Feynman says:
"What keeps the electrons from simply falling in? This principle: If they were in the nucleus, we would know their position precisely, and the uncertainty principle would then require that they have a very large (but uncertain) momentum, i.e., a very large kinetic energy. With this energy they would break away from the nucleus. They make a compromise: they leave themselves a little room for this uncertainty and then jiggle with a certain amount of minimum motion in accordance with this rule."
This is an informal analysis of why elecrons have a ground state that is outside of the nucleus.
If this was violated you can compute the momentum of the electron required to satisfy the Heisenberg Uncertainty Principle for position vs momentum ... and the momentum calculated this way is more than the "escape velocity" for the positive nucleus.