By the early 1920s, scientists had developed a reasonably satisfactory model of the atom. That model required three quantum numbers in order to explain the location and properties of the electrons in an atom. At this point, however, there remained a small number of observed properties that could not be explained by means of this model. For example, the number of spectral lines observed for an element was always twice what it ought to be, as predicted by the model.

In 1925, Wolfgang Pauli announced a method for dealing with this problem. He suggested adding a fourth quantum number to those already used in the atomic model. This new quantum number, he said, could have only two possible values. The inclusion of this new factor in existing equations, Pauli was able to show, explained the observed properties of spectral lines and resolved other remaining empirical difficulties. The...