One of my students asked me, "Why does the electron move at all?" I admitted I didn't know and would like to find out for myself and for her. Thanks - David DeCarli
Awesome question! (Give your student my compliments for thinking it up!) Naturally, one would think that because protons are positively charged, and electrons are negatively charged, the two should attract and stick together. The reason that doesn't happen can't even begin to be explained using classical physics. This was one of the key mysteries that were cleared up right away by the invention of quantum mechanics around 1925.
The picture you often see of electrons as small objects circling a nucleus in well defined "orbits" is actually quite wrong. As we now understand it, the electrons aren't really at any one place at any time at all. Instead they exist as a sort of cloud. The cloud can compress to a very small space briefly if you probe it in the right way, but before that it really acts like a spread-out cloud. For example, the electron in a hydrogen atom likes to occupy a spherical volume surrounding the proton. If you think of the proton as the size of a grain of salt, then the electron cloud would have about a ten foot radius. If you probe, you'll probably find the electron somewhere in that region.
The weird thing about that cloud is that its spread in space is related to the spread of possible momenta (or velocities) of the electron. So here's the key point, which we won't pretend to explain here. The more squashed in the cloud gets, the more spread-out the range of momenta has to get. That's called Heisenberg's uncertainty principle. It could quit moving if it spread out more, but that would mean not being as near the nucleus, and having higher potential energy. Big momenta mean big kinetic energies. So the cloud can lower its potential energy by squishing in closer to the nucleus, but when it squishes in too far its kinetic energy goes up more than its potential energy goes down. So it settles at a happy medium, with the lowest possible energy, and that gives the cloud and thus the atom its size.
That basically answers your question, although we admit that the answer sounds strange. There really are very definite mathematical descriptions to go along with those words.
You might be interested in some more properties of those electrons in atoms.
If just the right amount on energy is applied, it is possible to knock an electron up to a higher energy orbital (a different shape of cloud, not so close to the nucleus), or even completely off of the atom. If electrons are knocked off of the atoms, they can create electricity. (This is what you see when you look at a VanDeGraff Generator or at lightning.)
If they are only given some energy, but not enough to knock them loose, they will move from one orbital to another (say from the S-orbital to the P-orbital). But if there is no other electron in the lower-energy orbital, they will fall back down again. When they do, they release energy in the form of a photon (light). This is part of the concept that lasers are based on.
Well...I apologize for this answer being so long. Thanks for sticking with me up to here! I hope this answers your question.