I need help getting started solving the following. Show that when the recoil kinetic energy of the atom, p^2/2M, is taken into account the frequency of a photon emitted in a transition between two atomic levels of energy difference delta-E is reduced by a factor which is approximately (1 - delta E/2Mc62). (Hint: The recoil momentum is p=hv/c.) Compare the wavelength of the light emitted from a hydrogen atom in the 3-->1 transistion when the recoil is taken into account to the wavelength without accounting for recoil. My text book is very vague on this topic so I was wandering if anyone knows where to start answering a quesiton like this. Any useful formulas that I can use to do this proof. If so, do you have any good links relating to this material. What is recoil kinetic energy and momentum? I understand that a photon is emitted when an electron is reduced to a lower energy state. I just don't understand how this recoil KE fits in and how to relate everything. I need a starting point!! Thanks for any help you can provide. I am not looking for someone to answer this for me, just someone to help me through it. Thanks.
Start with conservation of momentum. Before the photon is emitted, the net momentum of the system is 0, therefore the momentum of atom P = Mv must equal the momentum of the photon p = E/c = h[itex]\nu[/itex] for the net momentum to remain 0. So the atom then recoils with a velocity v = P/M = p/M. Now since the atom moves, the wavelength/frequency are affected - Doppler effect.