The extent of localization of a particle is determined roughly by its de Broglie wave. If an electron is localized within the nucleus (of size about `10^(14)`m) of an atom, what is its energy? Compare this energy with the typical binding energies (of the order of a few MeV) in a nucleus and hence argue why electrons cannot reside in a nucleus.

Explanation

Since the electron has been localised within the nucleus (of size about `10^(-14)m`) of an atom. So `lambda=10^(-14)m`.
Momentum of electron, `p=h/lambda=(6.63xx10^(-34))/(10^(-14))`
`=6.63xx10^(-20)kgms^-1`
The relativistic relation for the energy of an electron is
`E=sqrt(p^2c^2+m_0^2c^4)`
Neglecting the rest-mass energy term (i.e., second term), we have
`E=pc=(6.63xx3xx10^(-12))/(1.6xx10^(-13)) MeV=124.3MeV`
This energy `E=(124.3 MeV)` is very large as compared to the binding energy which is provided by Coulomb's force within the nucleus. Since the energy of electron inside the nucleus is very large as compared to binding energy of nucleus, hence the electron does not reside inside the nucleus.