Trying to wrap my head around the explanation for why the negatively charged electron is not pulled into the positive nucleus.

I gather it's not because of angular momentum, like a satellite; the electron is a smear of possible locations in a globe around the nucleus.

I came up with this representation: The electron as like a negatively charged fog, and the closer it is pulled to the nucleus, the smaller its volume, and therefore the more fiercely it repels itself. And an electron with a higher energy level would repel itself to a more outer shell.

Is that weak metaphor or a bit of truth?

I think it's a bit weak as a metaphor. It has more to do with the uncertainty principle and not so much about the electron repelling itself. The smaller the volume in which the electron should lie (probabilistically), the larger the momentum. So if you try to squish the electron cloud too small, you've got way too much energy in the electron for it to really hang around the proton anymore. This means that you've actually got to use a lot of energy to keep the electron contained in that region, but nature doesn't really do that.

So there's a balance there where the electron cloud is small enough to keep the electron close to the proton, but not so small that it takes extra energy to keep it there.

[/handwaving]

Repels itself?

No.

Such classical explanations inevitably reduce to absurdity.

(As Feynman would argue, QM explanations are also absurd... but they work.)

So momentum is the right way to think about it, the electron flies away but for the charge attraction. And it doesn't get stuck to the nucleus because it is flashing in and out of existence (for some unfathomable reason) within a range around nucleus.

Electrons can get to the nucleus with some probability and be captured;

https://en.wikipedia.org/wiki/Electron_capture

Classically you can have electrons orbit the nucleus and lose energy over time to radiation (because an accelerated charge radiates in classical electromagnetism so eventually the electrons would drop to the nucleus over time if that were the case making atoms impossible to be stable neutral systems with their properties as observed, a problem that was "solved" by the development of QM). But if they were not losing energy they would be orbiting just fine like planets.

Of course none of this works this way as classical charges. They just emit radiation in specific energy differences between states that are quantized.

So its not correct to think they have any hard time getting to the nucleus. Its just that the chance is very small for the typical wave function to "find it there" to begin with and because getting to nucleus in a meaningful way as in interacting with it, altering the nucleus and losing the electron, is a very small probability event due to various different reasons. For example it's not favorable energetically typically and even when it is it has a small rate this happens (that depends on many details and can become a lot more probable in relative terms in some isotopes or even chemical bond situations).

You can imagine them visiting the nucleus and its neighborhood often though. For example you can integrate the wavefunction probability density (https://en.wikipedia.org/wiki/Probability_amplitude) within the neighborhood of the nucleus and not get 0 at all. See for Hydrogen atom wavefunctions but also for other atoms that is more complicated ;

https://en.wikipedia.org/wiki/Hydrog..._hydrogen_atom


Of course a proper calculation for that would have to use more than basic Schrodinger equation which is ignoring the actual weak interaction of the electron with the protons (quarks).

Yay me, I could follow most of a Masque post.

Electron's can turn a proton into a neutron, that's interesting. Makes sense. Tks.