romikgosai/squad_modified huggingface dataset:
Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (the approximate wavelength to which human eyes are most sensitive) has a frequency of 7014540000000000000♠540 THz (7014540000000000000♠540×1012 Hz). Each photon has an energy E = hf = 6981358000000000000♠3.58×10−19 J. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light compatible with everyday experience is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, NA ≈ 7023602200000000000♠6.022×1023 mol−1. The result is that green light of wavelength 555 nm has an energy of 7005216000000000000♠216 kJ/mol, a typical energy of everyday life.

Questions and answers:
['
Q: What are common things like furniture and stationary objects actually made of?
A: particles', '
Q: Which light wavelength is the human eye most sensitive to?
A: 555 nanometres', '
Q: What color of light is the human eye most sensitive to?
A: green', '
Q: What does the smallness of the Planck constant show?
A: the fact that everyday objects and systems are made of a large number of particles', '
Q: At about what wavelength of light are human eyes most sensitive?
A: 555 nanometres', '
Q: What frequency does green light with a wavelength of 555 nanmetres have?
A: 7014540000000000000♠540 THz', '
Q: How is the energy from one mole of photos computed?
A: by multiplying the photon energy by the Avogadro constant', '
Q: How much energy does a green light of wavelength 555 nm contain?
A: 7005216000000000000♠216 kJ/mol', '
Q: What is the wavelength of light to which human eyes are most sensitive?
A: 555 nanometres', '
Q: What is the frequency of the light to which the human eye is most sensitive?
A: 7014540000000000000♠540 THz', '
Q: What is the energy of a photon?
A: 6981358000000000000♠3.58×10−19 J', '
Q: How much energy is contained in the light to which human eyes are most sensitive?
A: 7005216000000000000♠216 kJ/mol']
In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

Questions and answers:
['
Q: What type of radiation was Planck studying in the late 19th century?
A: black-body', "
Q: How many years prior to Planck's study had the scientific community first discussed black body radiation?
A: forty", '
Q: What scientist first studied black body radiation?
A: Kirchhoff', '
Q: What is required for the electromagnetic field to come to thermal equilibrium?
A: hot atoms', '
Q: What does a hot object in equilibrium absorb as much as it emits?
A: light', '
Q: What was Planck studying in the last part of the nineteenth century?
A: the problem of black-body radiation', '
Q: Who posed the problem of black-body radiation?
A: Kirchhoff', '
Q: Cooler objects glow less than objects that are what?
A: hotter', '
Q: What does a black object do to any of the light that hits it?
A: it absorbs all the light', '
Q: What is maximized as a result of a black object absorbing all the light that hits it?
A: thermal light emission', '
Q: Planck studied what problem posed originally by Kirchhoff?
A: black-body radiation', '
Q: If an object is black, what is known about its thermal light emission?
A: its thermal light emission is maximized.', '
Q: What is known about the light absorption of a hot object in equilibrium with light?
A: absorbs just as much light as it emits', '
Q: Electromagnetic fields obey what laws?
A: laws of motion']
The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

Questions and answers:
['
Q: What do scientists assume black body radiation is?
A: thermal', '
Q: What kind of prediction does the assumption that black body radiation is thermal lead to?
A: accurate', "
Q: What type of changes in the light a hot object emits as the object's temperature changes?
A: colour", '
Q: What law describes the changes in light emitted by a hot object?
A: Stefan–Boltzmann law', '
Q: What assumption that black-body radiation is what leads to an accurate prediction?
A: thermal', '
Q: What does the Stefan-Boltzmann law state?
A: the total amount of emitted energy goes up with the temperature according to a definite rule', '
Q: What about a hot object changes with the temperature?
A: the colour of the light', '
Q: What color is hotter than "red hot"?
A: white hot', '
Q: What did Wilhelm Wien discover?
A: the mathematical relationship between the peaks of the curves at different temperatures', '
Q: What rule predicts that emitted energy increases with temperature?
A: the Stefan–Boltzmann law', '
Q: What characteristic of the light emitted by a hot object changes with temperature?
A: the colour of the light given off', '
Q: Who discovered the mathematical relationship between peaks and curves of light at different temperatures?
A: Wilhelm Wien', "
Q: The rule that adjust the curve at different temperatures is known as what?
A: Wien's displacement law", "
Q: Wien's spectrum model could not predict accurate at what end of the spectrum?
A: at low frequencies (long wavelength)"]
Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh–Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

Questions and answers:
['
Q: Before Planck, it was assumed that the energy of a body could take on what value?
A: any', '
Q: The Rayleigh-Jeans law makes close predictions for what amount of values?
A: a narrow range', "
Q: What does Planck's law correctly predict?
A: blackbody emissions", "
Q: In making Planck's law, what was in both the numerator and denominator of the formula that was used?
A: h", "
Q: Planck's work disproved what assumption?
A: that the energy of a body could take on any value whatsoever", '
Q: What rule predicted narrow range of energy values at lower temperatures?
A: The Rayleigh–Jeans', "
Q: Planck's law involved what necessary mathematical step to correctly predict blackbody emission?
A: multiply the classical expression by a complex factor that involves h in both the numerator and the denominator", "
Q: Changing values of n, the Boltzmann constant, or other variables resulted in learning what about Planck's law?
A: Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done", "
Q: The disparity between Planck's law and the Rayleigh-Jeans law led to what conclusion?
A: the picture given by classical physics is not duplicated by a range of results in the quantum picture"]
The black-body problem was revisited in 1905, when Rayleigh and Jeans (on the one hand) and Einstein (on the other hand) independently proved that classical electromagnetism could never account for the observed spectrum. These proofs are commonly known as the "ultraviolet catastrophe", a name coined by Paul Ehrenfest in 1911. They contributed greatly (along with Einstein's work on the photoelectric effect) to convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism. The very first Solvay Conference in 1911 was devoted to "the theory of radiation and quanta". Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".

Questions and answers:
['
Q: Einstein and what other two individuals revisited the black-body problem in 1905?
A: Rayleigh and Jeans', '
Q: Who came up with the term, "ultraviolet catastrophe"?
A: Paul Ehrenfest', '
Q: When did Paul Ehrenfest come up with the name "ultraviolet catastrophe"?
A: 1911', '
Q: When was the first Solvay Conference held?
A: 1911', '
Q: Who received the Nobel Prize in Physics in 1918?
A: Max Planck', '
Q: What did Rayleigh & Jeans and Einstein prove independently in 1905?
A: classical electromagnetism could never account for the observed spectrum', '
Q: What name did Paul Ehrenfest give to the proofs from Einstein and Rayleigh & Jeans?
A: the "ultraviolet catastrophe"', '
Q: When was the first Solvay Conference held?
A: 1911', '
Q: What was the topic of the first Solvay Conference?
A: "the theory of radiation and quanta"', '
Q: In what year did Planck receive the Nobel Prize in Physics for his discovery of energy quanta?
A: 1918']
The photoelectric effect is the emission of electrons (called "photoelectrons") from a surface when light is shone on it. It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887. Another particularly thorough investigation was published by Philipp Lenard in 1902. Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, when his predictions had been confirmed by the experimental work of Robert Andrews Millikan. The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.

Questions and answers:
['
Q: Who first observed the photoelectric effect?
A: Alexandre Edmond Becquerel', '
Q: When was the photoelectric effect first observed?
A: 1839', '
Q: Who published the first thorough investigation of the photoelectric effect?
A: Heinrich Hertz', '
Q: Who received the Nobel Prize in 1921 for his work on the photoelectric effect?
A: Einstein', '
Q: What did Einstein with the 1921 Nobel Prize for?
A: his work on the photo-electric effect', '
Q: What is the photoelectric effect?
A: the emission of electrons (called "photoelectrons") from a surface when light is shone on it', '
Q: Who first observed the photoelectric effect?
A: Alexandre Edmond Becquerel', "
Q: Einstein's paper on the photoelectric effect earned him the Nobel Prize in what year?
A: 1921", "
Q: Einstein's photoelectric effect work was rewards as opposed to his work on what other topic?
A: relativity"]
Prior to Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms "frequency" and "wavelength" to characterise different types of radiation. The energy transferred by a wave in a given time is called its intensity. The light from a theatre spotlight is more intense than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space(and hence consumes more electricity) than the ordinary bulb, even though the colour of the light might be very similar. Other waves, such as sound or the waves crashing against a seafront, also have their own intensity. However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.

Questions and answers:
['
Q: Before Einstein, electromagnetic radiation was considered to behave as what?
A: a wave', '
Q: What terms describe different types of radiation?
A: "frequency" and "wavelength"', '
Q: What other types of wave besides light has its own intensity?
A: sound', '
Q: What is the energy transferred by a wave in a given time called?
A: intensity', "
Q: Prior to Einstein's work, light behavior was modeled as what?
A: a wave", '
Q: What is the name for the amount of energy transfered by a wave in a given time?
A: intensity', '
Q: What portion of the photoelectric effect was in disagreement with the believed description of light behavior?
A: the energy account', '
Q: What does it mean for a light source to be more intense than another?
A: gives out more energy per unit time and per unit space']
The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect)  Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.

Questions and answers:
['
Q: What is emitted as a result of the photoelectric effect?
A: photoelectrons', '
Q: What does the kinetic energy of a photoelectron depend on?
A: the frequency', "
Q: What happens if the photoelectron's frequency is too low?
A: no photoelectrons are emitted at all", '
Q: What is the term used when photoelectrons act virtually at the same time?
A: multiphoton effect', '
Q: What type of energy due photoelectrons emitted due to the photoelectric effect have?
A: kinetic', '
Q: What factor of the initial light source does the energy of the photoelectrons depend on?
A: frequency', '
Q: When the photon energy is less than the work function of the material the light is shone upon, how many photoelectrons are emitted?
A: no photoelectrons are emitted at all', '
Q: If the photoelectric effect is occuring, increasing the intensity of the light source causes what?
A: more photoelectrons to be emitted with the same kinetic energy']
Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies En

Questions and answers:
['
Q: Who introduced the first quantized model of the atom?
A: Niels Bohr', '
Q: When was the first quantized model of the atom introduced?
A: 1913', "
Q: Why was the first quantized model of the atom introduced?
A: to overcome a major shortcoming of Rutherford's classical model", '
Q: In classical electrodynamics, a charge moving in a circle should do what?
A: radiate electromagnetic radiation', "
Q: Who modeled the atom in 1913, challenging Rutherford's model?
A: Niels Bohr", "
Q: What was predicted to happen to a nucleus-orbiting electron under Rutherford's model?
A: the radiation would cause it to lose energy and spiral down into the nucleus", "
Q: What statement did Bohr make about the electron of an atom, citing Planck's work?
A: an electron in a Bohr atom could only have certain defined energies"]
Bohr also introduced the quantity , now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction, these quantities can only take on the values

Questions and answers:
['
Q: Who introduced the reduced Planck constant?
A: Bohr', '
Q: What is the reduced Planck constant also known as?
A: the quantity', '
Q: Who helped to give the correct quantization rules for electrons in 1925?
A: Heisenberg', '
Q: Who helped to give the correct quantization rules for electrons in 1926?
A: Schrödinger', '
Q: According to Heisenberg and Schrödinger, the reduced Planck constant remains what?
A: the fundamental quantum of angular momentum', '
Q: Bohr introduced what value as the quantum of angular momentum?
A: the reduced Planck constant', '
Q: What incorrect belief did Bohr hold about the reduced Planck constant?
A: Bohr thought that this was the angular momentum of each electron in an atom', '
Q: What scientist used matrix mechanics to bring electron behavior in line with the Bohr model?
A: Heisenberg', '
Q: When was the Schrödinger wave equation proposed?
A: 1926']
where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

Questions and answers:
['
Q:  What measurable value obeys a similar rule of angular momentum?
A: time vs. energy', '
Q: What forces measurement attempts to choose between trade-offs, in quanta?
A: either-or nature of uncertainty', '
Q: What form do measurement attempt trade-offs for quanta take the form of?
A: either-or (as in Fourier analysis)', '
Q: How is uncertainly measured in this experience?
A: the standard deviation of the measured value from its expected value', '
Q: What type of analysis fits the either-or nature of the uncertainty?
A: Fourier analysis', '
Q: What example is given as another paired relationship of uncertainly related to standard deviation?
A: time vs. energy']
The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h1/2 (r2 > 0.995) can be found by expanding the variables.

Questions and answers:
['
Q: What is the unit of magentic properties of the electron?
A: Bohr magneton', '
Q: What is the unit of magentic properties of atomic nuclei?
A: nuclear magneton', '
Q: The Bohr magneton is the magnetic moment of an electron under what restriction?
A: behaved as a spinning charge according to classical electrodynamics', '
Q: What three terms define the Bohr magneton value?
A: the reduced Planck constant, the elementary charge and the electron mass']
In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

Questions and answers:
['
Q: How was the Planck constant calculated in the early 20th century?
A: the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons', '
Q: The value quoted here for the Planck constant is based on a measurement in what year?
A: 2007', '
Q: Where was this measurement made?
A: the U.S. National Institute of Standards and Technology (NIST)', '
Q: What method was was used to obtain the measurement?
A: watt-balance measurement', '
Q: One other measure involved the molar volume of what element?
A: silicon']
There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being there is no indication which method is at fault.

Questions and answers:
['
Q: What is a main practical difficulty in determining n?
A: the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another', '
Q: Why does this difficulty occur?
A: it is (or they are) not as precise as is currently believed', '
Q: Which method is at fault or the discrepancy?
A: there is no indication which method is at fault']