Chapter I
Too Many Elements
By 1910 chemists had separated about forty radioactive substances, each with its own half-life, but there were only a dozen or so places for them in the periodic table. Frederick Soddy, now in Glasgow, saw in 1913 that many of them could not be separated from known elements by any chemistry. They were the same element with different masses. He called them isotopes, from the Greek for "same place". Henry Moseley showed the same year that an element's place in the table is set by the charge of its nucleus, not its weight.
Francis Aston, J. J. Thomson's assistant in Cambridge, built the instrument that proved it. His mass spectrograph of 1919 sorted charged atoms by mass with great precision. Ordinary neon was a mixture of neon-20 and neon-22. Nearly every isotope weighed almost exactly a whole number of hydrogen masses, but not quite. Helium weighed about 0.7% less than four hydrogen atoms. By Einstein's from special relativity, that missing mass was energy given off when the nucleus formed.
Chapter II
Protons and Neutrons
What was the nucleus made of? In 1919 Ernest Rutherford, firing alpha particles through nitrogen, knocked out hydrogen nuclei. He had, as Patrick Blackett showed in 1925, changed nitrogen into oxygen, the first nuclear reaction made by hand, and the hydrogen nucleus, the proton, was clearly a building block. But protons alone gave the wrong masses. Helium has twice the charge of hydrogen and four times the mass.
In 1932 James Chadwick found the missing piece. The Joliot-Curies in Paris had seen beryllium emit a radiation that knocked protons out of wax, and took it for gamma rays. Chadwick showed it was a neutral particle about as heavy as the proton: the neutron. A nucleus is built of protons and neutrons, and isotopes differ in their neutrons. Something must hold the protons together against their electrical repulsion. In 1935 Hideki Yukawa proposed a force carried by a new, heavy particle, the first theory of the strong force and the start of a long road to particle physics.
Chapter III
A Drop and a Shell
Quantum mechanics could not yet calculate a nucleus from its parts. Physicists used models instead. In 1935 Carl Friedrich von Weizsäcker treated the nucleus as a drop of liquid, whose binding energy grows with its volume, is reduced at its surface, and is weakened by the protons' repulsion. The formula fitted the measured masses remarkably well. Niels Bohr used the same picture to explain how a nucleus swallows a neutron. Four years later it would explain fission.
Yet some nuclei did not fit. Those with 2, 8, 20, 28, 50, 82 or 126 protons or neutrons were unusually stable and common, like the noble gases among atoms. In 1949 Maria Goeppert Mayer, an unpaid "voluntary associate professor" at the University of Chicago, found the explanation after Enrico Fermi asked her whether there was any evidence of spin–orbit coupling. There was. If each particle's spin is strongly tied to its orbit, the energy levels group into shells that close at exactly those numbers. Hans Jensen, with Otto Haxel and Hans Suess, found the same answer in Germany. A drop and a set of orbits were both right, for different questions.
Chapter IV
A Closer Look: Weighing the Glue
Atomic masses are measured in atomic mass units, u, and 1 u of mass is equivalent to 931.5 MeV of energy. A hydrogen atom weighs 1.007825 u and a neutron 1.008665 u. A helium-4 atom, two of each, weighs 4.002602 u. The parts add up to
so the helium atom is lighter by u. That mass defect is the binding energy:
about 7.1 MeV for each of its four particles. Breaking the bonds between atoms in a molecule takes a few electronvolts. Nuclear binding is a million times stronger.
Doing the same for other nuclei gives the binding energy per particle:
| Nucleus | Mass (u) | Binding energy (MeV) | Per particle (MeV) |
|---|---|---|---|
| Deuterium, ²H | 2.014102 | 2.2 | 1.1 |
| Helium-4 | 4.002602 | 28.3 | 7.1 |
| Carbon-12 | 12.000000 | 92.2 | 7.7 |
| Iron-56 | 55.934936 | 492.3 | 8.8 |
| Uranium-235 | 235.043930 | 1783.9 | 7.6 |
The numbers rise steeply among the light nuclei, peak near iron, and fall slowly towards uranium. This curve is the most important fact in nuclear energy. Joining light nuclei moves up the steep side and releases energy, which is fusion. Splitting a heavy nucleus into two medium ones moves up the gentle side, about 0.9 MeV per particle, which is fission. Iron sits at the top, and neither process can get energy out of it.
Chapter V
Splitting and Joining
The binding-energy curve pointed two ways. Its heavy side led, in 1938, to nuclear fission and to the reactor and the bomb. Its light side, already known to power the stars, led to the effort to build fusion energy on Earth. The shell model, meanwhile, predicted that beyond the heaviest known elements there may be an island of stability that no one has yet reached.