013 2\n\u2013 3\n m = 600 nm\n10 5\nK/4\n10" + }, + { + "Chapter": "9", + "sentence_range": "3987-3990", + "Text": "4\n\uf06c \uf03d\n\uf0b4\n\uf0b4\n\uf0b4\n\uf0b4\n1 2 10\n0 28 10\n4 14 \u2013 2\n\u2013 3\n m = 600 nm\n10 5\nK/4\n10 6\n(a) 1" + }, + { + "Chapter": "9", + "sentence_range": "3988-3991", + "Text": "\u2013 2\n\u2013 3\n m = 600 nm\n10 5\nK/4\n10 6\n(a) 1 17 mm\n(b) 1" + }, + { + "Chapter": "9", + "sentence_range": "3989-3992", + "Text": "5\nK/4\n10 6\n(a) 1 17 mm\n(b) 1 56 mm\n10" + }, + { + "Chapter": "9", + "sentence_range": "3990-3993", + "Text": "6\n(a) 1 17 mm\n(b) 1 56 mm\n10 7\n0" + }, + { + "Chapter": "9", + "sentence_range": "3991-3994", + "Text": "17 mm\n(b) 1 56 mm\n10 7\n0 15\u00b0\n10" + }, + { + "Chapter": "9", + "sentence_range": "3992-3995", + "Text": "56 mm\n10 7\n0 15\u00b0\n10 8\ntan\u20131(1" + }, + { + "Chapter": "9", + "sentence_range": "3993-3996", + "Text": "7\n0 15\u00b0\n10 8\ntan\u20131(1 5) ~ 56" + }, + { + "Chapter": "9", + "sentence_range": "3994-3997", + "Text": "15\u00b0\n10 8\ntan\u20131(1 5) ~ 56 3o\nRationalised 2023-24\n351\nAnswers\n10" + }, + { + "Chapter": "9", + "sentence_range": "3995-3998", + "Text": "8\ntan\u20131(1 5) ~ 56 3o\nRationalised 2023-24\n351\nAnswers\n10 9\n5000 \u00c5, 6 \u00d7 1014 Hz; 45\u00b0\n10" + }, + { + "Chapter": "9", + "sentence_range": "3996-3999", + "Text": "5) ~ 56 3o\nRationalised 2023-24\n351\nAnswers\n10 9\n5000 \u00c5, 6 \u00d7 1014 Hz; 45\u00b0\n10 10 40 m\nCHAPTER 11\n11" + }, + { + "Chapter": "9", + "sentence_range": "3997-4000", + "Text": "3o\nRationalised 2023-24\n351\nAnswers\n10 9\n5000 \u00c5, 6 \u00d7 1014 Hz; 45\u00b0\n10 10 40 m\nCHAPTER 11\n11 1\n(a)\n7" + }, + { + "Chapter": "9", + "sentence_range": "3998-4001", + "Text": "9\n5000 \u00c5, 6 \u00d7 1014 Hz; 45\u00b0\n10 10 40 m\nCHAPTER 11\n11 1\n(a)\n7 24 \u00d7 1018 Hz (b) 0" + }, + { + "Chapter": "9", + "sentence_range": "3999-4002", + "Text": "10 40 m\nCHAPTER 11\n11 1\n(a)\n7 24 \u00d7 1018 Hz (b) 0 041 nm\n11" + }, + { + "Chapter": "9", + "sentence_range": "4000-4003", + "Text": "1\n(a)\n7 24 \u00d7 1018 Hz (b) 0 041 nm\n11 2\n(a)\n0" + }, + { + "Chapter": "9", + "sentence_range": "4001-4004", + "Text": "24 \u00d7 1018 Hz (b) 0 041 nm\n11 2\n(a)\n0 34 eV = 0" + }, + { + "Chapter": "9", + "sentence_range": "4002-4005", + "Text": "041 nm\n11 2\n(a)\n0 34 eV = 0 54 \u00d7 10\u201319J (b) 0" + }, + { + "Chapter": "9", + "sentence_range": "4003-4006", + "Text": "2\n(a)\n0 34 eV = 0 54 \u00d7 10\u201319J (b) 0 34 V (c) 344 km/s\n11" + }, + { + "Chapter": "9", + "sentence_range": "4004-4007", + "Text": "34 eV = 0 54 \u00d7 10\u201319J (b) 0 34 V (c) 344 km/s\n11 3\n1" + }, + { + "Chapter": "9", + "sentence_range": "4005-4008", + "Text": "54 \u00d7 10\u201319J (b) 0 34 V (c) 344 km/s\n11 3\n1 5 eV = 2" + }, + { + "Chapter": "9", + "sentence_range": "4006-4009", + "Text": "34 V (c) 344 km/s\n11 3\n1 5 eV = 2 4 \u00d7 10\u201319 J\n11" + }, + { + "Chapter": "9", + "sentence_range": "4007-4010", + "Text": "3\n1 5 eV = 2 4 \u00d7 10\u201319 J\n11 4\n(a)\n3" + }, + { + "Chapter": "9", + "sentence_range": "4008-4011", + "Text": "5 eV = 2 4 \u00d7 10\u201319 J\n11 4\n(a)\n3 14 \u00d7 10\u201319J, 1" + }, + { + "Chapter": "9", + "sentence_range": "4009-4012", + "Text": "4 \u00d7 10\u201319 J\n11 4\n(a)\n3 14 \u00d7 10\u201319J, 1 05 \u00d7 10\u201327 kg m/s (b) 3 \u00d7 1016 photons/s\n(c) 0" + }, + { + "Chapter": "9", + "sentence_range": "4010-4013", + "Text": "4\n(a)\n3 14 \u00d7 10\u201319J, 1 05 \u00d7 10\u201327 kg m/s (b) 3 \u00d7 1016 photons/s\n(c) 0 63 m/s\n11" + }, + { + "Chapter": "9", + "sentence_range": "4011-4014", + "Text": "14 \u00d7 10\u201319J, 1 05 \u00d7 10\u201327 kg m/s (b) 3 \u00d7 1016 photons/s\n(c) 0 63 m/s\n11 5\n6" + }, + { + "Chapter": "9", + "sentence_range": "4012-4015", + "Text": "05 \u00d7 10\u201327 kg m/s (b) 3 \u00d7 1016 photons/s\n(c) 0 63 m/s\n11 5\n6 59 \u00d7 10\u201334 J s\n11" + }, + { + "Chapter": "9", + "sentence_range": "4013-4016", + "Text": "63 m/s\n11 5\n6 59 \u00d7 10\u201334 J s\n11 6\n2" + }, + { + "Chapter": "9", + "sentence_range": "4014-4017", + "Text": "5\n6 59 \u00d7 10\u201334 J s\n11 6\n2 0 V\n11" + }, + { + "Chapter": "9", + "sentence_range": "4015-4018", + "Text": "59 \u00d7 10\u201334 J s\n11 6\n2 0 V\n11 7\nNo, because n < no\n11" + }, + { + "Chapter": "9", + "sentence_range": "4016-4019", + "Text": "6\n2 0 V\n11 7\nNo, because n < no\n11 8\n4" + }, + { + "Chapter": "9", + "sentence_range": "4017-4020", + "Text": "0 V\n11 7\nNo, because n < no\n11 8\n4 73 \u00d7 1014 Hz\n11" + }, + { + "Chapter": "9", + "sentence_range": "4018-4021", + "Text": "7\nNo, because n < no\n11 8\n4 73 \u00d7 1014 Hz\n11 9\n2" + }, + { + "Chapter": "9", + "sentence_range": "4019-4022", + "Text": "8\n4 73 \u00d7 1014 Hz\n11 9\n2 16 eV = 3" + }, + { + "Chapter": "9", + "sentence_range": "4020-4023", + "Text": "73 \u00d7 1014 Hz\n11 9\n2 16 eV = 3 46 \u00d7 10\u201319J\n11" + }, + { + "Chapter": "9", + "sentence_range": "4021-4024", + "Text": "9\n2 16 eV = 3 46 \u00d7 10\u201319J\n11 10 (a)\n1" + }, + { + "Chapter": "9", + "sentence_range": "4022-4025", + "Text": "16 eV = 3 46 \u00d7 10\u201319J\n11 10 (a)\n1 7 \u00d7 10\u201335 m (b) 1" + }, + { + "Chapter": "9", + "sentence_range": "4023-4026", + "Text": "46 \u00d7 10\u201319J\n11 10 (a)\n1 7 \u00d7 10\u201335 m (b) 1 1 \u00d7 10\u201332 m (c) 3" + }, + { + "Chapter": "9", + "sentence_range": "4024-4027", + "Text": "10 (a)\n1 7 \u00d7 10\u201335 m (b) 1 1 \u00d7 10\u201332 m (c) 3 0 \u00d7 10\u201323 m\n11" + }, + { + "Chapter": "9", + "sentence_range": "4025-4028", + "Text": "7 \u00d7 10\u201335 m (b) 1 1 \u00d7 10\u201332 m (c) 3 0 \u00d7 10\u201323 m\n11 11 l = h/p = h/(hn/c) = c/n\nCHAPTER 12\n12" + }, + { + "Chapter": "9", + "sentence_range": "4026-4029", + "Text": "1 \u00d7 10\u201332 m (c) 3 0 \u00d7 10\u201323 m\n11 11 l = h/p = h/(hn/c) = c/n\nCHAPTER 12\n12 1\n(a) No different from\n(b) Thomson\u2019s model; Rutherford\u2019s model\n(c) Rutherford\u2019s model\n(d) Thomson\u2019s model; Rutherford\u2019s model\n(e) Both the models\n12" + }, + { + "Chapter": "9", + "sentence_range": "4027-4030", + "Text": "0 \u00d7 10\u201323 m\n11 11 l = h/p = h/(hn/c) = c/n\nCHAPTER 12\n12 1\n(a) No different from\n(b) Thomson\u2019s model; Rutherford\u2019s model\n(c) Rutherford\u2019s model\n(d) Thomson\u2019s model; Rutherford\u2019s model\n(e) Both the models\n12 2\nThe nucleus of a hydrogen atom is a proton" + }, + { + "Chapter": "9", + "sentence_range": "4028-4031", + "Text": "11 l = h/p = h/(hn/c) = c/n\nCHAPTER 12\n12 1\n(a) No different from\n(b) Thomson\u2019s model; Rutherford\u2019s model\n(c) Rutherford\u2019s model\n(d) Thomson\u2019s model; Rutherford\u2019s model\n(e) Both the models\n12 2\nThe nucleus of a hydrogen atom is a proton The mass of it is\n1" + }, + { + "Chapter": "9", + "sentence_range": "4029-4032", + "Text": "1\n(a) No different from\n(b) Thomson\u2019s model; Rutherford\u2019s model\n(c) Rutherford\u2019s model\n(d) Thomson\u2019s model; Rutherford\u2019s model\n(e) Both the models\n12 2\nThe nucleus of a hydrogen atom is a proton The mass of it is\n1 67 \u00d7 10\u201327 kg, whereas the mass of an incident a-particle is\n6" + }, + { + "Chapter": "9", + "sentence_range": "4030-4033", + "Text": "2\nThe nucleus of a hydrogen atom is a proton The mass of it is\n1 67 \u00d7 10\u201327 kg, whereas the mass of an incident a-particle is\n6 64 \u00d7 10\u201327 kg" + }, + { + "Chapter": "9", + "sentence_range": "4031-4034", + "Text": "The mass of it is\n1 67 \u00d7 10\u201327 kg, whereas the mass of an incident a-particle is\n6 64 \u00d7 10\u201327 kg Because the scattering particle is more massive than\nthe target nuclei (proton), the a-particle won\u2019t bounce back in even\nin a head-on collision" + }, + { + "Chapter": "9", + "sentence_range": "4032-4035", + "Text": "67 \u00d7 10\u201327 kg, whereas the mass of an incident a-particle is\n6 64 \u00d7 10\u201327 kg Because the scattering particle is more massive than\nthe target nuclei (proton), the a-particle won\u2019t bounce back in even\nin a head-on collision It is similar to a football colliding with a tenis\nball at rest" + }, + { + "Chapter": "9", + "sentence_range": "4033-4036", + "Text": "64 \u00d7 10\u201327 kg Because the scattering particle is more massive than\nthe target nuclei (proton), the a-particle won\u2019t bounce back in even\nin a head-on collision It is similar to a football colliding with a tenis\nball at rest Thus, there would be no large-angle scattering" + }, + { + "Chapter": "9", + "sentence_range": "4034-4037", + "Text": "Because the scattering particle is more massive than\nthe target nuclei (proton), the a-particle won\u2019t bounce back in even\nin a head-on collision It is similar to a football colliding with a tenis\nball at rest Thus, there would be no large-angle scattering 12" + }, + { + "Chapter": "9", + "sentence_range": "4035-4038", + "Text": "It is similar to a football colliding with a tenis\nball at rest Thus, there would be no large-angle scattering 12 3\n5" + }, + { + "Chapter": "9", + "sentence_range": "4036-4039", + "Text": "Thus, there would be no large-angle scattering 12 3\n5 6 \u00b4 1014 Hz\n12" + }, + { + "Chapter": "9", + "sentence_range": "4037-4040", + "Text": "12 3\n5 6 \u00b4 1014 Hz\n12 4\n13" + }, + { + "Chapter": "9", + "sentence_range": "4038-4041", + "Text": "3\n5 6 \u00b4 1014 Hz\n12 4\n13 6 eV; \u201327" + }, + { + "Chapter": "9", + "sentence_range": "4039-4042", + "Text": "6 \u00b4 1014 Hz\n12 4\n13 6 eV; \u201327 2 eV\n12" + }, + { + "Chapter": "9", + "sentence_range": "4040-4043", + "Text": "4\n13 6 eV; \u201327 2 eV\n12 5\n9" + }, + { + "Chapter": "9", + "sentence_range": "4041-4044", + "Text": "6 eV; \u201327 2 eV\n12 5\n9 7 \u00d7 10 \u2013 8 m; 3" + }, + { + "Chapter": "9", + "sentence_range": "4042-4045", + "Text": "2 eV\n12 5\n9 7 \u00d7 10 \u2013 8 m; 3 1 \u00d7 1015 Hz" + }, + { + "Chapter": "9", + "sentence_range": "4043-4046", + "Text": "5\n9 7 \u00d7 10 \u2013 8 m; 3 1 \u00d7 1015 Hz 12" + }, + { + "Chapter": "9", + "sentence_range": "4044-4047", + "Text": "7 \u00d7 10 \u2013 8 m; 3 1 \u00d7 1015 Hz 12 6\n(a) 2" + }, + { + "Chapter": "9", + "sentence_range": "4045-4048", + "Text": "1 \u00d7 1015 Hz 12 6\n(a) 2 18 \u00d7 106 m/s; 1" + }, + { + "Chapter": "9", + "sentence_range": "4046-4049", + "Text": "12 6\n(a) 2 18 \u00d7 106 m/s; 1 09 \u00d7 106 m/s; 7" + }, + { + "Chapter": "9", + "sentence_range": "4047-4050", + "Text": "6\n(a) 2 18 \u00d7 106 m/s; 1 09 \u00d7 106 m/s; 7 27 \u00d7 105 m/s\n(b) 1" + }, + { + "Chapter": "9", + "sentence_range": "4048-4051", + "Text": "18 \u00d7 106 m/s; 1 09 \u00d7 106 m/s; 7 27 \u00d7 105 m/s\n(b) 1 52 \u00d7 10\u201316 s; 1" + }, + { + "Chapter": "9", + "sentence_range": "4049-4052", + "Text": "09 \u00d7 106 m/s; 7 27 \u00d7 105 m/s\n(b) 1 52 \u00d7 10\u201316 s; 1 22 \u00d7 10\u201315 s; 4" + }, + { + "Chapter": "9", + "sentence_range": "4050-4053", + "Text": "27 \u00d7 105 m/s\n(b) 1 52 \u00d7 10\u201316 s; 1 22 \u00d7 10\u201315 s; 4 11 \u00d7 10\u201315 s" + }, + { + "Chapter": "9", + "sentence_range": "4051-4054", + "Text": "52 \u00d7 10\u201316 s; 1 22 \u00d7 10\u201315 s; 4 11 \u00d7 10\u201315 s 12" + }, + { + "Chapter": "9", + "sentence_range": "4052-4055", + "Text": "22 \u00d7 10\u201315 s; 4 11 \u00d7 10\u201315 s 12 7\n2" + }, + { + "Chapter": "9", + "sentence_range": "4053-4056", + "Text": "11 \u00d7 10\u201315 s 12 7\n2 12\u00b410\u201310 m; 4" + }, + { + "Chapter": "9", + "sentence_range": "4054-4057", + "Text": "12 7\n2 12\u00b410\u201310 m; 4 77 \u00b4 10\u201310 m\n12" + }, + { + "Chapter": "9", + "sentence_range": "4055-4058", + "Text": "7\n2 12\u00b410\u201310 m; 4 77 \u00b4 10\u201310 m\n12 8\nLyman series: 103 nm and 122 nm; Balmer series: 656 nm" + }, + { + "Chapter": "9", + "sentence_range": "4056-4059", + "Text": "12\u00b410\u201310 m; 4 77 \u00b4 10\u201310 m\n12 8\nLyman series: 103 nm and 122 nm; Balmer series: 656 nm 12" + }, + { + "Chapter": "9", + "sentence_range": "4057-4060", + "Text": "77 \u00b4 10\u201310 m\n12 8\nLyman series: 103 nm and 122 nm; Balmer series: 656 nm 12 9\n2" + }, + { + "Chapter": "9", + "sentence_range": "4058-4061", + "Text": "8\nLyman series: 103 nm and 122 nm; Balmer series: 656 nm 12 9\n2 6 \u00d7 1074\nCHAPTER 13\n13" + }, + { + "Chapter": "9", + "sentence_range": "4059-4062", + "Text": "12 9\n2 6 \u00d7 1074\nCHAPTER 13\n13 1\n104" + }, + { + "Chapter": "9", + "sentence_range": "4060-4063", + "Text": "9\n2 6 \u00d7 1074\nCHAPTER 13\n13 1\n104 7 MeV\n13" + }, + { + "Chapter": "9", + "sentence_range": "4061-4064", + "Text": "6 \u00d7 1074\nCHAPTER 13\n13 1\n104 7 MeV\n13 2\n8" + }, + { + "Chapter": "9", + "sentence_range": "4062-4065", + "Text": "1\n104 7 MeV\n13 2\n8 79 MeV, 7" + }, + { + "Chapter": "9", + "sentence_range": "4063-4066", + "Text": "7 MeV\n13 2\n8 79 MeV, 7 84 MeV\n13" + }, + { + "Chapter": "9", + "sentence_range": "4064-4067", + "Text": "2\n8 79 MeV, 7 84 MeV\n13 3\n1" + }, + { + "Chapter": "9", + "sentence_range": "4065-4068", + "Text": "79 MeV, 7 84 MeV\n13 3\n1 584 \u00d7 1025 MeV or 2" + }, + { + "Chapter": "9", + "sentence_range": "4066-4069", + "Text": "84 MeV\n13 3\n1 584 \u00d7 1025 MeV or 2 535\u00d71012J\n13" + }, + { + "Chapter": "9", + "sentence_range": "4067-4070", + "Text": "3\n1 584 \u00d7 1025 MeV or 2 535\u00d71012J\n13 4\n1" + }, + { + "Chapter": "9", + "sentence_range": "4068-4071", + "Text": "584 \u00d7 1025 MeV or 2 535\u00d71012J\n13 4\n1 23\nRationalised 2023-24\n352\nPhysics\n13" + }, + { + "Chapter": "9", + "sentence_range": "4069-4072", + "Text": "535\u00d71012J\n13 4\n1 23\nRationalised 2023-24\n352\nPhysics\n13 5\n(i) Q = \u20134" + }, + { + "Chapter": "9", + "sentence_range": "4070-4073", + "Text": "4\n1 23\nRationalised 2023-24\n352\nPhysics\n13 5\n(i) Q = \u20134 03 MeV; endothermic\n(ii) Q = 4" + }, + { + "Chapter": "9", + "sentence_range": "4071-4074", + "Text": "23\nRationalised 2023-24\n352\nPhysics\n13 5\n(i) Q = \u20134 03 MeV; endothermic\n(ii) Q = 4 62 MeV; exothermic\n13" + }, + { + "Chapter": "9", + "sentence_range": "4072-4075", + "Text": "5\n(i) Q = \u20134 03 MeV; endothermic\n(ii) Q = 4 62 MeV; exothermic\n13 6\nQ = \n(\n)\n(\n)\n56\n28\n26\n13\nFe \u2013 2\nAl\nm\nm\n= 26" + }, + { + "Chapter": "9", + "sentence_range": "4073-4076", + "Text": "03 MeV; endothermic\n(ii) Q = 4 62 MeV; exothermic\n13 6\nQ = \n(\n)\n(\n)\n56\n28\n26\n13\nFe \u2013 2\nAl\nm\nm\n= 26 90 MeV; not possible" + }, + { + "Chapter": "9", + "sentence_range": "4074-4077", + "Text": "62 MeV; exothermic\n13 6\nQ = \n(\n)\n(\n)\n56\n28\n26\n13\nFe \u2013 2\nAl\nm\nm\n= 26 90 MeV; not possible 13" + }, + { + "Chapter": "9", + "sentence_range": "4075-4078", + "Text": "6\nQ = \n(\n)\n(\n)\n56\n28\n26\n13\nFe \u2013 2\nAl\nm\nm\n= 26 90 MeV; not possible 13 7\n4" + }, + { + "Chapter": "9", + "sentence_range": "4076-4079", + "Text": "90 MeV; not possible 13 7\n4 536 \u00d7 1026 MeV\n13" + }, + { + "Chapter": "9", + "sentence_range": "4077-4080", + "Text": "13 7\n4 536 \u00d7 1026 MeV\n13 8\nAbout 4" + }, + { + "Chapter": "9", + "sentence_range": "4078-4081", + "Text": "7\n4 536 \u00d7 1026 MeV\n13 8\nAbout 4 9 \u00d7 104 y\n13" + }, + { + "Chapter": "9", + "sentence_range": "4079-4082", + "Text": "536 \u00d7 1026 MeV\n13 8\nAbout 4 9 \u00d7 104 y\n13 9\n360 KeV\nCHAPTER 14\n14" + }, + { + "Chapter": "9", + "sentence_range": "4080-4083", + "Text": "8\nAbout 4 9 \u00d7 104 y\n13 9\n360 KeV\nCHAPTER 14\n14 1\n(c)\n14" + }, + { + "Chapter": "9", + "sentence_range": "4081-4084", + "Text": "9 \u00d7 104 y\n13 9\n360 KeV\nCHAPTER 14\n14 1\n(c)\n14 2\n(d)\n14" + }, + { + "Chapter": "9", + "sentence_range": "4082-4085", + "Text": "9\n360 KeV\nCHAPTER 14\n14 1\n(c)\n14 2\n(d)\n14 3\n(c)\n14" + }, + { + "Chapter": "9", + "sentence_range": "4083-4086", + "Text": "1\n(c)\n14 2\n(d)\n14 3\n(c)\n14 4\n(c)\n14" + }, + { + "Chapter": "9", + "sentence_range": "4084-4087", + "Text": "2\n(d)\n14 3\n(c)\n14 4\n(c)\n14 5\n(c)\n14" + }, + { + "Chapter": "9", + "sentence_range": "4085-4088", + "Text": "3\n(c)\n14 4\n(c)\n14 5\n(c)\n14 6\n50 Hz for half-wave, 100 Hz for full-wave\nRationalised 2023-24\nBIBLIOGRAPHY\nTEXTBOOKS\nFor additional reading on the topics covered in this book, you may like to consult one or more of the following\nbooks" + }, + { + "Chapter": "9", + "sentence_range": "4086-4089", + "Text": "4\n(c)\n14 5\n(c)\n14 6\n50 Hz for half-wave, 100 Hz for full-wave\nRationalised 2023-24\nBIBLIOGRAPHY\nTEXTBOOKS\nFor additional reading on the topics covered in this book, you may like to consult one or more of the following\nbooks Some of these books however are more advanced and contain many more topics than this book" + }, + { + "Chapter": "9", + "sentence_range": "4087-4090", + "Text": "5\n(c)\n14 6\n50 Hz for half-wave, 100 Hz for full-wave\nRationalised 2023-24\nBIBLIOGRAPHY\nTEXTBOOKS\nFor additional reading on the topics covered in this book, you may like to consult one or more of the following\nbooks Some of these books however are more advanced and contain many more topics than this book 1\nOrdinary Level Physics, A" + }, + { + "Chapter": "9", + "sentence_range": "4088-4091", + "Text": "6\n50 Hz for half-wave, 100 Hz for full-wave\nRationalised 2023-24\nBIBLIOGRAPHY\nTEXTBOOKS\nFor additional reading on the topics covered in this book, you may like to consult one or more of the following\nbooks Some of these books however are more advanced and contain many more topics than this book 1\nOrdinary Level Physics, A F" + }, + { + "Chapter": "9", + "sentence_range": "4089-4092", + "Text": "Some of these books however are more advanced and contain many more topics than this book 1\nOrdinary Level Physics, A F Abbott, Arnold-Heinemann (1984)" + }, + { + "Chapter": "9", + "sentence_range": "4090-4093", + "Text": "1\nOrdinary Level Physics, A F Abbott, Arnold-Heinemann (1984) 2\nAdvanced Level Physics, M" + }, + { + "Chapter": "9", + "sentence_range": "4091-4094", + "Text": "F Abbott, Arnold-Heinemann (1984) 2\nAdvanced Level Physics, M Nelkon and P" + }, + { + "Chapter": "9", + "sentence_range": "4092-4095", + "Text": "Abbott, Arnold-Heinemann (1984) 2\nAdvanced Level Physics, M Nelkon and P Parker, 6th Edition, Arnold-Heinemann (1987)" + }, + { + "Chapter": "9", + "sentence_range": "4093-4096", + "Text": "2\nAdvanced Level Physics, M Nelkon and P Parker, 6th Edition, Arnold-Heinemann (1987) 3\nAdvanced Physics, Tom Duncan, John Murray (2000)" + }, + { + "Chapter": "9", + "sentence_range": "4094-4097", + "Text": "Nelkon and P Parker, 6th Edition, Arnold-Heinemann (1987) 3\nAdvanced Physics, Tom Duncan, John Murray (2000) 4\nFundamentals of Physics, David Halliday, Robert Resnick and Jearl Walker, 7th Edition\nJohn Wily (2004)" + }, + { + "Chapter": "9", + "sentence_range": "4095-4098", + "Text": "Parker, 6th Edition, Arnold-Heinemann (1987) 3\nAdvanced Physics, Tom Duncan, John Murray (2000) 4\nFundamentals of Physics, David Halliday, Robert Resnick and Jearl Walker, 7th Edition\nJohn Wily (2004) 5\nUniversity Physics (Sears and Zemansky\u2019s), H" + }, + { + "Chapter": "9", + "sentence_range": "4096-4099", 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Benson, John Wiley (1996) 19 University Physics, William P Crummet and Arthur B" + }, + { + "Chapter": "9", + "sentence_range": "4156-4159", + "Text": "18 University Physics, Harris Benson, John Wiley (1996) 19 University Physics, William P Crummet and Arthur B Western, Wm" + }, + { + "Chapter": "9", + "sentence_range": "4157-4160", + "Text": "19 University Physics, William P Crummet and Arthur B Western, Wm C" + }, + { + "Chapter": "9", + "sentence_range": "4158-4161", + "Text": "Crummet and Arthur B Western, Wm C Brown (1994)" + }, + { + "Chapter": "9", + "sentence_range": "4159-4162", + "Text": "Western, Wm C Brown (1994) 20 General Physics, Morton M" + }, + { + "Chapter": "9", + "sentence_range": "4160-4163", + "Text": "C Brown (1994) 20 General Physics, Morton M Sternheim and Joseph W" + }, + { + "Chapter": "9", + "sentence_range": "4161-4164", + "Text": "Brown (1994) 20 General Physics, Morton M Sternheim and Joseph W Kane, John Wiley (1988)" + }, + { + "Chapter": "9", + "sentence_range": "4162-4165", + "Text": "20 General Physics, Morton M Sternheim and Joseph W Kane, John Wiley (1988) 21 Physics, Hans C" + }, + { + "Chapter": "9", + "sentence_range": "4163-4166", + "Text": "Sternheim and Joseph W Kane, John Wiley (1988) 21 Physics, Hans C Ohanian, W" + }, + { + "Chapter": "9", + "sentence_range": "4164-4167", + "Text": "Kane, John Wiley (1988) 21 Physics, Hans C Ohanian, W W" + }, + { + "Chapter": "9", + "sentence_range": "4165-4168", + "Text": "21 Physics, Hans C Ohanian, W W Norton (1989)" + }, + { + "Chapter": "9", + "sentence_range": "4166-4169", + "Text": "Ohanian, W W Norton (1989) Bibligraphy\nRationalised 2023-24\n22 Advanced Physics, Keith Gibbs, Cambridge University Press (1996)" + }, + { + "Chapter": "9", + "sentence_range": "4167-4170", + "Text": "W Norton (1989) Bibligraphy\nRationalised 2023-24\n22 Advanced Physics, Keith Gibbs, Cambridge University Press (1996) 23 Understanding Basic Mechanics, F" + }, + { + "Chapter": "9", + "sentence_range": "4168-4171", + "Text": "Norton (1989) Bibligraphy\nRationalised 2023-24\n22 Advanced Physics, Keith Gibbs, Cambridge University Press (1996) 23 Understanding Basic Mechanics, F Reif, John Wiley (1995)" + }, + { + "Chapter": "9", + "sentence_range": "4169-4172", + "Text": "Bibligraphy\nRationalised 2023-24\n22 Advanced Physics, Keith Gibbs, Cambridge University Press (1996) 23 Understanding Basic Mechanics, F Reif, John Wiley (1995) 24 College Physics, Jerry D" + }, + { + "Chapter": "9", + "sentence_range": "4170-4173", + "Text": "23 Understanding Basic Mechanics, F Reif, John Wiley (1995) 24 College Physics, Jerry D Wilson and Anthony J" + }, + { + "Chapter": "9", + "sentence_range": "4171-4174", + "Text": "Reif, John Wiley (1995) 24 College Physics, Jerry D Wilson and Anthony J Buffa, Prentice Hall (1997)" + }, + { + "Chapter": "9", + "sentence_range": "4172-4175", + "Text": "24 College Physics, Jerry D Wilson and Anthony J Buffa, Prentice Hall (1997) 25 Senior Physics, Part \u2013 I, I" + }, + { + "Chapter": "9", + "sentence_range": "4173-4176", + "Text": "Wilson and Anthony J Buffa, Prentice Hall (1997) 25 Senior Physics, Part \u2013 I, I K" + }, + { + "Chapter": "9", + "sentence_range": "4174-4177", + "Text": "Buffa, Prentice Hall (1997) 25 Senior Physics, Part \u2013 I, I K Kikoin and A" + }, + { + "Chapter": "9", + "sentence_range": "4175-4178", + "Text": "25 Senior Physics, Part \u2013 I, I K Kikoin and A K" + }, + { + "Chapter": "9", + "sentence_range": "4176-4179", + "Text": "K Kikoin and A K Kikoin, MIR Publishers (1987)" + }, + { + "Chapter": "9", + "sentence_range": "4177-4180", + "Text": "Kikoin and A K Kikoin, MIR Publishers (1987) 26 Senior Physics, Part \u2013 II, B" + }, + { + "Chapter": "9", + "sentence_range": "4178-4181", + "Text": "K Kikoin, MIR Publishers (1987) 26 Senior Physics, Part \u2013 II, B Bekhovtsev, MIR Publishers (1988)" + }, + { + "Chapter": "9", + "sentence_range": "4179-4182", + "Text": "Kikoin, MIR Publishers (1987) 26 Senior Physics, Part \u2013 II, B Bekhovtsev, MIR Publishers (1988) 27 Understanding Physics, K" + }, + { + "Chapter": "9", + "sentence_range": "4180-4183", + "Text": "26 Senior Physics, Part \u2013 II, B Bekhovtsev, MIR Publishers (1988) 27 Understanding Physics, K Cummings, Patrick J" + }, + { + "Chapter": "9", + "sentence_range": "4181-4184", + "Text": "Bekhovtsev, MIR Publishers (1988) 27 Understanding Physics, K Cummings, Patrick J Cooney, Priscilla W" + }, + { + "Chapter": "9", + "sentence_range": "4182-4185", + "Text": "27 Understanding Physics, K Cummings, Patrick J Cooney, Priscilla W Laws and Edward F" + }, + { + "Chapter": "9", + "sentence_range": "4183-4186", + "Text": "Cummings, Patrick J Cooney, Priscilla W Laws and Edward F Redish, John Wiley (2005)" + }, + { + "Chapter": "9", + "sentence_range": "4184-4187", + "Text": "Cooney, Priscilla W Laws and Edward F Redish, John Wiley (2005) 28 Essentials of Physics, John D" + }, + { + "Chapter": "9", + "sentence_range": "4185-4188", + "Text": "Laws and Edward F Redish, John Wiley (2005) 28 Essentials of Physics, John D Cutnell and Kenneth W" + }, + { + "Chapter": "9", + "sentence_range": "4186-4189", + "Text": "Redish, John Wiley (2005) 28 Essentials of Physics, John D Cutnell and Kenneth W Johnson, John Wiley (2005)" + }, + { + "Chapter": "9", + "sentence_range": "4187-4190", + "Text": "28 Essentials of Physics, John D Cutnell and Kenneth W Johnson, John Wiley (2005) GENERAL BOOKS\nFor instructive and entertaining general reading on science, you may like to read some of the following books" + }, + { + "Chapter": "9", + "sentence_range": "4188-4191", + "Text": "Cutnell and Kenneth W Johnson, John Wiley (2005) GENERAL BOOKS\nFor instructive and entertaining general reading on science, you may like to read some of the following books Remember however, that many of these books are written at a level far beyond the level of the present book" + }, + { + "Chapter": "9", + "sentence_range": "4189-4192", + "Text": "Johnson, John Wiley (2005) GENERAL BOOKS\nFor instructive and entertaining general reading on science, you may like to read some of the following books Remember however, that many of these books are written at a level far beyond the level of the present book 1\nMr" + }, + { + "Chapter": "9", + "sentence_range": "4190-4193", + "Text": "GENERAL BOOKS\nFor instructive and entertaining general reading on science, you may like to read some of the following books Remember however, that many of these books are written at a level far beyond the level of the present book 1\nMr Tompkins in paperback, G" + }, + { + "Chapter": "9", + "sentence_range": "4191-4194", + "Text": "Remember however, that many of these books are written at a level far beyond the level of the present book 1\nMr Tompkins in paperback, G Gamow, Cambridge University Press (1967)" + }, + { + "Chapter": "9", + "sentence_range": "4192-4195", + "Text": "1\nMr Tompkins in paperback, G Gamow, Cambridge University Press (1967) 2\nThe Universe and Dr" + }, + { + "Chapter": "9", + "sentence_range": "4193-4196", + "Text": "Tompkins in paperback, G Gamow, Cambridge University Press (1967) 2\nThe Universe and Dr Einstein, C" + }, + { + "Chapter": "9", + "sentence_range": "4194-4197", + "Text": "Gamow, Cambridge University Press (1967) 2\nThe Universe and Dr Einstein, C Barnett, Time Inc" + }, + { + "Chapter": "9", + "sentence_range": "4195-4198", + "Text": "2\nThe Universe and Dr Einstein, C Barnett, Time Inc New York (1962)" + }, + { + "Chapter": "9", + "sentence_range": "4196-4199", + "Text": "Einstein, C Barnett, Time Inc New York (1962) 3\nThirty years that Shook Physics, G" + }, + { + "Chapter": "9", + "sentence_range": "4197-4200", + "Text": "Barnett, Time Inc New York (1962) 3\nThirty years that Shook Physics, G Gamow, Double Day, New York (1966)" + }, + { + "Chapter": "9", + "sentence_range": "4198-4201", + "Text": "New York (1962) 3\nThirty years that Shook Physics, G Gamow, Double Day, New York (1966) 4\nSurely You\u2019re Joking, Mr" + }, + { + "Chapter": "9", + "sentence_range": "4199-4202", + "Text": "3\nThirty years that Shook Physics, G Gamow, Double Day, New York (1966) 4\nSurely You\u2019re Joking, Mr Feynman, R" + }, + { + "Chapter": "9", + "sentence_range": "4200-4203", + "Text": "Gamow, Double Day, New York (1966) 4\nSurely You\u2019re Joking, Mr Feynman, R P" + }, + { + "Chapter": "9", + "sentence_range": "4201-4204", + "Text": "4\nSurely You\u2019re Joking, Mr Feynman, R P Feynman, Bantam books (1986)" + }, + { + "Chapter": "9", + "sentence_range": "4202-4205", + "Text": "Feynman, R P Feynman, Bantam books (1986) 5\nOne, Two, Three\u2026 Infinity, G" + }, + { + "Chapter": "9", + "sentence_range": "4203-4206", + "Text": "P Feynman, Bantam books (1986) 5\nOne, Two, Three\u2026 Infinity, G Gamow, Viking Inc" + }, + { + "Chapter": "9", + "sentence_range": "4204-4207", + "Text": "Feynman, Bantam books (1986) 5\nOne, Two, Three\u2026 Infinity, G Gamow, Viking Inc (1961)" + }, + { + "Chapter": "9", + "sentence_range": "4205-4208", + "Text": "5\nOne, Two, Three\u2026 Infinity, G Gamow, Viking Inc (1961) 6\nThe Meaning of Relativity, A" + }, + { + "Chapter": "9", + "sentence_range": "4206-4209", + "Text": "Gamow, Viking Inc (1961) 6\nThe Meaning of Relativity, A Einstein, (Indian Edition) Oxford and IBH Pub" + }, + { + "Chapter": "9", + "sentence_range": "4207-4210", + "Text": "(1961) 6\nThe Meaning of Relativity, A Einstein, (Indian Edition) Oxford and IBH Pub Co" + }, + { + "Chapter": "9", + "sentence_range": "4208-4211", + "Text": "6\nThe Meaning of Relativity, A Einstein, (Indian Edition) Oxford and IBH Pub Co (1965)" + }, + { + "Chapter": "9", + "sentence_range": "4209-4212", + "Text": "Einstein, (Indian Edition) Oxford and IBH Pub Co (1965) 7\nAtomic Theory and the Description of Nature, Niels Bohr, Cambridge (1934)" + }, + { + "Chapter": "9", + "sentence_range": "4210-4213", + "Text": "Co (1965) 7\nAtomic Theory and the Description of Nature, Niels Bohr, Cambridge (1934) 8\nThe Physical Principles of Quantum Theory, W" + }, + { + "Chapter": "9", + "sentence_range": "4211-4214", + "Text": "(1965) 7\nAtomic Theory and the Description of Nature, Niels Bohr, Cambridge (1934) 8\nThe Physical Principles of Quantum Theory, W Heisenberg, University of Chicago Press\n(1930)" + }, + { + "Chapter": "9", + "sentence_range": "4212-4215", + "Text": "7\nAtomic Theory and the Description of Nature, Niels Bohr, Cambridge (1934) 8\nThe Physical Principles of Quantum Theory, W Heisenberg, University of Chicago Press\n(1930) 9\nThe Physics\u2014Astronomy Frontier, F" + }, + { + "Chapter": "9", + "sentence_range": "4213-4216", + "Text": "8\nThe Physical Principles of Quantum Theory, W Heisenberg, University of Chicago Press\n(1930) 9\nThe Physics\u2014Astronomy Frontier, F Hoyle and J" + }, + { + "Chapter": "9", + "sentence_range": "4214-4217", + "Text": "Heisenberg, University of Chicago Press\n(1930) 9\nThe 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"sentence_range": "4227-4230", + "Text": "Kitaigorodski, MIR Publisher (1978) Book 1: Physical Bodies\nBook 2: Molecules\nBook 3: Electrons\nBook 4: Photons and Nuclei 12 Physics can be Fun, Y Perelman, MIR Publishers (1986)" + }, + { + "Chapter": "9", + "sentence_range": "4228-4231", + "Text": "Book 1: Physical Bodies\nBook 2: Molecules\nBook 3: Electrons\nBook 4: Photons and Nuclei 12 Physics can be Fun, Y Perelman, MIR Publishers (1986) 13 Power of Ten, Philip Morrison and Eames, W" + }, + { + "Chapter": "9", + "sentence_range": "4229-4232", + "Text": "12 Physics can be Fun, Y Perelman, MIR Publishers (1986) 13 Power of Ten, Philip Morrison and Eames, W H" + }, + { + "Chapter": "9", + "sentence_range": "4230-4233", + "Text": "Perelman, MIR Publishers (1986) 13 Power of Ten, Philip Morrison and Eames, W H Freeman (1985)" + }, + { + "Chapter": "9", + "sentence_range": "4231-4234", + "Text": "13 Power of Ten, Philip Morrison and Eames, W H Freeman (1985) 14 Physics in your Kitchen Lab" + }, + { + "Chapter": "9", + "sentence_range": "4232-4235", + "Text": "H Freeman (1985) 14 Physics in your Kitchen Lab , I" + }, + { + "Chapter": "9", + "sentence_range": "4233-4236", + "Text": "Freeman (1985) 14 Physics in your Kitchen Lab , I K" + }, + { + "Chapter": "9", + "sentence_range": "4234-4237", + "Text": "14 Physics in your Kitchen Lab , I K Kikoin, MIR Publishers (1985)" + }, + { + "Chapter": "9", + "sentence_range": "4235-4238", + "Text": ", I K Kikoin, MIR Publishers (1985) 15 How Things Work: The Physics of Everyday Life, Louis A" + }, + { + "Chapter": "9", + "sentence_range": "4236-4239", + "Text": "K Kikoin, MIR Publishers (1985) 15 How Things Work: The Physics of Everyday Life, Louis A Bloomfield, John Wiley (2005)" + }, + { + "Chapter": "9", + "sentence_range": "4237-4240", + "Text": "Kikoin, MIR Publishers (1985) 15 How Things Work: The Physics of Everyday Life, Louis A Bloomfield, John Wiley (2005) 16 Physics Matters: An Introduction to Conceptual Physics, James Trefil and Robert M" + }, + { + "Chapter": "9", + "sentence_range": "4238-4241", + "Text": "15 How Things Work: The Physics of Everyday Life, Louis A Bloomfield, John Wiley (2005) 16 Physics Matters: An Introduction to Conceptual Physics, James Trefil and Robert M Hazen, John Wiley (2004)" + }, + { + "Chapter": "9", + "sentence_range": "4239-4242", + "Text": "Bloomfield, John Wiley (2005) 16 Physics Matters: An Introduction to Conceptual Physics, James Trefil and Robert M Hazen, John Wiley (2004) Physics\n354\nRationalised 2023-24" + } +] \ No newline at end of file