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Questions and Answers
What does the Stefan-Boltzmann law state about the energy radiated by a blackbody?
What does the Stefan-Boltzmann law state about the energy radiated by a blackbody?
- It is independent of its absolute temperature.
- It is proportional to the fourth power of its absolute temperature. (correct)
- It is proportional to the square of its absolute temperature.
- It is proportional to the third power of its absolute temperature.
What is the value of the Stefan constant, σ?
What is the value of the Stefan constant, σ?
- 4.67 × 10^-8 J/(s m^2 K^4)
- 6.67 × 10^-8 J/(s m^2 K^4)
- 3.67 × 10^-8 J/(s m^2 K^4)
- 5.67 × 10^-8 J/(s m^2 K^4) (correct)
How is the intensity of the emitted radiation Eλ related to the energy density uλ?
How is the intensity of the emitted radiation Eλ related to the energy density uλ?
- Eλ = 2uλ
- Eλ = uλ/4 (correct)
- Eλ = c uλ
- Eλ = 4uλ
What is the relationship between the total energy E and intensity Eλ for a blackbody?
What is the relationship between the total energy E and intensity Eλ for a blackbody?
If x is defined as λ K_B T, what does it represent in the context of the emitted radiation?
If x is defined as λ K_B T, what does it represent in the context of the emitted radiation?
What limitation does classical theory face when explaining black body radiation?
What limitation does classical theory face when explaining black body radiation?
What is the term used to describe the discrete packets of energy emitted by a black body according to quantum theory?
What is the term used to describe the discrete packets of energy emitted by a black body according to quantum theory?
Who proposed the theory that describes black body radiation through discrete energy packets?
Who proposed the theory that describes black body radiation through discrete energy packets?
What defines the threshold frequency in the context of the photoelectric effect?
What defines the threshold frequency in the context of the photoelectric effect?
What phenomenon occurs when light of sufficient frequency falls on a metal surface?
What phenomenon occurs when light of sufficient frequency falls on a metal surface?
Planck's law of black body radiation relates to which aspect of electromagnetic radiation?
Planck's law of black body radiation relates to which aspect of electromagnetic radiation?
What does the ultraviolet catastrophe signify in classical physics?
What does the ultraviolet catastrophe signify in classical physics?
According to Planck's law, the distribution of electromagnetic radiation from a black body ultimately depends on which factor?
According to Planck's law, the distribution of electromagnetic radiation from a black body ultimately depends on which factor?
What is the functional form of the energy density of blackbody radiation as proposed by Rayleigh and Jeans?
What is the functional form of the energy density of blackbody radiation as proposed by Rayleigh and Jeans?
At which limit does the Rayleigh-Jeans law fails, leading to the ultraviolet catastrophe?
At which limit does the Rayleigh-Jeans law fails, leading to the ultraviolet catastrophe?
Which law does Planck’s law reduce to at short wavelengths?
Which law does Planck’s law reduce to at short wavelengths?
In the context of blackbody radiation, what happens to the exponential term for short wavelengths?
In the context of blackbody radiation, what happens to the exponential term for short wavelengths?
What does the constant 'a' in the Rayleigh-Jeans law represent?
What does the constant 'a' in the Rayleigh-Jeans law represent?
What happens to the energy density of radiation as the temperature of a blackbody increases?
What happens to the energy density of radiation as the temperature of a blackbody increases?
What is the behavior of the energy density of blackbody radiation as the wavelength approaches infinity?
What is the behavior of the energy density of blackbody radiation as the wavelength approaches infinity?
What is the significance of the term $8\pi h c$ in the equations defining blackbody radiation?
What is the significance of the term $8\pi h c$ in the equations defining blackbody radiation?
According to Wien's displacement law, what is constant when considering the peak wavelength and temperature of a blackbody?
According to Wien's displacement law, what is constant when considering the peak wavelength and temperature of a blackbody?
In the limiting case for very short wavelengths, which equation simplifies to an exponential form?
In the limiting case for very short wavelengths, which equation simplifies to an exponential form?
What can be inferred from the form of Planck's law regarding the energy density of a blackbody?
What can be inferred from the form of Planck's law regarding the energy density of a blackbody?
What is the relation between wavelength and temperature according to Wien's displacement law?
What is the relation between wavelength and temperature according to Wien's displacement law?
What is the significance of the limit as $λ$ approaches infinity in the derived equations?
What is the significance of the limit as $λ$ approaches infinity in the derived equations?
Which expression describes how to obtain the wavelength at which the energy density of radiation becomes maximum?
Which expression describes how to obtain the wavelength at which the energy density of radiation becomes maximum?
What does the term $u_λ$ refer to in the context of blackbody radiation?
What does the term $u_λ$ refer to in the context of blackbody radiation?
What is the relationship between the coefficients 8, π, ℎ, and $K_B$ in the derived expressions?
What is the relationship between the coefficients 8, π, ℎ, and $K_B$ in the derived expressions?
What is the threshold frequency in the context of the photoelectric effect?
What is the threshold frequency in the context of the photoelectric effect?
What role do photons play in the photoelectric effect?
What role do photons play in the photoelectric effect?
Which expression correctly describes the relationship between the maximum kinetic energy of the emitted photoelectrons and the incident light frequency?
Which expression correctly describes the relationship between the maximum kinetic energy of the emitted photoelectrons and the incident light frequency?
What is the stopping potential related to in the photoelectric effect?
What is the stopping potential related to in the photoelectric effect?
In the context of the photoelectric effect, if the energy of the incident light is less than the work function, what occurs?
In the context of the photoelectric effect, if the energy of the incident light is less than the work function, what occurs?
What is the significance of Planck's constant in the photoelectric effect?
What is the significance of Planck's constant in the photoelectric effect?
What would happen if ultraviolet light with a longer wavelength than 2300Ã… is used on a tungsten cathode?
What would happen if ultraviolet light with a longer wavelength than 2300Ã… is used on a tungsten cathode?
When calculating the stopping potential, which variables are necessary?
When calculating the stopping potential, which variables are necessary?
Study Notes
Stefan-Boltzmann Law
- The Stefan-Boltzmann law states the total energy radiated per unit surface area of a blackbody across all wavelengths per unit time is proportional to the fourth power of its absolute temperature.
- The corresponding proportionality constant is the Stefan constant, denoted as σ, which is 5.67 × 10−8J/(s m2 K4).
Wien's Displacement Law
- The product of the wavelength (λmax) at which the energy density of radiation of a blackbody becomes maximum, and the corresponding temperature (T) of the blackbody, is a constant.
- As the temperature of a blackbody increases, the overall radiated energy increases, and the peak of the radiation curve moves to shorter wavelengths.
Planck's Law of Blackbody Radiation
- Planck’s law describes the amount of radiation at each wavelength.
- It agrees with the experimentally measured spectrum, overcoming the limitations of the Classical theory.
- The law can be derived from the concept of quanta of energy emission.
Rayleigh-Jeans Law
- It gives the energy density of blackbody radiation as a function of wavelength.
- It is derived from classical theory arguments and empirical facts, but only agrees with the experimentally measured spectra of radiation of the blackbody at long wavelengths.
- It fails at short wavelengths, known as the ultraviolet catastrophe.
- It is derived from the assumption that the energy density of radiation is proportional to the temperature (T) of the blackbody.
Photoelectric Effect
- When light falls on a metal surface, electrons are emitted if the frequency of the incident light is greater than the minimum frequency, known as the threshold frequency of the metal.
- The maximum kinetic energy of the emitted photoelectrons is determined by the difference between the energy of the incident photon (hν) and the work function (φ0) of the metal.
- The stopping potential (Vs) is the minimum negative potential required to stop the fastest moving photoelectron.
Ultraviolet Catastrophe
- This occurs when the Rayleigh-Jeans law predicts an infinite amount of energy radiated at short wavelengths, which is not observed experimentally.
- This contradiction highlights the limitations of the Classical theory in explaining the observed distribution of electromagnetic radiation emitted by a blackbody.
- Planck's law of Blackbody Radiation successfully resolves the Ultraviolet Catastrophe.
Einstein's Postulate of Photoelectric Effect
- Albert Einstein proposed that light energy is built up of discrete units, called quanta of energy, also known as photons.
- The energy of each photon is hν, where h is Planck’s constant and ν is the frequency of light.
- Photoelectric emission occurs when the energy of the incident photon (hν) is greater than the work function (φ0) of the metal.
- The excess energy (hν – φ0) is taken by the electrons as kinetic energy.
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Test your understanding of the Stefan-Boltzmann Law, Wien's Displacement Law, and Planck's Law of Blackbody Radiation. This quiz covers the fundamental principles and equations that describe blackbody radiation and its implications. Perfect for those studying thermodynamics and quantum mechanics.
