Absorption of a photon by atom - where does the energy go?

[wotanub]

I recently thought about this. Let's say there's a hydrogen-like atom with a transition energy \omega. If it is hit with a photon of frequency \omega, it will make a transition to the excited state, so the change in internal energy is \omega. But by conservation of momentum, the atom will also receive a momentum kick \vec{k}, causing a change in kinetic energy as perceived from the lab frame if we initially take the atom to be at rest in that frame.

So does some of the energy become the kinetic and some the internal? Does that mean we actually use off-resonant light to induce transitions since some of the energy will go into the kinetic?

Pretty sure this is simple and has to do with kinetic energy being frame dependent? In the center-of-mass frame, there is never any kinetic energy since there is only one massive body...

 

[Nugatory]

Pretty sure this is simple and has to do with kinetic energy being frame dependent? In the center-of-mass frame, there is never any kinetic energy since there is only one massive body...

Try working the problem in the center-of-momentum frame, not the center-of-mass frame - the photon does have momentum.

Once you've done that you can transform to the frame in which the atom is at rest. In that frame the frequency and the energy of the photon will be slightly different.

 

[mfb]

Yes, energy levels with/without recoil will be different. Mössbauer spectroscopy can avoid the recoil energy.