nc33/MultiSpan_SQUAD huggingface dataset:
Planck_constant

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.

Question: What type of radiation was Planck studying in the late 19th century?
Answer: black-body

Question: How many years prior to Planck's study had the scientific community first discussed black body radiation?
Answer: forty

Question: What scientist first studied black body radiation?
Answer: Kirchhoff

Question: What is required for the electromagnetic field to come to thermal equilibrium?
Answer: hot atoms

Question: What does a hot object in equilibrium absorb as much as it emits?
Answer: light

Question: What was Planck studying in the last part of the nineteenth century?
Answer: the problem of black-body radiation

Question: Who posed the problem of black-body radiation?
Answer: Kirchhoff

Question: Cooler objects glow less than objects that are what?
Answer: hotter

Question: What does a black object do to any of the light that hits it?
Answer: it absorbs all the light

Question: What is maximized as a result of a black object absorbing all the light that hits it?
Answer: thermal light emission

Question: Planck studied what problem posed originally by Kirchhoff?
Answer: black-body radiation

Question: If an object is black, what is known about its thermal light emission?
Answer: its thermal light emission is maximized.

Question: What is known about the light absorption of a hot object in equilibrium with light?
Answer: absorbs just as much light as it emits

Question: Electromagnetic fields obey what laws?
Answer: laws of motion
Planck_constant

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).

Question: What do scientists assume black body radiation is?
Answer: thermal

Question: What kind of prediction does the assumption that black body radiation is thermal lead to?
Answer: accurate

Question: What type of changes in the light a hot object emits as the object's temperature changes?
Answer: colour

Question: What law describes the changes in light emitted by a hot object?
Answer: Stefan–Boltzmann law

Question: What assumption that black-body radiation is what leads to an accurate prediction?
Answer: thermal

Question: What does the Stefan-Boltzmann law state?
Answer: the total amount of emitted energy goes up with the temperature according to a definite rule

Question: What about a hot object changes with the temperature?
Answer: the colour of the light

Question: What color is hotter than "red hot"?
Answer: white hot

Question: What did Wilhelm Wien discover?
Answer: the mathematical relationship between the peaks of the curves at different temperatures

Question: What rule predicts that emitted energy increases with temperature?
Answer: the Stefan–Boltzmann law

Question: What characteristic of the light emitted by a hot object changes with temperature?
Answer: the colour of the light given off

Question: Who discovered the mathematical relationship between peaks and curves of light at different temperatures?
Answer: Wilhelm Wien

Question: The rule that adjust the curve at different temperatures is known as what?
Answer: Wien's displacement law

Question: Wien's spectrum model could not predict accurate at what end of the spectrum?
Answer: at low frequencies (long wavelength)
Planck_constant

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.

Question: Before Planck, it was assumed that the energy of a body could take on what value?
Answer: any

Question: The Rayleigh-Jeans law makes close predictions for what amount of values?
Answer: a narrow range

Question: What does Planck's law correctly predict?
Answer: blackbody emissions

Question: In making Planck's law, what was in both the numerator and denominator of the formula that was used?
Answer: h

Question: Planck's work disproved what assumption?
Answer: that the energy of a body could take on any value whatsoever

Question: What rule predicted narrow range of energy values at lower temperatures?
Answer: The Rayleigh–Jeans

Question: Planck's law involved what necessary mathematical step to correctly predict blackbody emission?
Answer: multiply the classical expression by a complex factor that involves h in both the numerator and the denominator

Question: Changing values of n, the Boltzmann constant, or other variables resulted in learning what about Planck's law?
Answer: Making an equation out of Planck's law that would reproduce the Rayleigh–Jeans law could not be done

Question: The disparity between Planck's law and the Rayleigh-Jeans law led to what conclusion?
Answer: the picture given by classical physics is not duplicated by a range of results in the quantum picture
Planck_constant

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".

Question: Einstein and what other two individuals revisited the black-body problem in 1905?
Answer: Rayleigh and Jeans

Question: Who came up with the term, "ultraviolet catastrophe"?
Answer: Paul Ehrenfest

Question: When did Paul Ehrenfest come up with the name "ultraviolet catastrophe"?
Answer: 1911

Question: When was the first Solvay Conference held?
Answer: 1911

Question: Who received the Nobel Prize in Physics in 1918?
Answer: Max Planck

Question: What did Rayleigh & Jeans and Einstein prove independently in 1905?
Answer: classical electromagnetism could never account for the observed spectrum

Question: What name did Paul Ehrenfest give to the proofs from Einstein and Rayleigh & Jeans?
Answer: the "ultraviolet catastrophe"

Question: When was the first Solvay Conference held?
Answer: 1911

Question: What was the topic of the first Solvay Conference?
Answer: "the theory of radiation and quanta"

Question: In what year did Planck receive the Nobel Prize in Physics for his discovery of energy quanta?
Answer: 1918
Planck_constant

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.

Question: Who first observed the photoelectric effect?
Answer: Alexandre Edmond Becquerel

Question: When was the photoelectric effect first observed?
Answer: 1839

Question: Who published the first thorough investigation of the photoelectric effect?
Answer: Heinrich Hertz

Question: Who received the Nobel Prize in 1921 for his work on the photoelectric effect?
Answer: Einstein

Question: What did Einstein with the 1921 Nobel Prize for?
Answer: his work on the photo-electric effect

Question: What is the photoelectric effect?
Answer: the emission of electrons (called "photoelectrons") from a surface when light is shone on it

Question: Who first observed the photoelectric effect?
Answer: Alexandre Edmond Becquerel

Question: Einstein's paper on the photoelectric effect earned him the Nobel Prize in what year?
Answer: 1921

Question: Einstein's photoelectric effect work was rewards as opposed to his work on what other topic?
Answer: relativity
Planck_constant

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.

Question: Before Einstein, electromagnetic radiation was considered to behave as what?
Answer: a wave

Question: What terms describe different types of radiation?
Answer: "frequency" and "wavelength"

Question: What other types of wave besides light has its own intensity?
Answer: sound

Question: What is the energy transferred by a wave in a given time called?
Answer: intensity

Question: Prior to Einstein's work, light behavior was modeled as what?
Answer: a wave

Question: What is the name for the amount of energy transfered by a wave in a given time?
Answer: intensity

Question: What portion of the photoelectric effect was in disagreement with the believed description of light behavior?
Answer: the energy account

Question: What does it mean for a light source to be more intense than another?
Answer: gives out more energy per unit time and per unit space
Planck_constant

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.

Question: What is emitted as a result of the photoelectric effect?
Answer: photoelectrons

Question: What does the kinetic energy of a photoelectron depend on?
Answer: the frequency

Question: What happens if the photoelectron's frequency is too low?
Answer: no photoelectrons are emitted at all

Question: What is the term used when photoelectrons act virtually at the same time?
Answer: multiphoton effect

Question: What type of energy due photoelectrons emitted due to the photoelectric effect have?
Answer: kinetic

Question: What factor of the initial light source does the energy of the photoelectrons depend on?
Answer: frequency

Question: When the photon energy is less than the work function of the material the light is shone upon, how many photoelectrons are emitted?
Answer: no photoelectrons are emitted at all

Question: If the photoelectric effect is occuring, increasing the intensity of the light source causes what?
Answer: more photoelectrons to be emitted with the same kinetic energy
Planck_constant

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

Question: Who introduced the first quantized model of the atom?
Answer: Niels Bohr

Question: When was the first quantized model of the atom introduced?
Answer: 1913

Question: Why was the first quantized model of the atom introduced?
Answer: to overcome a major shortcoming of Rutherford's classical model

Question: In classical electrodynamics, a charge moving in a circle should do what?
Answer: radiate electromagnetic radiation

Question: Who modeled the atom in 1913, challenging Rutherford's model?
Answer: Niels Bohr

Question: What was predicted to happen to a nucleus-orbiting electron under Rutherford's model?
Answer: the radiation would cause it to lose energy and spiral down into the nucleus

Question: What statement did Bohr make about the electron of an atom, citing Planck's work?
Answer: an electron in a Bohr atom could only have certain defined energies
Planck_constant

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

Question: Who introduced the reduced Planck constant?
Answer: Bohr

Question: What is the reduced Planck constant also known as?
Answer: the quantity

Question: Who helped to give the correct quantization rules for electrons in 1925?
Answer: Heisenberg

Question: Who helped to give the correct quantization rules for electrons in 1926?
Answer: Schrödinger

Question: According to Heisenberg and Schrödinger, the reduced Planck constant remains what?
Answer: the fundamental quantum of angular momentum

Question: Bohr introduced what value as the quantum of angular momentum?
Answer: the reduced Planck constant

Question: What incorrect belief did Bohr hold about the reduced Planck constant?
Answer: Bohr thought that this was the angular momentum of each electron in an atom

Question: What scientist used matrix mechanics to bring electron behavior in line with the Bohr model?
Answer: Heisenberg

Question: When was the Schrödinger wave equation proposed?
Answer: 1926
Planck_constant

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.

Question:  What measurable value obeys a similar rule of angular momentum?
Answer: time vs. energy

Question: What forces measurement attempts to choose between trade-offs, in quanta?
Answer: either-or nature of uncertainty

Question: What form do measurement attempt trade-offs for quanta take the form of?
Answer: either-or (as in Fourier analysis)

Question: How is uncertainly measured in this experience?
Answer: the standard deviation of the measured value from its expected value

Question: What type of analysis fits the either-or nature of the uncertainty?
Answer: Fourier analysis

Question: What example is given as another paired relationship of uncertainly related to standard deviation?
Answer: time vs. energy
Planck_constant

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.

Question: What is the unit of magentic properties of the electron?
Answer: Bohr magneton

Question: What is the unit of magentic properties of atomic nuclei?
Answer: nuclear magneton

Question: The Bohr magneton is the magnetic moment of an electron under what restriction?
Answer: behaved as a spinning charge according to classical electrodynamics

Question: What three terms define the Bohr magneton value?
Answer: the reduced Planck constant, the elementary charge and the electron mass
Planck_constant

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.

Question: How was the Planck constant calculated in the early 20th century?
Answer: the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons

Question: The value quoted here for the Planck constant is based on a measurement in what year?
Answer: 2007

Question: Where was this measurement made?
Answer: the U.S. National Institute of Standards and Technology (NIST)

Question: What method was was used to obtain the measurement?
Answer: watt-balance measurement

Question: One other measure involved the molar volume of what element?
Answer: silicon
Planck_constant

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.

Question: What is a main practical difficulty in determining n?
Answer: the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another

Question: Why does this difficulty occur?
Answer: it is (or they are) not as precise as is currently believed

Question: Which method is at fault or the discrepancy?
Answer: there is no indication which method is at fault
Planck_constant

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.

Question: Other than the X-ray crystal density method, other methods rely on what two effects?
Answer: the Josephson effect and the quantum Hall effect

Question: Why does relying on these effects create concern?
Answer: If these theories are slightly inaccurate

Question: Using Planck constant values from these effects would lead to what logical issue?
Answer: a circular argument

Question: What is the saving grace of relying on these theories?
Answer: there are other statistical ways of testing the theories, and the theories have yet to be refuted.
Planck_constant

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. From the definition of the conventional watt W90, this gives a measure of the product KJ2RK in SI units, where RK is the von Klitzing constant which appears in the quantum Hall effect. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that RK = h/e2, the measurement of KJ2RK is a direct determination of the Planck constant.

Question: What is a watt balance?
Answer: an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units

Question: What value does RK represent?
Answer: the von Klitzing constant which appears in the quantum Hall effect

Question: If the effects are valid, for RK = n/e2, what is the measurement of KJ2RK equal to?
Answer: the Planck constant