why electon cannot exist in the nucleus?

Dear student!

On the basis of Heisenberg's uncertainty principle, it can be shown as to why electron cannot exist within the atomic nucleus. 

Heisenberg's uncertainty principle has described that,

The diameter of atomic nucleus = 10^-15 m,

So,if electrons have to be in nucleus , they must have a maximum uncertainty in position as ,Δx = 10^-15 m

Now, taking the mass of electron as , m = 9.1 x 10^-31 kg, the minimum uncertainty in velocity could be determined as:

Δx . Δp = h/4π

or, Δx . mΔv = h/4π

or Δv = h/(4π . Δx . m)

Putting all the values of the constants, Δv = (6.6 x 10^-34 kg m²/s) / (4 x 3.14 x 10^-15 m x9.1 x10^-31 kg)

Or, Δv = 5.77 x 10¹⁰ m/s

Here, we see that the velocity is much higher than the usual velocity of light as 3 x 10⁸ m/s, which is not possible to have in electrons and so the existence of electron in nucleus is not possible.