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Photon frequency change taking recoil into account

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that if atom's recoil in transition is [itex]\frac{p^2}{2m}[/itex], the emitted photon's frequency changes by a factor of [itex]1-\frac{\Delta E}{2mc^2}.[/itex]


    2. Relevant equations
    Recoil momentum [itex]p = \frac{hf}{c}[/itex]
    m = mass of the atom
    p = momentum of the electron

    3. The attempt at a solution
    When photon is absorbed
    [itex]E_{atom} = mc^2 + E_{\gamma} = mc^2 + hf_0[/itex]

    When the photon is emitted
    [itex]\Delta E_{atom} = E_{atom} - E_{\gamma(emitted)} - E_r[/itex] where E_r = recoil energy.
    Solving that only leads to
    [itex]h(f_0 - f_1) = \Delta E_{atom} - mc^2 + \frac{p^2}{2m}[/itex]
    Which doesn't look right... So, what am i doing wrong?
     
  2. jcsd
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