Electrons *don’t* spin around the center.
In fact, for the first electron in an atom, the most likely place for it to be is in fact inside the nucleus, and that electron has no average orbital angular momentum at all!
The answer to your question comes from the fact that, at that scale, particles don’t have definite positions. They’re “smeared out”, and the lower their energy is, the more smeared out they are.
Making the electron “stay” inside the nucleus (that is, smushing all of it into that volume) requires confining it to a very small area, which takes much more energy than that electron actually has. Imagine a very hyperactive hamster: to keep it in one place you’re gonna need strong walls around it, otherwise it’s gonna run all over the place. Protons and neutrons, which are much larger than electrons (and therefore have much higher energies, because mass and energy are equivalent) smear out much less, but in fact they obey the same sort of behavior – there are ‘orbitals’ of sorts within the nucleus as well.
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