137 - Arthur I. Miller [24]
One of the ways in which Bohr’s original theory had been developed was to allow electrons to move in three dimensions, transforming the orbits into shells. In his lecture he described his latest work, which concerned how the electrons in an atom distributed themselves. The essence of the problem was the way in which atoms were built up, beginning with the hydrogen atom with its single electron. Understanding this would be a first step to explaining why the periodic table of chemical elements fell into place as it did, a key problem that everyone recognized needed to be cracked.
Examining the experimental data, Bohr proposed that there were two electrons in the first shell, eight in the second, and so on. He was then able to deduce these numbers from a series, each of which could be obtained from the formula 2n2, where n is the principal quantum number for the shell (in Bohr’s original model, n was the principal quantum number for an orbit, but orbits had now been replaced by shells). If n is 1 then the total number of electrons in the first shell is 2; if n is 2, the number of electrons in the second shell is 8; the next shell becomes 18, and so on. The assembled scientists discussed this series of numbers with great intensity. But as they listened, both Heisenberg and Pauli realized that there was no basis in fact to what Bohr referred to as the “building up principle.” As for Sommerfeld, he dismissed Bohr’s reasoning as “somewhat Kabbalistic.”
Bohr’s reasoning also failed to answer the problem of why every electron did not simply drop into the lowest shell—at least for atoms other than hydrogen and helium.
Pauli and Heisenberg argued fiercely with Bohr, who was impressed with their knowledge of physics and their uninhibited critical give-and-take. Bohr was also impressed with Pauli’s work on the H+2 ion and the helium atom, although in each case he had come up with a result that seemed to disprove Bohr’s own theory. Discussions continued into the evening in coffeehouses and on walks. Heisenberg complained that no one went to bed before 1 a.m. Pauli, of course, was in his element.
After the meeting, Bohr invited Pauli to visit Copenhagen for a year, from September 1922, to help in his research. Pauli replied rather arrogantly, “I hardly think that the scientific demands which you will make on me will cause me any difficulty, but the learning of a foreign language like Danish far exceeds my abilities.” He accepted nonetheless.
In Copenhagen Bohr set a problem that was to haunt Pauli for years and was one of the factors that led to his breakdown. The problem was on the anomalous Zeeman effect. To understand it, we have to go back to Pauli’s old mentor at Munich, Arnold Sommerfeld, and his work on the structure of spectral lines.
The discovery of 137
According to Bohr’s theory, when an electron drops from a higher to a lower orbit it emits light, which is recorded in the laboratory as a spectral line. Bohr was able to work out equations for these spectral lines that could be compared with the data obtained in the laboratory.
By 1915 scientists had more accurate spectroscopes that enabled them to make closer inspection of spectral lines. This revealed that many of the individual lines were in turn made up of several more closely spaced lines: they were said to have a “fine structure.” Certain spectral lines also split into several lines or “multiplets” when the atom was placed near a magnet, but the fine structure was always there.