Blackbody Radiation Laws Quiz

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

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?

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?

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?

E = ∫ Eλ dλ from 0 to ∞ Signup and view all the answers

If x is defined as λ K_B T, what does it represent in the context of the emitted radiation?

A dimensionless variable related to spectral energy distribution Signup and view all the answers

What limitation does classical theory face when explaining black body radiation?

It predicts infinite radiation emission. Signup and view all the answers

What is the term used to describe the discrete packets of energy emitted by a black body according to quantum theory?

Quanta Signup and view all the answers

Who proposed the theory that describes black body radiation through discrete energy packets?

Max Planck Signup and view all the answers

What defines the threshold frequency in the context of the photoelectric effect?

The frequency below which electrons are emitted Signup and view all the answers

What phenomenon occurs when light of sufficient frequency falls on a metal surface?

Photoelectric effect Signup and view all the answers

Planck's law of black body radiation relates to which aspect of electromagnetic radiation?

Temperature dependence Signup and view all the answers

What does the ultraviolet catastrophe signify in classical physics?

Limitations in predicting radiation at high frequencies Signup and view all the answers

According to Planck's law, the distribution of electromagnetic radiation from a black body ultimately depends on which factor?

Temperature Signup and view all the answers

What is the functional form of the energy density of blackbody radiation as proposed by Rayleigh and Jeans?

$\frac{aT}{\lambda^4} d\lambda$ Signup and view all the answers

At which limit does the Rayleigh-Jeans law fails, leading to the ultraviolet catastrophe?

Short wavelengths Signup and view all the answers

Which law does Planck’s law reduce to at short wavelengths?

Wien’s Law Signup and view all the answers

In the context of blackbody radiation, what happens to the exponential term for short wavelengths?

It approaches infinity Signup and view all the answers

What does the constant 'a' in the Rayleigh-Jeans law represent?

A constant related to temperature Signup and view all the answers

What happens to the energy density of radiation as the temperature of a blackbody increases?

It increases. Signup and view all the answers

What is the behavior of the energy density of blackbody radiation as the wavelength approaches infinity?

It tends to zero Signup and view all the answers

What is the significance of the term $8\pi h c$ in the equations defining blackbody radiation?

It is a derived constant from experimental data Signup and view all the answers

According to Wien's displacement law, what is constant when considering the peak wavelength and temperature of a blackbody?

The wavelength at maximum energy density and temperature. Signup and view all the answers

In the limiting case for very short wavelengths, which equation simplifies to an exponential form?

$u_\lambda \propto \frac{1}{\lambda^5} e^{(-\frac{h c}{\lambda K_B T})}$ Signup and view all the answers

What can be inferred from the form of Planck's law regarding the energy density of a blackbody?

The maximum energy density occurs when the denominator is minimum. Signup and view all the answers

What is the relation between wavelength and temperature according to Wien's displacement law?

Shorter wavelengths correspond to higher temperatures. Signup and view all the answers

What is the significance of the limit as $λ$ approaches infinity in the derived equations?

It leads to validation of Rayleigh-Jeans law. Signup and view all the answers

Which expression describes how to obtain the wavelength at which the energy density of radiation becomes maximum?

By differentiating Planck’s law with respect to wavelength. Signup and view all the answers

What does the term $u_λ$ refer to in the context of blackbody radiation?

The energy density at a specific wavelength. Signup and view all the answers

What is the relationship between the coefficients 8, π, ℎ, and $K_B$ in the derived expressions?

They represent physical constants that govern blackbody radiation. Signup and view all the answers

What is the threshold frequency in the context of the photoelectric effect?

The minimum frequency below which no photoelectrons are emitted Signup and view all the answers

What role do photons play in the photoelectric effect?

They represent discrete packets of energy that can eject electrons Signup and view all the answers

Which expression correctly describes the relationship between the maximum kinetic energy of the emitted photoelectrons and the incident light frequency?

KE_max = hν - φ0 Signup and view all the answers

What is the stopping potential related to in the photoelectric effect?

The maximum speed of the ejected photoelectrons Signup and view all the answers

In the context of the photoelectric effect, if the energy of the incident light is less than the work function, what occurs?

No photoelectrons are ejected from the metal surface Signup and view all the answers

What is the significance of Planck's constant in the photoelectric effect?

It relates the energy of a photon to its frequency Signup and view all the answers

What would happen if ultraviolet light with a longer wavelength than 2300Å is used on a tungsten cathode?

No photoelectrons will be emitted Signup and view all the answers

When calculating the stopping potential, which variables are necessary?

Charge of the electron and maximum speed of the photoelectron Signup and view all the answers

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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

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.