Radioactivity

Three types of ionizing radiation

An unstable nucleus can shed energy and charge in three fundamentally different ways. Alpha and beta radiation were already distinguished in 1899 by Ernest Rutherford based on their different penetrating power; the even more penetrating gamma radiation, discovered in 1900 by Paul Villard, was fitted into this scheme by Rutherford in 1903 — long before the exact nature of all three types of radiation was understood.

Penetrating power compared: alpha is stopped by skin or paper alone, beta needs aluminum, gamma requires a thick lead shield.

Half-life

Radioactive decay is a purely random process at the level of the individual nucleus — no one can predict exactly when a given atom will decay. For a large number of nuclei, however, this randomness gives rise to an exact statistical law: in every equal span of time, the half-life t_½, exactly half of the nuclei still present always decay — regardless of how many there were at the start.

Half-lives vary enormously: Polonium-214 decays within a tenth of a millisecond, while Uranium-238 takes 4.5 billion years — almost the age of the Earth. This constancy turns radioactive isotopes into precise "clocks," as used in radiocarbon dating.

Decay chains & radioactive equilibrium

Many heavy nuclei don't reach stability in a single step. Uranium-238, for instance, runs through an entire decay chain of fourteen consecutive alpha and beta decays before finally arriving at stable Lead-206. Every intermediate product in this chain is itself radioactive again, each with its own, often very different half-life.

The 1.17-minute value belongs to the short-lived isomer Protactinium-234m, which forms in over 99.8% of cases; the remaining, longer-lived Protactinium-234 (ground state, half-life ≈ 6.7 hours) also ends up at Uranium-234, but via a rarer side path.

The first step of this chain — the alpha decay of Uranium-238 — shows just how sensitively half-lives react to the physics behind them. For an alpha particle (a helium nucleus) to break free of the uranium nucleus, it would classically have to overcome the Coulomb barrier — the electric repulsion between it and the positively charged remaining nucleus, against which it doesn't actually have enough energy. It escapes anyway, but only via quantum tunneling: a small, but nonzero, probability of crossing this barrier per attempt, rather than surmounting it. How small that probability is depends extremely sensitively on the energy released in the decay — and Uranium-238 releases unusually little of it (about 4.3 instead of the up to 9 megaelectronvolts (MeV) of other alpha emitters). That makes the barrier comparatively thick and the tunneling attempt succeed only extremely rarely: a single uranium nucleus "tries" an inconceivable number of times per second, but almost always fails — on statistical average, it only succeeds after 4.47 billion years.

The same decay chain, but plotted on the nuclide chart (N vs. Z) instead of as a table: each alpha decay jumps two fields to the left and two down (Z−2, N−2), each beta decay moves one field to the right and one down (Z+1, N−1). Same color = same element, regardless of mass number — U, Po, and Pb each appear more than once as different isotopes.