Atomic Nucleus

[LJP07]

I just want to pose two simplistic questions about the atomic nucleus.

First, if the center of the nucleus it full of positive charge and like repels like, why don't the nucleus just disperse away from each other? I think a common explanation might be that the negative electrons negate the positive protons, but the problem here is that the electrons are weak and are spread as far apart as possible from each other and the dense nucleus would be stronger and have stronger repulsions which would exceed the negative charge attraction?

Does the nucleus have a definite shape, if so, how can this exist in a wave-like property?

[Mercedes Benzene]

The nucleus is held together by what's called nuclear force. I'm not very good with quantum mechanics, so if you want to know more about how this force works, I would try google.

As for the nucleus having a "definite shape", I don't really know how to approach an answer for that. Subatomic particles are always moving to some degree, so I don't think there would be a definite shape in that sense.
Do you mean to ask if the protons/neutrons always remain in the same position with regards to one another? If so, I would guess the answer is no, but they're definitely held together by nuclear force.