Why are protons allowed in the nucleus?

[snorkack]

The "nucleus" is not one thing; it's multiple particles. Unless you are considering a hydrogen-1 nucleus, but in that case the center of the orbital is where the proton is, so your objections don't even apply to that case in the first place.
I have no idea what you are talking about here. Do you have a reference?

Basic Newton´ s 3rd Law.
A force must have an equal and opposite force. When a proton attracts an electron, the electron must attract the proton with equal and opposite force. Force is rate of change of momentum. You may therefore choose a frame of reference where the momenta of electron and proton are always equal and opposite - once they are such, they stay this way.
Proton is indeed at the centre of orbital on average, just as the electron is at the centre of orbital on average. But proton can only be at the centre of orbital when the electron is at the cusp. When electron moves away from the centre of orbital, so must the proton, by Newton´ s 3rd Law.
But the distance relevant to electrostatic attraction between electron and proton is not the one between electron and the (empty) centre of orbit. It is the (longer, because consisting of both arms) full distance between electron and proton.

 

[PeterDonis]

Basic Newton´ s 3rd Law.

We're not talking Newtonian physics, we're talking quantum mechanics. Nothing you are saying makes sense in quantum mechanics.

 

[PeterDonis]

The OP question has been answered. Thread closed.