|MadSci Network: Chemistry|
Unfortunately the model you have been taught is very limited. The images of electrons "circling" the nucleus analogous to the planets around the sun is not correct. The more accurate model requires an understanding of the theories of Bohr, Planck, Heisenberg, Schroedinger, and others. It is collectively referred to as the quantum mechanical model.
What is missing from the simple Rutherford-Bohr orbit model you see in most elementary textbooks, is the concept that electrons have an intrinsic magnetic component. This property is referred to as "spin," which is not really quite correct either, but let it be described simply by saying that each electron in an atom has a magnetic orientation. We can refer to it the same way we may describe the position of bar magnets.
Therefore to start things off: in order that two electrons might occupy the same space they must have opposite magnetic orientations. Just as two bar magnets put near each other would repel unless the orientations are opposite, two electrons occupying the same space (or orbital) must have opposite spins.
This would describe the stable configuration of Helium with two electrons in the lowest energy level (1s) having opposite spins. Helium is very stable and unlikely to engage in chemical reactions. This explains why it is so useful in welding.
Moving up the periodic table makes life more difficult. Lithium and Beryllium have two more electrons which occupy the next energy level (2s). These too must have opposite magnetic orientations. Unfortunately this idea of succesive energy levels having two more electrons of opposite spins does not apply for the next 6 elements.
The electrons of the non-metals represented by Boron-Neon do not occupy the simple spherical energy levels like H-Be. Instead they have a more complex shape (called p) oriented as oblong regions in the x, y, and z three dimensional coordinate system. Thus by the time you reach Neon there are 6 electrons paired with opposite spins in the x (left and right), y (up and down), and z (forward and back) directions. This configuration with 2 s electrons and 6 p electrons gives you the stable octete configurations of Argon, Krypton, Xenon, and Radon.
Complications arise when you exceed 20 total electrons but that is a very advanced topic better suited for a graduate chemistry student.
Try the links in the MadSci Library for more information on Chemistry.