Radioactive decay: a clock built from pure chance

Before you sit a thousand atoms of a radioactive element. Every one of them will decay — but which one next, and when? Nobody knows: not us, not the atom itself. Quantum mechanics says it is an event without a cause, pure roulette. Start the simulation and watch what happens when a thousand roulette wheels spin at once.

An atom has no memory

An old uranium atom is not one bit "closer" to decaying than a freshly made one. In every second of its existence it has exactly the same, unchanging probability of decay — it does not age, wear out or give warning. This is a radically different randomness from machines: a lightbulb burns out because its filament wears down. An atom decays for no reason at all.

If the probability per second is constant, then in every moment the same fraction of what remains is lost. And that leads straight to the most important number of this article: the time after which half the sample is gone.

Order out of chaos

Look at the curve on the right of the figure. Although every individual decay is unpredictable, the points line up obediently along a smooth exponential curve — crossing the ½, ¼ and ⅛ levels almost exactly every T½. This is the law of large numbers: chance averaged over thousands of trials becomes certainty. That is why a physicist can say nothing about one atom, and everything about a gram of uranium.

A single atom is capricious. A trillion atoms are as punctual as a clock.

A clock made of carbon

That punctuality is a ready-made clock. A living organism constantly exchanges carbon with its surroundings, so it maintains a steady trace level of radioactive carbon-14. Death stops the exchange — and from that moment C-14 only dwindles, by half every 5,730 years. By measuring how much is left in a piece of wood, bone or cloth, we read off when the organism stopped living. This is how mummies, sediments and medieval manuscripts are dated.

Different isotopes are clocks with different ticks: carbon-14 measures thousands of years, potassium-40 and uranium — millions and billions. They are how we know the Earth is 4.54 billion years old.

A simplificationThe simulation ignores what an atom decays into (decay chains, α, β and γ radiation), and the time scale is symbolic — the slider sets T½ in seconds so you can watch. Real dating also needs corrections for the varying level of C-14 in the atmosphere. The core stays exact: a constant per-atom probability yields exponential decay.