In the textbook I am reading for class it is talking about the interactions of photons with atoms and how when an atom emits a photon it must have the same and opposite momentum of the emitted photon. I am confused on what the book means by "the atom must also have a 'recoil' kinetic energy". 
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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Jul 22 '23 at 22:55
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If the atom gets momentum ($mv$) how does it not get kinetic energy ($0.5mv^{2}$) as well? – Jon Custer Jul 23 '23 at 01:12
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The recoil is the momentum m*v the atom gets and one needs it for the total momentum is always conserved – trula Jul 23 '23 at 12:39
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A simple research gives several references of a recoil energy, it appears in another question appears in a similar question, an electron is a particle and a photon is also a particle, their interaction should respect the conservation of the energy and the momentum (often ignored in this case). A simple case where the energy and the momentum are important : absorption or emission of free electrons.
In this case of free atoms, the effect depends on the mass of the atom, the photon momentum is given by $p_\lambda=E/c$ and this recoil kinetic energy is given by : $K=1/2 M_{at} (p_\lambda/M_{at})^2 = 1/2 E^2/(M_{at}c^2)$, $K$ is very weak and negligible especially for heavy atoms.
M06-2x
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