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Questions and Answers
According to Wien's law, how are temperature and wavelength related?
According to Wien's law, how are temperature and wavelength related?
- Wavelength increases as temperature increases
- They are directly proportional
- They have no relationship
- They are inversely proportional (correct)
What happens to the peak of the blackbody radiation curve when the temperature increases?
What happens to the peak of the blackbody radiation curve when the temperature increases?
- Moves to lower intensities
- Remains unchanged
- Moves towards shorter wavelengths (correct)
- Moves towards longer wavelengths
What characteristic defines a blackbody?
What characteristic defines a blackbody?
- It absorbs all thermal radiation and emits based on its temperature (correct)
- It emits only ultraviolet radiation
- It emits radiation of fixed wavelengths regardless of temperature
- It reflects all radiation
At what wavelength is cavity radiation most visible to the human eye when sensitivity is highest?
At what wavelength is cavity radiation most visible to the human eye when sensitivity is highest?
How does the intensity of electromagnetic radiation behave as the wavelength decreases?
How does the intensity of electromagnetic radiation behave as the wavelength decreases?
What is the thermal emissivity of a perfect blackbody?
What is the thermal emissivity of a perfect blackbody?
If the effective surface temperature of the sun is 5800 K, what is the expected wavelength at which it radiates most strongly?
If the effective surface temperature of the sun is 5800 K, what is the expected wavelength at which it radiates most strongly?
According to the wave model, at what region does intensity tend to zero as wavelength increases?
According to the wave model, at what region does intensity tend to zero as wavelength increases?
What is the formula to calculate the energy of a photon from its wavelength?
What is the formula to calculate the energy of a photon from its wavelength?
Given a photon with a wavelength of 589 nm, what is the energy of the photon?
Given a photon with a wavelength of 589 nm, what is the energy of the photon?
If a photon has an energy of 1.35 MeV, what is its corresponding wavelength?
If a photon has an energy of 1.35 MeV, what is its corresponding wavelength?
What is the formula to calculate the momentum of a photon?
What is the formula to calculate the momentum of a photon?
During radioactive decay, a certain nucleus emits a gamma ray. Which of these represents the photon energy?
During radioactive decay, a certain nucleus emits a gamma ray. Which of these represents the photon energy?
What would be the energy of a photon with a wavelength of 35 pm?
What would be the energy of a photon with a wavelength of 35 pm?
If the speed of light is $3 x 10^8 \text{ m/s}$, how would the frequency of a photon be calculated?
If the speed of light is $3 x 10^8 \text{ m/s}$, how would the frequency of a photon be calculated?
For a photon with a wavelength of 589 nm, what is the momentum?
For a photon with a wavelength of 589 nm, what is the momentum?
If the energy of a photon is increased, what happens to its wavelength?
If the energy of a photon is increased, what happens to its wavelength?
For a lamp emitting light at a wavelength of 589 nm, what is the frequency of emitted photons?
For a lamp emitting light at a wavelength of 589 nm, what is the frequency of emitted photons?
What is the kinetic energy of photoelectrons when the work function is 2.3 eV and the frequency is $3 \times 10^{15}$ Hz?
What is the kinetic energy of photoelectrons when the work function is 2.3 eV and the frequency is $3 \times 10^{15}$ Hz?
Does sodium exhibit a photoelectric effect with a red light wavelength of 680 nm if the energy required to remove an electron is 2.28 eV?
Does sodium exhibit a photoelectric effect with a red light wavelength of 680 nm if the energy required to remove an electron is 2.28 eV?
What is the cutoff wavelength for photoelectric emission from sodium with a work function of 2.28 eV?
What is the cutoff wavelength for photoelectric emission from sodium with a work function of 2.28 eV?
What is the fastest speed of photoelectrons emitted from tungsten when the energy of incident photons is 5.8 eV?
What is the fastest speed of photoelectrons emitted from tungsten when the energy of incident photons is 5.8 eV?
For aluminum, if light of wavelength 200 nm falls on it, what is the energy of the incident photons?
For aluminum, if light of wavelength 200 nm falls on it, what is the energy of the incident photons?
How is the maximum kinetic energy of a photoelectron derived?
How is the maximum kinetic energy of a photoelectron derived?
If the work function of tungsten is 4.5 eV, what happens when photons of 5.8 eV energy strike it?
If the work function of tungsten is 4.5 eV, what happens when photons of 5.8 eV energy strike it?
What is the energy of red light with a wavelength of 680 nm using the relationship $E = \frac{hc}{\lambda}$?
What is the energy of red light with a wavelength of 680 nm using the relationship $E = \frac{hc}{\lambda}$?
How is the work function defined in relation to photon energy?
How is the work function defined in relation to photon energy?
What formula is used to calculate the power radiated by a black body?
What formula is used to calculate the power radiated by a black body?
Using Wien's displacement law, what is the relationship between the maximum wavelength ($ ext{λ}_{max}$) and the temperature (T) of a black body?
Using Wien's displacement law, what is the relationship between the maximum wavelength ($ ext{λ}_{max}$) and the temperature (T) of a black body?
What is the value of the Stefan-Boltzmann constant ($σ$)?
What is the value of the Stefan-Boltzmann constant ($σ$)?
If the surface temperature of the sun is 5700 K, what is the radiated power from 1 cm² of the sun's surface?
If the surface temperature of the sun is 5700 K, what is the radiated power from 1 cm² of the sun's surface?
What does Planck's quantum hypothesis state about the energy of molecules?
What does Planck's quantum hypothesis state about the energy of molecules?
What determines the maximum wavelength of radiation emitted by a star?
What determines the maximum wavelength of radiation emitted by a star?
Which of the following is NOT a component of Max Planck’s formula for spectral radiancy?
Which of the following is NOT a component of Max Planck’s formula for spectral radiancy?
How is the power radiated related to the area (A) of the black body according to the Stefan-Boltzmann law?
How is the power radiated related to the area (A) of the black body according to the Stefan-Boltzmann law?
What is the stopping potential for photoelectrons when the work function is 1.8 eV and the light wavelength is 400 nm?
What is the stopping potential for photoelectrons when the work function is 1.8 eV and the light wavelength is 400 nm?
What is the maximum kinetic energy of photoelectrons emitted when the light wavelength is 400 nm?
What is the maximum kinetic energy of photoelectrons emitted when the light wavelength is 400 nm?
What is the cutoff wavelength for aluminum if its work function is 4.2 eV?
What is the cutoff wavelength for aluminum if its work function is 4.2 eV?
If the stopping potential changes from 0.71 V to 1.43 V, what is the new wavelength of the incident light?
If the stopping potential changes from 0.71 V to 1.43 V, what is the new wavelength of the incident light?
What is the kinetic energy of the photoelectrons when illuminated with light having a wavelength of 491 nm and finding a stopping potential of 0.71 V?
What is the kinetic energy of the photoelectrons when illuminated with light having a wavelength of 491 nm and finding a stopping potential of 0.71 V?
What would be the maximum speed of emitted photoelectrons if the stopping potential is 1.3 V?
What would be the maximum speed of emitted photoelectrons if the stopping potential is 1.3 V?
What is the work function for the surface if the stopping potential is found to be 1.43 V?
What is the work function for the surface if the stopping potential is found to be 1.43 V?
What is the relationship between work function, stopping potential, and maximum kinetic energy of emitted photoelectrons?
What is the relationship between work function, stopping potential, and maximum kinetic energy of emitted photoelectrons?
How is the maximum kinetic energy of electrons related to wavelength and stopping potential?
How is the maximum kinetic energy of electrons related to wavelength and stopping potential?
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Study Notes
Blackbody Radiation
- Blackbody radiation is emitted from a hot body due to the oscillation of electric charges in the molecules of the material.
- A blackbody absorbs all thermal radiation incident on its surface and emits radiation of wavelengths that depends only on its temperature.
- Wien's law states that the relationship between the temperature of a black body and the wavelength at which the intensity is maximum is inversely proportional.
- The formula 𝝀𝐦𝐚𝐱 × То = 𝟐𝟖𝟗𝟖 × 𝟏𝟎−𝟔 𝒎.K can be used to find the peak wavelength of radiation.
- Planck's quantum hypothesis explained that blackbody radiation is due to oscillating molecules at its surface.
- The energy of molecules has only discrete values given by 𝑬𝒏 = 𝒏𝒉𝒇 , where f is the frequency and n is the quantum number.
- Molecules emit or absorb energy in discrete packets (photons) by jumping between quantum states.
Photon Model
- The energy of a photon is directly proportional to its frequency.
- The energy of a photon is inversely proportional to its wavelength.
- The momentum of a photon is inversely proportional to its wavelength.
Photoelectric Effect
- The photoelectric effect is the emission of electrons from a metal when light shines on it.
- The work function (Φ) of a metal is the minimum energy required to remove an electron from the metal’s surface.
- The maximum kinetic energy of a photoelectron is equal to the energy of the incident photon minus the work function of the metal.
- The stopping potential is the potential difference that must be applied to the metal to stop the most energetic photoelectrons.
- The cutoff wavelength is the longest wavelength of light that can eject electrons from a metal.
Key Equations
- 𝝀𝐦𝐚𝐱 × 𝑻 = 𝟐𝟖𝟗𝟖 × 𝟏𝟎−𝟔 𝒎.𝑲 - Wien's displacement law
- 𝑬 = 𝜱 + 𝑲𝒎𝒂𝒙 - Einstein's photoelectric equation
- 𝑬 = 𝒉𝒇 - Einstein's photoelectric equation
- p= h/𝝀 - momentum of a photon
Key Figures
- ℎ = 6.626 x 10⁻³⁴ J.s - Planck constant
- 𝒄 = 3 x 10⁸ m/s - Speed of light
- k = 1.38 x 10⁻²³ J/K - Boltzmann constant
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