Atomic stability

Okay, We all know that protons and electrons are oppositely charged particles and as such should be drawn towards each other but in the atom the electron maintains a respectful distance from the core. Could someone please explain how this process works (the less math the better), what is it that keeps them from coaleseing?

you can look at an electron as a wave. this is the wave/particle duality which states that particles can act like waves. this is proven by young's double slit experiment when light is replaced by electrons. this means that interference can occur between two or more electrons, or even one, which is in this case. when looking at the electron it starts to orbit around the nucleus. only where an electron constructively interferes with itself will an electron be found. this is where a crest meets a crest. this would mean that the closest an electron can get to the nucleus is where it is one wavelength long. this also explains why when an electron moves to a higher energy level it is never found between them.