Why electron can not exist in the nucleus of an atom?

Electrons

• They have a negative charge, and if they can exist in the nucleus, the positive charges will neutralize them. The radius of atomic nuclei is ${10}^{-15}\mathrm{m}$ when Heisenberg's uncertainty principle is applied, and if electrons were in the nucleus, the highest uncertainty inside its position would have been ${10}^{-15}\mathrm{m}$.

• We know that the size of an atomic nucleus is in the range of ${10}^{-15}\mathrm{m}$.
• The uncertainty in the position of an electron inside a nucleus should be ${10}^{-15}\mathrm{m}$
• Mass of electron$=9.1\mathrm{x}{10}^{-31}\mathrm{Kg}$

Heisenberg's uncertainty principle

• By Heisenberg's uncertainty principle
  $$\begin{gathered} ∆\mathrm{x}.∆\mathrm{p}\ge \frac{\mathrm{h}}{4\mathrm{\pi }} \\ \mathrm{momentum}(\mathrm{p})=\mathrm{mass}\left(\mathrm{m}\right)\mathrm{x}\mathrm{velocity}\left(\mathrm{v}\right) \\ \mathrm{v}\ge \frac{\mathrm{h}}{4\mathrm{\pi }∆\mathrm{x}.\mathrm{m}} \\ =\frac{6.626\mathrm{x}{10}^{-34}}{4\mathrm{x}3.14\mathrm{x}{10}^{-15}\mathrm{x}9.1\mathrm{x}{10}^{-31}} \\ =5.79\mathrm{x}{10}^{10}\mathrm{m}/\mathrm{s} \end{gathered}$$
  
• As a result, the velocity uncertainty will be $5.79\mathrm{x}{10}^{10}\mathrm{m}/\mathrm{s}$ which is far more than the speed of light, which is not possible.
• In the atom, no electron or particle has an energy greater than $4\mathrm{M}\mathrm{eV}$. As a result, electrons do not exist within the nucleus.