why an electron in an excited state is unstable but in the ground state it is stable??

The electrons themselves are not unstable; their excited states are. The excited state is unstable because it can be: it has extra energy that can be emitted spontaneously, sending the electron back to its ground state. The ground state has nowhere to go but up, and it requires an injection of energy from outside to go back up to an excited state. So it can’t, on its own, go anywhere.