I believe this question to be different from the usual "Why don't electrons fall into the nucleus" because this
A: asks about the details of explanations for why electrons don't fall into the nucleus.
B: comes from a different level of understanding about the electron models and doesn't start with a 'bohr' model.
C: assumes the explanations to be true and instead asks about Why they are true, Especially when talking about 'infinite' energies.
I have stackoverflow experience so I try to follow the rules best I can but this is my first question on this stack exchange variant so I apologize if I do anything wrong with regards to the specifics of physics stack exchange (I've tried reading the help page so thats what I'm going off of).
My current level of understanding is that I've taken Physics 1 and 2 college courses so I have a basic understanding of the basic newtonian laws + Electromagentism and some of the more modern stuff and I know a (tiny) bit about quantum effects. Wave particle duality is familiar to me but I don't understand why it is so, only that it is that way. So please if you have any equations I'd appreciate links and a reference to what the variables mean as I won't recognize them (unless its like e=mc^2 or something), But I am good at math.
What I'm doing/what I know
I'm trying to understand the explanation(s) for why electrons don't fall into the nucleus because my physics 2 professor wasn't able to provide an explanation. So far I understand that:
electrons are not balls of matter orbiting the nucleus like in the bohr modle, rather they are a probability cloud around the nucleus.
that electrons have a smaller mass and negative charge that when interacting with a positive charge of a nucleus causes an attraction force and that when this happens photons are emitted
The Heisenberg Uncertianty principle means that determining an electron's position and momentum at the same time is impossible and that when you know an electron's position you can't have any idea what momentum it has and vice versa.
The main question
The question I have is mainly about the details of the explanation(s) for why the electron doesn't 'fall into' the nucleus (even though I've heard it can spend non trivial amounts of time in the nucleus). So far I've seen it said that as the electron cloud approaches the nucleus it's kinetic energy approaches positive infinity and it's potential energy approaches negative infinity. Also, one of the provided explanations is that when the electron reaches the nucelus, it has a position which is almost certain, thus due to the Hiesenberg uncertianty principle, that means its momentum must be very uncertian and thus large. I have many questions about this explanation for why this cloud of electron probabilities has a limit of infinities (potential energy -infinity to kinetic energy +infinity) and why it is said that it converges to around a factor of 2 (with kinetic energy being greater thus causing a 'stable orbit' because the electron can escape but not too much).
I've also heard that the reason for electrons not falling into the nucleus is because they are already in the lowest energy state possible and thus are stable. I don't see where this stability is coming from unless its from the above balance between kinetic and potential energies because I can't see any reason for the nucleus to repel the electron 'cloud'.
How I've tried to envision it
From a simple energy perspective I can understand why a kinetic energy dominance would cause a stable orbit but the problem I have is seeing why the kinetic energy dominates in the first place, why the kinetic energy dominates by a factor of about 2, and why it approaches positive infinity and why the potential energy approaches negative infinity when the electron approaches the nucleus. The infinity part of this is the most confusing part to me because;
From my simplistic point of view, I have a finite distance from electron cloud to nucleus and I have two 'particles' with finite masses with finite energies and an interaction in finite time. If this is true then where does this 'infinite' kinetic energy come from?
I try to compare this to what I would imagine a more standard model of the 'motion' would be. For example, modeling a planet falling into a star with gravity as the force of interaction doesn't cause the planet to gain infinite kinetic energy because it can only ever have a finite potential energy because it is a finite distance away and has finite mass and falls inside the star in finite time. Sure the planet can escape but only if it has enough potential energy to begin with. It doesn't ever have infinite kinetic or potential energy. Even if you make the planet a 'cloud' with no determinable momentum AND position and change gravity to electromagnetic attrraction wouldn't the same basic laws of motion still apply? Yes I know quantum effects are weird with regard to motion and stuff but I want to know if/how/why its different in this case.
Is it truly Infinite?
The other thing that confuses me about these 'infinite' energies is that they are infinite, which means we should see some crazy things, like crazy amounts of heat or mass or light being created right? So how in the world does this work? Is there some other limit I'm not taking into account here?
The only thing I could possibly envision as a solution to this problem is that
A(likely): I'm thinking about it entirely wrong OR
B: the kinetic energy doesn't actually become infinite and rather it is simply always large enough to enable an eventual escape of the electron cloud from the nucleus.
I could only see B coming from some sort of repulsive force from the nucleus. I can't however see where that force comes from, gravity wouldn't matter on that small a scale, I think the strong force would only attract the particles, the weak force I don't know much about, and the electromagnetic force is already the main force of attraction being discussed so where would any repulsion come in? I remember seeing somewhere that neutrons might repel electrons in some cases but then that leaves open the question of electrons falling into hydrogen nuclei with no extra neutron.
Maybe I'm reading it wrong and it isn't infinite
But if the energies wern't infinite then how can it be garenteed that electrons shouldn't always/almost always fall into the nucleus? Is it garenteed at all? Because according to my current understanding it seems to be garenteed at least somewhat because if it weren't it would break almost everything. Clearly that isn't happening since I can type right now and my atoms aren't just spontaneously collapsing in on themselves and becoming neutrons. Perhaps only a small number actually do this and that number is so small it becomes trivial? I don't really know but I thought that (at least for stable isotopes) there wouldn't be any decay or something like that but radioactive decay is totally different from an atom collapsing in on itself so I could be misunderstanding this.
Sidepoint: If electrons can and do spend non-trivial time inside the nucleus, does that change the behavior of the atom itself while the electron is inside the nucleus? Do they actually contact each other? Because supposedly thats supposed to create a nuetron and that would probably affect alot of things.
So, I humbly request some clarification on this issue. Why infinite energies? Why do they converge to two? Why does kinetic energy dominate here? Is any of this right at all? Do they actually fall into each other and create neutrons? Do they never do this and its garenteed to be so?