137 - Arthur I. Miller [33]
The first was this: Suppose relativity had something to contribute on the subject. Pauli looked into it. He found that in the models of the atom proposed by Bohr and Heisenberg, electrons within the core moved at speeds comparable to that of light. They should therefore be expected to display variations in mass consistent with Einstein’s equation E = mc2. These variations should show up in the spacing between the multiplets, but experiments had not revealed any such effect and could mean only one thing: the core in these models had to be inert; it did not interact and so played no role at all. In other words, every model of the atom that featured a core was wrong.
Then he came across a paper by Edmund Stoner, a twenty-five-year-old physicist at Leeds University. Stoner went far beyond the anomalous Zeeman effect, although he himself had not realized the full significance of what he had found. It had to do with the problem constantly on Pauli’s mind: What stopped every electron in an atom from falling into the atom’s lowest energy level—its ground state?
By clever manipulation of the three quantum numbers for an electron in an atom, Stoner had succeeded in calculating the total number of multiplets of an alkali atom undergoing the anomalous Zeeman effect (that is, when it is placed within a weak magnetic field). He did this, as Heisenberg and Bohr had, by imagining the alkali atom to be made up of a closed core—made of shells filled to their maximum with electrons and so inactive chemically—with a single lone electron revolving around it. From this he was able to show that the total number of electrons in each closed shell was related to twice the total amount of angular momentum of the closed core with the lone electron.
What struck Pauli was the appearance of the number two. Bohr had inserted this number into his model of the core simply so that only halves would appear in formulas for the anomalous Zeeman effect. In other words, when the atom was in a magnetic field, the core containing the closed shells full of electrons could be distorted in two ways, which would give one of its quantum numbers a value of plus or minus a half.
But Pauli had established that the core was inert and that only the lone electron played any role in the chemical activity of an alkali atom. So why not transfer the two possible values of the core to this electron? Pauli began to suspect that Stoner’s work contained the seeds of something new and exciting. He decided to see what would happen if he extended Stoner’s method of manipulating quantum numbers to include a fourth quantum number that had the values of plus and minus a half for the lone electron. The result was astounding. He figured out that the total number of electrons in each closed shell was twice the principal quantum number of that shell squared. It was 2n2, the same number that Bohr had proposed with no basis from his theory of the atom. Now there was one.
Pauli went yet further, proposing that the two possible values for the fourth quantum number be assigned to every electron in every atom, regardless of whether the atom was in a magnetic field.
The conclusion had to be that each electron in an atom required four not three quantum numbers, and, to explain the periodic table of chemical elements, that no two electrons in an atom could have the same four quantum numbers. Basically, two electrons with the same quantum numbers cannot occupy the same shell. (This is Pauli’s famous exclusion principle. The name was given it by Paul Dirac, a physicist at Cambridge University.) This was the reason why Bohr’s building-up principle for atoms worked—why there are precisely two electrons in the inner shell, eight in the next, then eighteen, and so on. This was also why every electron in an atom did not fall into its lowest stationary state. They were prohibited from doing so.
To get a grip on this complicated concept, imagine that an atom is an apartment