Pauli Exclusion Principle

In the early 1920s, Pauli reached an important insight about the nature of an electron's quantum numbers. Suppose, Pauli said, that an atom contains eight electrons. Then it should be impossible, he predicted, for any two of those electrons to have exactly the same set of quantum numbers.

As an example, consider an electron in the first orbit. All first-orbit electrons have a primary quantum number of 1. Then, mathematical rules determine the quantum numbers that are possible for any given primary quantum number. For example, Sommerfeld's secondary quantum number can be any integer (whole number) from 0 to one less than the primary quantum number, or, l = 0 n - 1. For an electron in the first shell (n = 1), l can only be 0. The third quantum number can have values that range from +l to -l. In this example, the third quantum number must also be 0. Finally, the fourth quantum number represents the spin of the electron on its own axis and can have values only of +1/2 or -1/2.

What Pauli's exclusion principle says about this situation is that there can be no more than two electrons in the first shell. One has quantum numbers of 1, 0, 0, +1/2 and the other, of 1, 0, 0, -1/2.

More variety is available for electrons in the second shell. Electrons in this shell have quantum number 2 (for second shell). Mathematically, then, the secondary quantum number can be either 1 or 0, providing more options for the value of the magnetic quantum number (+1, 0, or -1). If one writes out all possible sets of quantum numbers of the second shell, eight combinations are obtained. They are as follows: