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It struck me that in college textbooks, there are always derivations or explanations of equations of conversation of energy for the photoelectric effect, which contains work function, etc. However, there is no explanation for the conservation of momentum for the photoelectric effect.

I mean, considering the Compton Effect, while there are always explanations of both the conservation of energy and the conservation of momentum for the Compton Effect, there are none for the Photoelectric effect or only for the conservation of energy but not for the conservation of momentum.

Why does this situation occur? Is there a link between them that I seem to miss?

Is there a link between them that once you explain conservation rules for Compton there is no need for an explanation for the photoelectric effect?

What is the deal here?

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    $\begingroup$ It's probably because the photoelectric effect is really a multi-quantum phenomenon, we just neglect to treat the bulk of the metal quantum mechanically, which means that we also don't care where the momentum goes. Total momentum is, of course, conserved. A better example that's somewhat similar because the bulk is important and where we care about the momentum is the Moessbauer effect, I believe. $\endgroup$
    – FlatterMann
    Commented Jun 6, 2023 at 21:27

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For the Compton effect, the change in photon momentum must happen as a single event, just like in the photoelectric effect, the absorption of the photon energy must be a single event. When this is the case, the conservation must be strict; the electron alone must be able to extract the energy and momentum in that single event.

But after the electron absorbs the energy and momentum, it would be moving inwards the solid. Another mechnanism bounces it back out so that it exits the material. The whole solid crystal then absorbs the discrepancy in momentum.

This is actually rather complicated, because if the electron is free, then conservation of energy and momentum forbids the absorption of the single photon. Photoelectric effect is thus rather much more complicated than Compton scattering.

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  • $\begingroup$ Why would electron "be moving inwards the solid" after it absorbs the energy and momentum of incoming photon? $\endgroup$
    – medical physics
    Commented Jun 7, 2023 at 4:31
  • $\begingroup$ Remember the collision is supposed to be like billiard balls. The incoming photon, scattered or absorbed, delivers inward momentum to the electron. $\endgroup$
    – naturallyInconsistent
    Commented Jun 7, 2023 at 6:29

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