(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Photon frequency change taking recoil into account

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