I Electron capture and electron transitions.

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When a nucleus captures an electron from the innermost orbit, its proton number reduces one. Therefore, energy levels in the atom have to change accordingly, meaning all the electrons have to move lower energy levels. From this point of view, during an electron capture, can it be said that the electrons give off EM waves due to the transition between energy levels?

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can it be said that the electrons give off EM waves due to the transition between energy levels?
Yes. The effect of changing the energies of the levels because of the change in atomic number is actually pretty small; the bigger effect is that there is now a "hole" in a low energy level, and an electron from a higher level can occupy the hole, emitting EM radiation as it does so (usually the emitted radiation is X rays). That leaves another hole that a still higher electron can occupy, etc., until the new atom is in its ground state.
 

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