OK. This is some weird stuff for people who haven't seen the math in a proper class. Do you know what a wavve function is? It describes where you are likely to find a particle in around an atom. Consider a one dimensional box. Just think of it as a very skinny slot that an electron can fit down into. Drawing a graph may help. Your x-axis is the length of the box going from zero to L (the opposite end of the box). The Y-axis is the probabilty of finding the electron (actually it's the square of the wave function). The wave function for an electron is a sine wave, it starts at 0 (almost) probability on one side of the box (x=0) reaches its maximum at 0.5L (you're most likely to find the electron in the middle of the box), and falls back to zero (almost, it's a weird phenomenon, gives rise to tunneling, don't worry about it for now) at L. The length L will be one half wavelength with respect to the wave-function. When you solve for the electron in three dimensions you get a nice even sphere. With p-orbital electrons you get a different wavefunction. You also start at y=0 at x=0, but it is one full wavelength in the box, that is the wave function rises to it's peak at x=.25L, falls back down to 0 at x=.5L, goes down to a minimum at x=0.75L, and goes back to zero at x=L. Remember,probability is the square of the wavefunction, so when it's squared the wavefunction in the negative becomes positive, but 0 squared is still zero, at the probability is still 0 at x=0.5L. So you've basically got two bumps at x=0.25 and x=0.75L where you are likely to find the electron and a node right in the middle where you don't find the electron at all. When solved for three dimensions, the p-orbital gives the dumbell shape. When you solve for the d-orbital you change wave functions again (giving a crest, trough, crest) which results in two nodes. And you get three nodes with the f-orbital.
Hope this didn't confuse you worse.
