why an electron cannot stay inside nucleus?

Answer 1

An electron interacts with the nucleus primarily via the Coulomb interaction. Since this interaction is very weak relative to the hadronic interaction that binds the nucleus together, the lowest energy solution to the Schrodinger equation of quantum mechanics is widely dispersed around the nucleus.

To show this, the S. equation obeys the Heisenberg uncertainty principle p*x>h where h is constant, p is momentum uncertainty and x is position uncertainty. Since Coulomb interaction is weak, it effects momentum and, therefore, its uncertainly very little. That means the uncertainty in x is larger. That means the orbit is large.

Answer 2

If an electron does collide with the nucleus, it will be electrostatically drawn to a proton, which it will convert to a neutron by means of (inverse) beta decay with electron capture. After that, it is no longer an electron.

Answer 3

If you apply the Heisenberg uncertainty principle, you will see that with the electron so closely localized, its energy must be very high so it will escape quickly.