Question

why electrons don't fall into the nucleus while moving around it in an atom

Answer 1

according to the bohr's model of atom , the nucleus consists of only protons and neutrons and the electrons must move around in the atom. if the electron falls into the nucleus , those matters which exist now will not be possible!!

Answer 2

The electrons have a lot of energy and speed. They move around the nucleus. The force of attraction of protons and electrons makes them curve in circle around nucleus.  It is similar to Earth and Sun or   moon and Earth.

If electrons were stationary, then they would fall into nucleus. Because of attraction they get continuously attracted and go in orbits around nucleus.