# Homework Help: Photon frequency change taking recoil into account

1. Oct 5, 2011

### Uniquebum

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

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

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

When the photon is emitted
$\Delta E_{atom} = E_{atom} - E_{\gamma(emitted)} - E_r$ where E_r = recoil energy.
$h(f_0 - f_1) = \Delta E_{atom} - mc^2 + \frac{p^2}{2m}$