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.

You know how the moon and the earth are positively attracted to one another via gravity?   It's the exact same concept.

Of course this is a simplified classical model of the atom, but unless you're getting into quantum mechanics it's a useful model.  It can even be used, with a small modification, to get a good approximation of orbital radii.

>>3
No, actually, no, it is not the exact same concept because gravity is an entirely different force than EM. The problem with an orbit caused by EM is that, were it an accurate depiction of the electron-nucleus system, the electron would radiate energy and spiral into the nucleus, which does not happen with gravity. That's the problem that requires wave-particle duality to solve.

>>2
This may flaunt my severally limited grasp of this subject but does this tie in with confinement energy aka. quantum mechanical kinetic energy? I found a article dealing with this subject which was a little math heavy for me but it states "The electron does not collapse into (coalesce with) the proton under the influence of the attractive Coulombic interaction because of the repulsive effect of the confinement energy - that is, kinetic energy." (http://www.users.csbsju.edu/~frioux/stability/hatomvar.htm).

>>4
GR also predicts radiating gravity waves.

Without turning this into a maths lecture, if the electron's energy is non-zero (which it must be as it is not at rest) the minimum-energy configuration of the system is the electrons existing outside the nucleus.  Pushing the electron into the nucleus requires energy input.

To think of the electron as a little concrete hunk of matter moving in a circle around the nucleus is helpful under certain circumstances but it is a grave oversimplification that can hinder your understanding.

It is what it is.  The mathematics is only a description of what we can observe of it, and quantum mechanics puts extremely strict limits on what we can observe of the universe at that level.  The map is not the territory.  C'est n'est pas un pipe.