Question

why do electrons stay far from protons​

Answer 1

The answer is that electrons do in fact “fly right into the nucleus of an atom.” The lowest energy orbitals in most atoms do overlap the nucleus, and so the electrons spend some of their time moving through that volume of space. Electrons and protons aren't little cannonballs orbiting around each other.

Answer 2

Answer:

The reason that protons and electrons don't just “stick together” is that as electrons are attracted closer and closer to protons, they lose potential energy (resulting in a “lower energy state”). But this energy has to go somewhere, and a lot of it is converted to kinetic energy.