The law of radioactive decay
Radioactivity is the spontaneous transformation of unstable nuclei into other nuclei with emission of a particle or radiation; A. Becquerel discovered it in uranium salts in 1896, and M. and P. Curie isolated polonium and radium. There are three kinds of radiation: α, helium nuclei; β, electrons; γ, high-energy photons; in a magnetic field α and β bend in opposite directions and γ does not bend. Decay is random: one cannot say when a particular nucleus will decay, but in a sample with many nuclei a law holds: N = N₀·2^(−t/T) = N₀·e^(−λt), where T is the half-life (the time in which half of the nuclei decay) and λ = ln 2/T ≈ 0.693/T is the decay constant. Every T the number of remaining nuclei halves: 1/2, 1/4, 1/8, … The activity is A = ΔN/Δt = λN, with the unit becquerel (1 Bq = 1 decay per second). T does not depend on temperature, pressure or chemical compound because the process happens inside the nucleus. T ranges from fractions of a second to billions of years. Radiation safety: natural background (a few mSv per year) is always present; to avoid extra dose, keep away from the source, shorten the time of exposure and use shielding (lead, concrete); never touch strange «metal» objects or sources, and if one is found tell adults and the authorities.
Model it with coins: toss 64 coins, set aside those that land heads as «decayed» and toss the rest again. The remaining numbers per round are about 32, 16, 8, …; make a table and draw the graph N(t). Experiments with real radioactive sources are not allowed.