Blackbody Radiation and Photon Model
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Questions and Answers

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?

  • Moves to lower intensities
  • Remains unchanged
  • Moves towards shorter wavelengths (correct)
  • Moves towards longer wavelengths

    • 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?

    <p>550 nm</p> Signup and view all the answers

    How does the intensity of electromagnetic radiation behave as the wavelength decreases?

    <p>Intensity increases infinitely</p> Signup and view all the answers

    What is the thermal emissivity of a perfect blackbody?

    <p>1</p> Signup and view all the answers

    If the effective surface temperature of the sun is 5800 K, what is the expected wavelength at which it radiates most strongly?

    <p>490 nm</p> Signup and view all the answers

    According to the wave model, at what region does intensity tend to zero as wavelength increases?

    <p>Infrared region</p> Signup and view all the answers

    What is the formula to calculate the energy of a photon from its wavelength?

    <p>$E = \frac{1240}{\lambda(\text{nm})}$</p> Signup and view all the answers

    Given a photon with a wavelength of 589 nm, what is the energy of the photon?

    <p>2.11 eV</p> Signup and view all the answers

    If a photon has an energy of 1.35 MeV, what is its corresponding wavelength?

    <p>9.2 x 10^-13 m</p> Signup and view all the answers

    What is the formula to calculate the momentum of a photon?

    <p>$P = \frac{h}{\lambda}$</p> Signup and view all the answers

    During radioactive decay, a certain nucleus emits a gamma ray. Which of these represents the photon energy?

    <p>1.35 MeV</p> Signup and view all the answers

    What would be the energy of a photon with a wavelength of 35 pm?

    <p>3542.86 eV</p> Signup and view all the answers

    If the speed of light is $3 x 10^8 \text{ m/s}$, how would the frequency of a photon be calculated?

    <p>$f = \frac{c}{\lambda}$</p> Signup and view all the answers

    For a photon with a wavelength of 589 nm, what is the momentum?

    <p>1.24 x 10^-27 kg.m/s</p> Signup and view all the answers

    If the energy of a photon is increased, what happens to its wavelength?

    <p>The wavelength decreases</p> Signup and view all the answers

    For a lamp emitting light at a wavelength of 589 nm, what is the frequency of emitted photons?

    <p>5.1 x 10^14 Hz</p> Signup and view all the answers

    What is the kinetic energy of photoelectrons when the work function is 2.3 eV and the frequency is $3 \times 10^{15}$ Hz?

    <p>10.1 eV</p> Signup and view all the answers

    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?

    <p>No, it does not</p> Signup and view all the answers

    What is the cutoff wavelength for photoelectric emission from sodium with a work function of 2.28 eV?

    <p>543.86 nm</p> Signup and view all the answers

    What is the fastest speed of photoelectrons emitted from tungsten when the energy of incident photons is 5.8 eV?

    <p>6.76 x $10^5$ m/s</p> Signup and view all the answers

    For aluminum, if light of wavelength 200 nm falls on it, what is the energy of the incident photons?

    <p>6.2 eV</p> Signup and view all the answers

    How is the maximum kinetic energy of a photoelectron derived?

    <p>$K_{max} = h u - \Phi$</p> Signup and view all the answers

    If the work function of tungsten is 4.5 eV, what happens when photons of 5.8 eV energy strike it?

    <p>Electrons are emitted with a maximum kinetic energy.</p> Signup and view all the answers

    What is the energy of red light with a wavelength of 680 nm using the relationship $E = \frac{hc}{\lambda}$?

    <p>1.82 eV</p> Signup and view all the answers

    How is the work function defined in relation to photon energy?

    <p>It is the energy required to remove an electron from the surface of a material.</p> Signup and view all the answers

    What formula is used to calculate the power radiated by a black body?

    <p>$P = ext{σ} A e (T_2^4 - T_1^4)$</p> Signup and view all the answers

    Using Wien's displacement law, what is the relationship between the maximum wavelength ($ ext{λ}_{max}$) and the temperature (T) of a black body?

    <p>$ ext{λ}_{max} T = 2.898 imes 10^{-3} m ullet K$</p> Signup and view all the answers

    What is the value of the Stefan-Boltzmann constant ($σ$)?

    <p>$5.67 imes 10^{-8} W m^{-2} K^{-4}$</p> Signup and view all the answers

    If the surface temperature of the sun is 5700 K, what is the radiated power from 1 cm² of the sun's surface?

    <p>$5.9 imes 10^{3} W$</p> Signup and view all the answers

    What does Planck's quantum hypothesis state about the energy of molecules?

    <p>Energy is quantized in discrete packets called photons.</p> Signup and view all the answers

    What determines the maximum wavelength of radiation emitted by a star?

    <p>Its surface temperature.</p> Signup and view all the answers

    Which of the following is NOT a component of Max Planck’s formula for spectral radiancy?

    <p>Speed of sound (c)</p> Signup and view all the answers

    How is the power radiated related to the area (A) of the black body according to the Stefan-Boltzmann law?

    <p>Power is proportional to area.</p> Signup and view all the answers

    What is the stopping potential for photoelectrons when the work function is 1.8 eV and the light wavelength is 400 nm?

    <p>1.3 V</p> Signup and view all the answers

    What is the maximum kinetic energy of photoelectrons emitted when the light wavelength is 400 nm?

    <p>1.3 eV</p> Signup and view all the answers

    What is the cutoff wavelength for aluminum if its work function is 4.2 eV?

    <p>200 nm</p> Signup and view all the answers

    If the stopping potential changes from 0.71 V to 1.43 V, what is the new wavelength of the incident light?

    <p>376.06 nm</p> Signup and view all the answers

    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?

    <p>1.8 eV</p> Signup and view all the answers

    What would be the maximum speed of emitted photoelectrons if the stopping potential is 1.3 V?

    <p>6.76 x 10^5 m/s</p> Signup and view all the answers

    What is the work function for the surface if the stopping potential is found to be 1.43 V?

    <p>1.87 eV</p> Signup and view all the answers

    What is the relationship between work function, stopping potential, and maximum kinetic energy of emitted photoelectrons?

    <p>Work function = Stopping potential + Maximum kinetic energy</p> Signup and view all the answers

    How is the maximum kinetic energy of electrons related to wavelength and stopping potential?

    <p>Kmax = (hc/λ) - φ</p> Signup and view all the answers

    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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    Description

    This quiz explores the concepts of blackbody radiation and the photon model, including Wien's law and Planck's quantum hypothesis. Understand how temperature affects radiation and the relationship between energy and frequency of photons. Test your knowledge of these fundamental physics principles.

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