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Threshold frequency and wavelength of electrons in the photoelectric effect

  1. Dec 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Electrons are emitted from a metal as a consequence of their absorption of energy from a light beam. Find the threshold frequency of the metal and the wavelength of emitted electrons.

    Wavelength of incident light λ = 500 nm
    Work function of the metal [itex]\phi[/itex] = 2.1 eV

    2. Relevant equations

    Threshold frequency:

    f0 = [itex]\frac{\phi}{h}[/itex]

    3. The attempt at a solution

    Threshold frequency:

    f0 = [itex]\frac{2.1 eV}{4.136 \times 10^{-15} eV·s }[/itex] = 5.08 × 1014 Hz

    Is this correct?

    How can I find the wavelength of emitted electrons?
     
  2. jcsd
  3. Dec 3, 2012 #2

    mfb

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    Staff: Mentor

  4. Dec 3, 2012 #3
    Thanks for the confirmation.

    As I understand the photoelectric effect, one photon transfers all of its energy to an electron, so the energy absorbed by any electron must be the same (for a monochromatic beam), in this case hc/(500 nm) = 2.48 eV. Electrons need at least 2.1 eV to escape this metal, so they must have a maximum kinetic energy of 0.38 eV. Since not all of them have the same kinetic energy (due to losses) I assume they must have different wavelengths as well, how can I find the wavelength of emitted electrons?
     
  5. Dec 3, 2012 #4

    mfb

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    You can assume that they all have 0.38 eV. If you like, use "<=" in the calculations, but that won't change much.
     
  6. Dec 3, 2012 #5
    Ok, so it would be λ = [itex]\frac{hc}{\sqrt{2mc^2K}} \approx[/itex] 2 nm, right?
     
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