Question

can an electron penetrate through nucleus.

Answer 1

It can’t be. Because each electron will be always at some discrete energy levels, that energy levels can be calculated by equation
〖 E〗_n=-(mq^3)/(8∈_0^2 h^2 ) 1/n^2

Here in this equation all are constants except ‘n’. ‘n’ is the electron state ‘a natural number’ and the lowest possible value of this is ‘1’. And ‘n’ can’t be zero or negative so theoretically there is a defined energy level for the closest possible state of an electron. For example, for hydrogen atom the lowest possible state of an electron will have -13.6eV. So mathematically it is not possible to define an electron into the nucleus. If you do it so in some way also, you can’t able to describe or prove a nucleus with electron.