Why electron cannot exist in the nucleus?

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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.

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.

In 1927, Erwin Schrodinger described the behavior of electrons around the nucleus by a mathematical equation known as Schrodinger wave equation. When the Schrodinger wave equation is solved, the solution gives information about the various energy states and other measurable properties of the system. For e.g., the solution of Schrodinger wave equation for an electron in a hydrogen atom provides information about the various energy states and other properties such as, radiation frequencies emitted or absorbed for the atom. The solutions are called wave functions and are denoted by the symbol Y.