Why does electrons hover around the core of the atom instead of moving towards protons...

look at OP's picture they're just flat rings it only looks like 3D motion because there's a lot of them

Before an electron is observed it exists in a superposition of all possible states, effectivly an assembly of different probabilities. A certain number of those states will be inside the radius of the nucleus. However once the electron is observed the probability collapses to a single state. the most likely state is (off the top of my head) [math]3a/4 [/math] where [math] a [/math] is the Bohr radius, normally when we do some experiment like this we take a large number of electrons and then look at the average, which is predicted (and experimentally verified) to be [math] a [/math].

The take away points from this are:
>The electron has no definite position before a measurement is made
>On measurement, the probability distribution collapses to single state
>The most likely position is [math] 3a/4 [/math]
>It has a small, but non-zero, probability of being found within the radius of the nucleus.

god doesn't play dice

>Einstein pls go

But seriously at this point it's pretty clear the man lost that debate (hell it was pretty clear during his life time).

>attract one another
because electrons hate each other
en.wikipedia.org/wiki/Pauli_exclusion_principle