E.3.6—Random radioactive decay

Treat each nucleus independently

Radioactive decay is spontaneous and random: the exact nucleus and instant of decay cannot be predicted. For a large sample, however, the fraction decaying per unit time follows a stable statistical law.

Separate random from law-like

Random decay does not mean the activity is random noise. The expected number of decays is predictable from the number of undecayed nuclei and the decay constant.

Apply the statistical model

You cannot identify which nucleus will decay next. But if two large samples contain the same nuclide and the second has twice as many undecayed nuclei, its expected activity is twice as large. Individual unpredictability and ensemble predictability coexist.

Common trap

Do not claim that randomness prevents prediction of half-life or activity. It prevents prediction of an individual decay, not the ensemble behaviour.