The chart of the nuclides. Each square is one kind of nucleus, a nuclide: its place is set by the number of neutrons, N (across), and the number of protons, Z (up). The mass number is A = N + Z. The white squares are the nuclides that are stable. They lie in a narrow band, the valley of stability. Light nuclei have about as many neutrons as protons, but heavier nuclei need more neutrons to stay together (the protons repel each other, and extra neutrons add attractive strong force without adding repulsion). All the other nuclei are unstable: they are radioactive, and they change by decaying towards the valley.

Alpha decay. A heavy nucleus gives out an alpha particle, a helium nucleus (2 protons and 2 neutrons). So Z goes down by 2 and A by 4. On the chart you move two down and two left. This is common in the heaviest nuclei, which are too big to be stable.

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

Beta-minus decay. A nucleus with too many neutrons changes a neutron into a proton, and gives out an electron and an antineutrino. Z goes up by 1 and N down by 1, so A stays the same. You move one up and one left. Beta-plus decay (a nucleus with too many protons changes a proton into a neutron, and gives out a positron and a neutrino) and electron capture go the other way: one down and one right.

²³⁴₉₀Th → ²³⁴₉₁Pa + ⁰₋₁e + antineutrino

Decay chains. The nucleus left behind is often unstable too, so there is a chain of decays until a stable nucleus is reached. Natural radioactivity has three long chains: the uranium-238 series (8 alpha and 6 beta decays, ending at lead-206), the thorium-232 series (6 alpha, 4 beta, ending at lead-208) and the uranium-235 series (7 alpha, 4 beta, ending at lead-207). In each decay, mass number and charge are conserved: add up the A and the Z on both sides. The neptunium series (here started from americium-241, the nuclide in smoke detectors) ends at bismuth-209. The half-lives in a chain go from billions of years (uranium-238) to a fraction of a microsecond (polonium-214). Where two arrows leave a nucleus, the decay goes either way with a fixed chance.

Radiation and shielding. The three kinds of radiation penetrate very differently. Alpha particles (large and doubly charged) lose their energy to the atoms in their way very quickly: a few centimetres of air, or a sheet of paper, or the dead outer layer of your skin, will stop them. Beta particles (electrons) go further: metres in air, and a few millimetres of aluminium stops most of them. Gamma rays (high energy photons) have no charge and go through a lot of material: their intensity falls off exponentially, I = I₀ e^−μx, and it takes thick lead (a few centimetres) to reduce them a lot. The half-value thickness is the thickness that halves the intensity: x_½ = ln 2 / μ. A Geiger counter detects each ionising particle that gets into the tube as a click. The radiation from a small source also falls off with the inverse square of the distance, because it spreads out in all directions.

What the model leaves out. The chart shows only the nuclides in the decay chains and the stable ones. The squares for other unstable nuclides are not drawn, and the band for the valley of stability is a rough guide. A few of the decays also give out gamma rays that are not shown. The half-lives are rounded. The counts are random (Poisson), with typical rates and absorption data (the beta absorption is approximately exponential, and the alpha range in air is 4 cm).

Things to try. (1) Run the uranium-238 chain, and count the alpha and beta steps. Check that A and Z end at lead-206. (2) Which step in the chain has the shortest half-life? (3) Why does the chain split in two places? (4) With the Geiger counter, show that paper stops alpha particles but not gamma rays. (5) Measure the half-value thickness of lead for gamma rays. (6) Double the distance from the source: what happens to the count rate?