Question

explain " electron Is a stable particle and is stable outside the nucleus of an atom" in DETAIL.

Answer 1

There are some rules of conservation of mass and charge that each particle follows:
The mass of a decaying particle must exceed the sum of the masses of the particles produced in its decay.
The total electric charge before and after a decay must be the same.

And since the electron is the lightest particle that has electric charge, there is nothing that it can decay to; only neutrinos, photons, gluons and gravitons are lighter, but they are all electrically neutral, so any combination of them would have zero electric charge. So the electron is stable.