On the basis of Heisenbergs uncertainty principle show that the electron cannot exist within the nucleus.

Explanation

The radius of the atomic nucleus is `10^(-15) m`. Now, if the electron were to exist within the nucleus, then the maxium uncertainty in its position would have been `10^(-15) m`.
or `" " Delta x = 10^(-15) m`
Now according to uncertainty principle,
`Delta x xx DeltaP ge h/(4pi)`
or `" " Delta x xx m Delta v ge h/(4pi)`
or `" " Delta v ge h/(4 pi m Delta x)`
Mass of electron , `m = 9.1 xx 10^(-31) kg`,
`Delta x = 1 xx 10^(-15) m`
`:. Delta v = (6.6 xx 10^(-34))/(4 xx 3.14 xx 9.1 xx 10^(-31) xx 1 xx 10^(-15))`
`= 5.77 xx 10^(10) ms^(-1)`
The value of uncertainty in velocity , `Delta v` is much higher than the velocity of light `(3.0 xx 10^8 ms^(-1))` and therefore, it is not possible. Hence an electron cannot be found within the atomic nucleus.