The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [58]
This is very encouraging, but we have a final piece of the jigsaw to explain: why is it that only two electrons can occupy each available energy level? This is a statement of the Pauli Exclusion Principle, and it is clearly necessary if everything we have been discussing is to hang together. Without it, the electrons would crowd together in the lowest possible energy level around every nucleus, and there would be no chemistry, which is worse than it sounds, because there would be no molecules and therefore no life in the Universe.
The idea that two and only two electrons can occupy each energy level does seem quite arbitrary, and historically nobody had any idea why it should be the case when the idea was first proposed. The initial breakthrough was made by Edmund Stoner, the son of a professional cricketer (who took eight wickets against South Africa in 1907, for those who read their Wisden Cricketers’ Almanack) and a former student of Rutherford’s who later ran the physics department at the University of Leeds. In October 1924, Stoner proposed that there should be two electrons allowed in each (n, l, m) energy level. Pauli developed Stoner’s proposal and in 1925 he published a rule that Dirac named after him a year later. The Exclusion Principle, as first proposed by Pauli, states that no two electrons in an atom can share the same quantum numbers. The problem he faced was that it appeared that two electrons could share each set of n, l and m values. Pauli got round the problem by simply introducing a new quantum number. This was an ansatz; he didn’t know what it represented, but it had to take on one of only two values. Pauli wrote that, ‘We cannot give a more precise reason for this rule.’ Further insight came in 1925, in a paper by George Uhlenbeck and Samuel Goudsmit. Motivated by precise measurements of atomic spectra, they identified Pauli’s extra quantum number with a real, physical property of the electron known as ‘spin’.
The basic idea of spin is quite simple, and dates back to 1903, well before quantum theory. Just a few years after its discovery, German physicist Max Abraham proposed that the electron was a tiny, spinning electrically charged sphere. If this were true, then electrons would be affected by magnetic fields, depending on the orientation of the field relative to their spin axis. In their 1925 paper, which was published three years after Abraham’s death, Uhlenbeck and Goudsmit noted that the spinning ball model couldn’t work because, in order to explain the observed data, the electron would have to be spinning faster than the speed of light. But the spirit of the idea was correct – the electron does possess a property called spin, and it does affect its behaviour in a magnetic field. Its true origin, however, is a direct and rather subtle consequence of Einstein’s Theory of Special Relativity that was only properly appreciated when Paul Dirac wrote down an equation describing the quantum behaviour of the electron in 1928. For our purposes, we shall need only acknowledge that electrons do come in two types, which we refer to as ‘spin up’ and ‘spin down’, and the two are distinguished by having opposite values of their angular momentum, i.e. it is like they are spinning in opposite directions. It’s a pity that Abraham died just a few years before the true nature of electron spin was discovered, because he never gave up his conviction that the electron was a little sphere. In his obituary in 1923, Max Born and Max Von Laue wrote: ‘He was an honourable opponent who fought with honest weapons and who did not cover up a defeat by lamentation and nonfactual arguments … He loved his absolute ether, his field equations, his rigid electron, just as a youth loves his first flame, whose memory no later experience