As an undergrad physics student, I am pondering on this question. If an (2 level) atom absorbs a single resonant photon, the energy of electronic state increases by $\hbar \omega$. At the same time conservation of momentum states, that the atom must have a nonzero total momentum equal to $\hbar k$ after the interaction and therefore a nonzero kinetic energy. How does this work with energy conservation, which states that the total photon energy is transfered into exciting the electrons?
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As you point out, not all of the energy of the photon goes into exciting the electron, Similarly when stationary atom emits a photon, some of the electon level enenrgy goes into the recoil kinetic energy of the atom and the emited photon has less energy than expected. So in both cases $E_{\rm phton}\ne E_2-E_1$. This is why the suppression of the KE loss by the Mossbauer effect is important in precssion measurement..
mike stone
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