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The ultraviolet catastrophe was a prediction derived from quantum physics, positing that energy emission would be unbounded at short wavelengths.
Answer: False
Explanation: The ultraviolet catastrophe was a prediction of classical physics, not quantum physics. Classical theories, such as the Rayleigh-Jeans law, incorrectly suggested that black body radiation would emit infinite energy at short wavelengths.
The ultraviolet catastrophe is also known as the Planck-Einstein catastrophe.
Answer: False
Explanation: The ultraviolet catastrophe is also referred to as the Rayleigh-Jeans catastrophe, highlighting the classical law that led to this problematic prediction. It is not typically referred to as the Planck-Einstein catastrophe.
The concept underlying the ultraviolet catastrophe originated with the 1900 derivation of Planck's Law.
Answer: False
Explanation: The concept underlying the ultraviolet catastrophe originated with the 1900 derivation of the Rayleigh-Jeans Law, which attempted to describe black body radiation, not Planck's Law, which later resolved it.
The image illustrating the ultraviolet catastrophe showed the Rayleigh-Jeans law matching experimental data perfectly at short wavelengths.
Answer: False
Explanation: The image illustrating the ultraviolet catastrophe typically shows the Rayleigh-Jeans law deviating significantly from experimental data at short wavelengths, highlighting its failure in that regime.
The term "ultraviolet catastrophe" has also been applied to similar problematic predictions in quantum electrodynamics.
Answer: True
Explanation: The term 'ultraviolet catastrophe' has indeed been applied metaphorically to similar issues, such as ultraviolet divergences, encountered in later theories like quantum electrodynamics.
The term "catastrophe" is used because the classical prediction led to a physically impossible outcome of infinite energy emission.
Answer: True
Explanation: The term 'catastrophe' is used because the classical physics prediction yielded a physically impossible outcome—infinite energy emission—at ultraviolet wavelengths, starkly contradicting experimental observations and revealing a fundamental flaw in the theory.
The term "ultraviolet catastrophe" refers to the failure of Planck's Law to match experimental data.
Answer: False
Explanation: The term 'ultraviolet catastrophe' refers to the failure of *classical physics*, specifically the Rayleigh-Jeans Law, to match experimental data for black body radiation at short wavelengths. Planck's Law successfully explained the data.
What was the primary prediction of classical physics regarding black body radiation at short wavelengths, leading to the "ultraviolet catastrophe"?
Answer: Energy emission would increase without bound.
Explanation: The primary prediction of classical physics regarding black body radiation at short wavelengths was that the intensity of energy emission would increase without bound, leading to the ultraviolet catastrophe.
The image illustrating the ultraviolet catastrophe shows a discrepancy between classical theory and experimental data primarily at:
Answer: Short wavelengths.
Explanation: The image illustrating the ultraviolet catastrophe typically shows a significant discrepancy between the classical theory (Rayleigh-Jeans Law) and experimental data primarily at short wavelengths.
The term "ultraviolet catastrophe" has also been applied to similar problematic predictions in which other area of physics?
Answer: Quantum Electrodynamics
Explanation: The term 'ultraviolet catastrophe' has also been applied metaphorically to similar problematic predictions, such as ultraviolet divergences, encountered in quantum electrodynamics.
Why is the term "catastrophe" fitting for the failure of classical physics in predicting black body radiation?
Answer: It resulted in a physically impossible prediction (infinite energy) contradicting observations.
Explanation: The term 'catastrophe' is fitting because the classical physics prediction yielded a physically impossible outcome—infinite energy emission—at ultraviolet wavelengths, starkly contradicting experimental observations and revealing a fundamental flaw in the theory.
The concept underlying the ultraviolet catastrophe originated around the year:
Answer: 1900
Explanation: The concept underlying the ultraviolet catastrophe, stemming from the failure of classical physics to explain black body radiation, originated around the year 1900 with the derivation of the Rayleigh-Jeans Law.
The failure of classical physics, described by the ultraviolet catastrophe, was primarily related to the inability to explain:
Answer: The spectrum of black body radiation at short (ultraviolet) wavelengths.
Explanation: The failure of classical physics, as highlighted by the ultraviolet catastrophe, was primarily its inability to accurately explain the observed spectrum of black body radiation at short (ultraviolet) wavelengths.
According to classical physics, the intensity of black body radiation increased infinitely as the wavelength decreased into the ultraviolet range.
Answer: True
Explanation: Classical physics, particularly through the Rayleigh-Jeans law, predicted that the intensity of black body radiation would increase without bound as the wavelength approached zero (i.e., into the ultraviolet spectrum), a phenomenon known as the ultraviolet catastrophe.
The Rayleigh-Jeans law accurately described black body radiation across all wavelengths.
Answer: False
Explanation: The Rayleigh-Jeans law provided an accurate description of black body radiation only at long wavelengths. At short wavelengths, it failed dramatically, predicting infinite energy emission.
The Rayleigh-Jeans law is based on the principle of equipartition theorem from classical statistical mechanics.
Answer: True
Explanation: The Rayleigh-Jeans law is indeed derived from the equipartition theorem of classical statistical mechanics, which assigns an average energy of $k_B T$ to each mode of oscillation.
The Rayleigh-Jeans law formula in terms of frequency ($B_{\nu }(T)$) approaches zero as frequency approaches infinity.
Answer: False
Explanation: The Rayleigh-Jeans law formula in terms of frequency ($B_{\nu }(T) = {\frac {2\nu ^{2}k_{\mathrm {B} }T}{c^{2}}}$) actually approaches infinity as frequency approaches infinity, which is the source of the ultraviolet catastrophe.
Classical physics suggested that energy was concentrated in longer wavelengths because there were fewer modes in those ranges.
Answer: False
Explanation: Classical physics, via the Rayleigh-Jeans law, suggested energy concentration in *shorter* wavelengths (higher frequencies) because it assumed a higher number of available modes in those ranges, each carrying the same average energy.
According to classical electromagnetism, the number of modes in a cavity is proportional to the cube of the frequency.
Answer: False
Explanation: According to classical electromagnetism, the number of electromagnetic modes in a cavity per unit frequency is proportional to the *square* of the frequency, not the cube.
The Rayleigh-Jeans law predicted that radiated power per unit frequency would be proportional to the frequency squared.
Answer: True
Explanation: The Rayleigh-Jeans law predicted that the spectral radiance per unit frequency ($B_{\nu }(T)$) would be proportional to the frequency squared ($\nu^2$), leading to the ultraviolet catastrophe.
The equipartition theorem implies that all modes of vibration in a black body have the same average energy at equilibrium.
Answer: True
Explanation: The equipartition theorem, a principle of classical statistical mechanics, implies that all harmonic oscillator modes (degrees of freedom) in a system at thermal equilibrium possess the same average energy, typically $k_B T$.
The classical physics implication was that energy was concentrated in longer wavelengths due to a higher density of modes.
Answer: False
Explanation: The classical physics implication was that energy was concentrated in *shorter* wavelengths (higher frequencies) due to a higher density of modes in those ranges, each assumed to have the same average energy.
The equipartition theorem, applied to black body radiation, assigned an average energy of $k_{\mathrm {B}}T$ to each frequency mode.
Answer: True
Explanation: The equipartition theorem, a principle of classical statistical mechanics, implies that all harmonic oscillator modes (degrees of freedom) in a system at thermal equilibrium possess the same average energy, typically $k_B T$.
The formula $B_{\lambda }(T) = {\frac {2ck_{\mathrm {B} }T}{\lambda ^{4}}}$ correctly describes spectral radiance as a function of wavelength for black bodies at all temperatures.
Answer: False
Explanation: This formula, $B_{\lambda }(T) = {\frac {2ck_{\mathrm {B} }T}{\lambda ^{4}}}$, represents the Rayleigh-Jeans law, which accurately describes black body radiation only at long wavelengths. It fails significantly at short wavelengths.
Which law, derived from classical physics principles like the equipartition theorem, failed to accurately describe black body radiation at short wavelengths?
Answer: Rayleigh-Jeans Law
Explanation: The Rayleigh-Jeans Law, derived from classical physics principles such as the equipartition theorem, failed to accurately describe black body radiation at short wavelengths, predicting infinite energy emission.
According to the source, how did the Rayleigh-Jeans law formula $B_{\nu }(T) = {\frac {2\nu ^{2}k_{\mathrm {B} }T}{c^{2}}}$ contribute to the ultraviolet catastrophe?
Answer: It predicted energy emission proportional to frequency squared, leading to infinite total energy.
Explanation: The Rayleigh-Jeans law formula $B_{\nu }(T) = {\frac {2\nu ^{2}k_{\mathrm {B} }T}{c^{2}}}$ contributed to the ultraviolet catastrophe by predicting that radiated power per unit frequency would be proportional to the frequency squared, thus implying infinite total energy emission at high frequencies.
The Rayleigh-Jeans law accurately predicted black body radiation behavior primarily in which spectral region?
Answer: Long wavelengths
Explanation: The Rayleigh-Jeans law accurately predicted black body radiation behavior primarily in the long wavelength (low frequency) region of the spectrum.
What was the unphysical consequence predicted by the Rayleigh-Jeans law regarding radiated power at higher frequencies?
Answer: Total radiated power would be unlimited and infinite.
Explanation: The unphysical consequence predicted by the Rayleigh-Jeans law regarding radiated power at higher frequencies was that the total radiated power would become unlimited and infinite, a direct contradiction of experimental observations.
According to classical electromagnetism, how does the number of electromagnetic modes in a cavity relate to frequency?
Answer: Proportional to the square of the frequency.
Explanation: According to classical electromagnetism, the number of electromagnetic modes within a cavity, per unit frequency, is proportional to the square of the frequency.
The failure of the Rayleigh-Jeans law at short wavelengths was a significant problem because:
Answer: It contradicted experimental observations of black body radiation.
Explanation: The failure of the Rayleigh-Jeans law at short wavelengths was a significant problem because it directly contradicted experimental observations of black body radiation, which did not exhibit infinite energy emission.
The classical physics implication that energy was concentrated in shorter wavelengths was due to:
Answer: A higher number of available modes at shorter wavelengths, each with average energy $k_B T$.
Explanation: The classical physics implication that energy was concentrated in shorter wavelengths was due to the assumption that there was a higher number of available modes at shorter wavelengths, and the equipartition theorem assigned an average energy of $k_B T$ to each mode.
The statement that "most of its energy is concentrated in shorter wavelengths and higher frequencies" relates to the classical physics view of:
Answer: The prediction of the ultraviolet catastrophe.
Explanation: The statement that 'most of its energy is concentrated in shorter wavelengths and higher frequencies' reflects the classical physics view that led to the prediction of the ultraviolet catastrophe.
What is the significance of the equipartition theorem in the context of the ultraviolet catastrophe?
Answer: It provided the classical basis for the Rayleigh-Jeans law's assumption of equal energy per mode.
Explanation: The significance of the equipartition theorem lies in its provision of the classical basis for the Rayleigh-Jeans law's assumption that each mode of oscillation in a black body cavity possesses an average energy of $k_B T$, which, when combined with the density of modes, leads to the catastrophe.
The Rayleigh-Jeans law's prediction of infinite energy emission stemmed from combining the equipartition theorem with the classical understanding that:
Answer: The number of modes increases with frequency.
Explanation: The Rayleigh-Jeans law's prediction of infinite energy emission stemmed from combining the equipartition theorem (assigning equal energy to all modes) with the classical understanding that the number of electromagnetic modes in a cavity increases with frequency.
Max Planck resolved the ultraviolet catastrophe by proposing that energy is quantized.
Answer: True
Explanation: Max Planck's groundbreaking resolution to the ultraviolet catastrophe involved proposing that energy is not emitted or absorbed continuously but in discrete packets, or quanta, thereby preventing the infinite energy accumulation predicted by classical physics.
Planck's quantum hypothesis suggested that energy could be divided into arbitrarily small fractions.
Answer: False
Explanation: Planck's quantum hypothesis fundamentally suggested the opposite: that energy could *not* be divided into arbitrarily small fractions, but rather existed in discrete, quantized units.
Max Planck's formula for the energy of a quantum of radiation was $E = h/\nu$.
Answer: False
Explanation: Max Planck's formula for the energy of a quantum of radiation was $E = h\nu$, not $E = h/\nu$. This direct proportionality between energy and frequency was a cornerstone of his quantum hypothesis.
The Planck constant ($h$) is a key component in the formula for the energy of a quantum.
Answer: True
Explanation: The Planck constant ($h$) is indeed a fundamental constant that appears in the formula $E = h\nu$, quantifying the energy of a quantum of electromagnetic radiation.
Planck's quantum hypothesis prevented the infinite energy accumulation predicted by classical physics at high frequencies.
Answer: True
Explanation: Planck's quantum hypothesis, by proposing that energy is emitted or absorbed in discrete quanta, effectively limited the energy contribution from high-frequency modes, thereby preventing the infinite accumulation predicted by classical physics.
Planck's quantum hypothesis suggested that energy emission was a continuous process, proportional to frequency.
Answer: False
Explanation: Planck's quantum hypothesis posited that energy emission is *not* a continuous process but occurs in discrete packets (quanta), with the energy of each quantum being directly proportional to its frequency ($E=h\nu$).
Max Planck resolved the ultraviolet catastrophe by introducing which fundamental concept?
Answer: The quantization of energy into discrete packets (quanta).
Explanation: Max Planck resolved the ultraviolet catastrophe by introducing the fundamental concept of energy quantization, proposing that energy is emitted or absorbed in discrete packets, or quanta.
What is the formula for the energy of a quantum of electromagnetic radiation, as proposed by Planck?
Answer: $E = h \nu$
Explanation: The formula for the energy of a quantum of electromagnetic radiation, as proposed by Max Planck, is $E = h\nu$, where $h$ is the Planck constant and $\nu$ is the frequency.
Max Planck's formula for the spectral distribution of black body radiation is known as:
Answer: Planck's Law
Explanation: Max Planck's formula that accurately describes the spectral distribution of black body radiation is known as Planck's Law.
How did Planck's quantum hypothesis resolve the ultraviolet catastrophe?
Answer: By limiting energy emission to discrete packets, preventing infinite accumulation at high frequencies.
Explanation: Planck's quantum hypothesis resolved the ultraviolet catastrophe by positing that energy emission occurs in discrete packets (quanta), thereby preventing the infinite accumulation of energy at high frequencies predicted by classical physics.
Max Planck's resolution of the ultraviolet catastrophe involved assuming that energy could only be emitted or absorbed in:
Answer: Discrete packets, or quanta.
Explanation: Max Planck's resolution of the ultraviolet catastrophe involved the revolutionary assumption that energy could only be emitted or absorbed in discrete packets, known as quanta.
The formula $E = h\nu$ relates the energy of a quantum to its:
Answer: Frequency
Explanation: The formula $E = h\nu$ relates the energy of a quantum directly to its frequency.
Albert Einstein proposed that Planck's quanta were merely a mathematical construct, not physical particles.
Answer: False
Explanation: Contrary to this statement, Albert Einstein proposed in 1905 that Planck's quanta were not merely mathematical constructs but represented real physical particles, which he termed photons.
Einstein's photon postulate helped explain the law of the photoelectric effect.
Answer: True
Explanation: Einstein's hypothesis of the photon, a discrete quantum of light, provided a powerful explanation for the observed laws of the photoelectric effect, a key success for quantum theory.
A photon's energy is inversely proportional to its frequency.
Answer: False
Explanation: A photon's energy is directly proportional to its frequency, as stated by the relationship $E = h\nu$, where $h$ is the Planck constant. Energy increases with frequency.
The relationship $E = h\nu$ shows that a photon's energy decreases as its frequency increases.
Answer: False
Explanation: The relationship $E = h\nu$ indicates that a photon's energy is *directly proportional* to its frequency; as frequency increases, energy also increases.
What did Albert Einstein propose in 1905 regarding Planck's quanta?
Answer: They were real physical particles, later known as photons.
Explanation: In 1905, Albert Einstein proposed that Planck's quanta were not merely a mathematical construct but represented real physical entities, which he termed photons.
What is the relationship between a photon's energy ($E$) and its frequency ($\nu$) according to Planck and Einstein?
Answer: $E = h \nu$
Explanation: According to Planck and Einstein, the relationship between a photon's energy ($E$) and its frequency ($\nu$) is given by $E = h\nu$, where $h$ is the Planck constant.
Einstein's photon postulate helped explain which phenomena, among others?
Answer: The photoelectric effect and Stokes' law.
Explanation: Einstein's photon postulate was instrumental in explaining the photoelectric effect and also helped clarify phenomena like Stokes' law.
Which of the following statements about Albert Einstein's contributions is accurate according to the source?
Answer: He proposed quanta were real particles (photons) and explained the photoelectric effect.
Explanation: According to the source, Albert Einstein's key contributions included proposing that quanta were real particles (photons) and providing an explanation for the photoelectric effect.
Paul Ehrenfest first used the term "ultraviolet catastrophe" in 1900.
Answer: False
Explanation: The term 'ultraviolet catastrophe' was first used by Paul Ehrenfest in 1911, not 1900.
Albert Einstein, Lord Rayleigh, and Sir James Jeans independently noted the unphysical nature of the Rayleigh-Jeans law's predictions in 1905.
Answer: True
Explanation: Indeed, Albert Einstein, Lord Rayleigh, and Sir James Jeans independently recognized the unphysical implications of the Rayleigh-Jeans Law's predictions around 1905, prior to Planck's resolution.
Albert Einstein received the Nobel Prize in Physics in 1921 for his work on the theory of relativity.
Answer: False
Explanation: Albert Einstein received the Nobel Prize in Physics in 1921 not for the theory of relativity, but specifically for his explanation of the photoelectric effect, which was based on his quantum hypothesis.
The book <i>Ultraviolet Radiation in the Solar System</i> was published by Springer in 2005.
Answer: True
Explanation: The 2005 book referenced is titled <i>Ultraviolet Radiation in the Solar System</i>, published by Springer.
Paul Ehrenfest's 1911 paper on the ultraviolet catastrophe was published in the journal <i>Physical Review</i>.
Answer: False
Explanation: Paul Ehrenfest's 1911 paper concerning the ultraviolet catastrophe was published in the esteemed German physics journal, 'Annalen der Physik', not 'Physical Review'.
The ISBN 978-0691139685 is associated with A. Douglas Stone's 2013 book <i>Einstein and the Quantum</i>.
Answer: True
Explanation: The ISBN 9780691139685 is indeed associated with A. Douglas Stone's 2013 book, <i>Einstein and the Quantum</i>.
Einstein's 1921 Nobel Prize citation mentioned his work on the theory of relativity.
Answer: False
Explanation: Einstein's 1921 Nobel Prize citation specifically mentioned his discovery of the law of the photoelectric effect, not his work on the theory of relativity.
The English translation of Ehrenfest's 1911 paper title is "Features of the Light Quantum Hypothesis in Thermal Radiation".
Answer: False
Explanation: The English translation of Paul Ehrenfest's 1911 paper title is "In which features of the light quantum hypothesis does thermal radiation play an essential role?", not "Features of the Light Quantum Hypothesis in Thermal Radiation".
The Bibcode for Ehrenfest's 1911 paper is 1911AnP...341...91E.
Answer: True
Explanation: The Bibcode for Paul Ehrenfest's 1911 paper is indeed 1911AnP...341...91E.
Chapter 4 and ISBN 0-7167-1088-9 are listed for Kroemer and Kittel's <i>Thermal Physics</i> (1980 edition).
Answer: True
Explanation: Chapter 4 and ISBN 0-7167-1088-9 are listed for the 1980 edition of <i>Thermal Physics</i> by Kroemer and Kittel.
Cohen-Tannoudji et al.'s <i>Quantum Mechanics: Volume One</i> is referenced with pages 624–626 and ISBN 0-471-16433-X.
Answer: True
Explanation: Pages 624–626 and ISBN 0-471-16433-X are provided for <i>Quantum Mechanics: Volume One</i> by Cohen-Tannoudji, Diu, Laloë, and Franck.
Who is credited with coining the term "ultraviolet catastrophe" in 1911?
Answer: Paul Ehrenfest
Explanation: The term 'ultraviolet catastrophe' is credited to the Austrian physicist Paul Ehrenfest, who first used it in 1911.
For which discovery did Albert Einstein win the Nobel Prize in Physics in 1921?
Answer: The explanation of the photoelectric effect.
Explanation: Albert Einstein was awarded the Nobel Prize in Physics in 1921 for his discovery of the law of the photoelectric effect, a phenomenon explained by his photon postulate.
Paul Ehrenfest's 1911 paper related to the ultraviolet catastrophe was published in which journal?
Answer: Annalen der Physik
Explanation: Paul Ehrenfest's 1911 paper concerning the ultraviolet catastrophe was published in the esteemed German physics journal, 'Annalen der Physik'.
The citation for Einstein's 1921 Nobel Prize specifically mentions his contribution to which field?
Answer: Theoretical Physics and the Photoelectric Effect
Explanation: The citation for Albert Einstein's 1921 Nobel Prize in Physics specifically mentions his contributions to 'Theoretical Physics, and especially for his discovery of the law of the photoelectric effect'.
According to the source, Stephen F. Mason's 1962 book <i>A History of the Sciences</i> contains relevant information on which page?
Answer: 550
Explanation: According to the source material, Stephen F. Mason's 1962 book, <i>A History of the Sciences</i>, contains relevant information on page 550.
The formula $B_{\lambda }(\lambda ,T) = {\frac {2hc^{2}}{\lambda ^{5}}}{\frac {1}{\exp \left({\frac {hc}{\lambda k_{\mathrm {B} }T}}\right)-1}}$ represents the Rayleigh-Jeans law.
Answer: False
Explanation: This formula represents Planck's Law, not the Rayleigh-Jeans law. The Rayleigh-Jeans law is a classical approximation that fails at short wavelengths.
What is the mathematical expression for the Rayleigh-Jeans law in terms of wavelength ($\lambda$)?
Answer: $B_{\lambda }(T) = {\frac {2ck_{\mathrm {B} }T}{\lambda ^{4}}}$
Explanation: The mathematical expression for the Rayleigh-Jeans law in terms of wavelength ($\lambda$) is $B_{\lambda }(T) = {\frac {2ck_{\mathrm {B} }T}{\lambda ^{4}}}$, indicating spectral radiance is proportional to $1/\lambda^4$.
Which of the following statements accurately reflects the relationship between the Rayleigh-Jeans law and Planck's Law?
Answer: The Rayleigh-Jeans Law is an approximation of Planck's Law at long wavelengths.
Explanation: The Rayleigh-Jeans Law is an accurate approximation of Planck's Law specifically at long wavelengths (low frequencies), but it fails at short wavelengths (high frequencies).
The Rayleigh-Jeans law formula $B_{\lambda }(T) = {\frac {2ck_{\mathrm {B} }T}{\lambda ^{4}}}$ implies that spectral radiance is proportional to:
Answer: $1/\lambda^4$
Explanation: The Rayleigh-Jeans law formula $B_{\lambda }(T) = {\frac {2ck_{\mathrm {B} }T}{\lambda ^{4}}}$ implies that spectral radiance is proportional to $1/\lambda^4$.