8. The Machinery Behind The      Periodic Table
The Better Theory: Wave Mechanics
 These quantum numbers describe electronic states of different energy and geometry. One radical difference between the new quantum theory and the Bohr theory is that we have to abandon forever any hope of knowing the exact path of an electron around the nucleus. Classical mechanics would have led us to believe that if we were skillful enough, we could know the position of the electron at every instant in time, and plot its precise trajectory. The Bohr theory replaced a billiard-ball electron by a stationary wave around a circular orbit, but still let us give a precise numerical value for the radius of the orbit. Wave mechanics take even this away from us. Instead of an electron's position, all that we know is the probability that an electron will be at any selected point in space. Solving the mathematical wave equations for an electron in a particular quantum state (n,l,m) around an atom yields a wave function, (x,y,z), which varies from one point in space (x,y,z) to another. The wave function, , has no direct physical meaning, but the square of the wave function, , is proportional to the probability of finding the electron at point (x,y,z) rather than somewhere else. The end result, when plotted, is a fuzzy cloud of electron probability around the nucleus for each (n,l,m) quantum state. The density of the probability cloud at each region in space represents the probability that the electron will be found there, and not elsewhere. These electron probability clouds are sketched on the next page for I = 0, 1, and 2, or for s, p, and d states.
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