Alpha Decay: Gamow's 1928 Tunnelling Explanation
An alpha particle is classically trapped inside the nucleus by a Coulomb barrier higher than its energy, yet alpha emitters demonstrably emit. In 1928 Gamow — and independently Gurney and Condon — showed it tunnels through. This explained both sub-barrier emission and the Geiger–Nuttall relation, where small changes in alpha energy produce decay-rate changes across twenty orders of magnitude. Note that beta decay and electron capture are weak-force processes, not tunnelling.
**Alpha decay** is the emission of an alpha particle — two protons and two neutrons, a helium-4 nucleus — from a heavy atomic nucleus. It was the first nuclear process explained by quantum mechanics, and it remains the clearest case of matter genuinely shedding pieces by Quantum Tunnelling: Passing Through a Barrier You Cannot Climb. ## The paradox it resolved Inside the nucleus, an alpha particle is bound by the strong nuclear force. Outside, it is pushed away by electrostatic repulsion from the remaining protons. Between the two lies a **Coulomb barrier** — an energy hill considerably higher than the energy the alpha particle actually has. Classically the particle is trapped. It cannot climb the barrier, so it can never leave. Yet alpha emitters demonstrably emit alpha particles, with energies *below* the barrier height. Worse, the observed decay rates spanned an extraordinary range — from microseconds to billions of years — while emitted alpha energies varied only by a factor of a few. No classical model could produce that sensitivity. ## Gamow's solution In 1928 **George Gamow**, and independently Ronald Gurney and Edward Condon, applied the new quantum mechanics: the alpha particle does not climb the barrier, it **tunnels** through it. This explained both puzzles at once. Emission below the barrier is permitted, and because transmission depends exponentially on barrier width and height, a small change in alpha energy produces an enormous change in decay rate — reproducing the empirical **Geiger–Nuttall relation** between decay constant and alpha energy across more than twenty orders of magnitude. It was among the first decisive successes of quantum mechanics applied to the nucleus, and gave the field its first quantitative handle on radioactivity. ## Two clarifications **The alpha is treated as pre-formed.** The standard model of the process assumes an alpha particle exists within the nucleus, rattling against the barrier at some attempt frequency, with a small tunnelling probability per attempt. Rate = attempts × probability. The pre-formation assumption is an approximation. **Not all radioactivity is tunnelling.** Beta decay and electron capture proceed via the **weak interaction**, not tunnelling. This matters for a common conflation: the roughly 7,000–8,000 decays per second occurring in a human body come mainly from potassium-40 and carbon-14, which are beta and electron-capture emitters. Alpha emitters are present only in traces. So the body is radioactive, but it is not measurably shedding matter by tunnelling. See Can You Tunnel Through the Floor? The Compound Probability and the Barrier Maths.