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Actually, its more of a matter of why don't they fall into the nucleus and stop moving. You see, electrons are very chaotic particles that always move around because of the kinetic energy (kinetic energy is the energy of a moving object) they carry, and at a subatomic scale it is very difficult, and practically impossible, to "stop" a particle i.e. reduce its kinetic energy to zero. So you see, when electrons are bound by electrostatic forces to atomic nuclei, they can't fly away because of the attraction between the protons of the nucleus and them, but they also can't just stick to said nuclei because they still have kinetic energy which keeps them moving.

A simple analogy is spinning a string with a small stone tied to the opposing end. The stone spins around the opposite end of the string because it is bound to that point by the string, but it can't fall towards it because it has a lot of kinetic energy that's trying to make it fly away.

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