Question

A typical atomic radius is about 5 x 10-15 m and the energy of (3-particle emitted from a nucleus is at most of the order of 1 mev. Prove on the basis of uncertainty principle that the electrons are not present in nuclei.

Answer 1

On the basis of Heisenberg's uncertainty principle, it can be shown as to why electron cannot exist within the atomic nucleus. The radius of the atomic nucleus is of the order of 10-15 m. Now, if the electron were to exist within the nucleus, then the maximum uncertainty in its position would have been 10-15 m.

         DELTA x  * DELTA p =h/4 pi

            DELTA v=h/4 pi m delta

Heisenbergs uncertainty principle  

                   delta v= 5.77 *10^10 ms^-1

DELTA x  * DELTA p =h/4 pi

            DELTA v=h/4 pi m delta

Mass of electron, m = 9.1 x 10-31 kg, Dx =1 x 10-15 m.

The value of uncertainty in velocity, Dv is much higher than the velocity of light (3.0 x 108 ms-1) and therefore, it is not possible. Hence an electron cannot be found within the atomic nucleus.