Radioactivity
The spontaneous emission of radiation (alpha, beta, or gamma) by unstable nuclei as they decay toward stability. Radioactive decay is a random process; the half-life t₁/₂ (time for the number of nuclei to halve) characterises the decay rate. Activity A = λN (number of decays per second), where λ is the decay constant. The number of nuclei decreases exponentially: N(t) = N₀ exp(−λt).
Formula
N(t) = N₀ e^(−λt)
Real World
Carbon-14 dating was used to confirm that the Shroud of Turin dates to the 13th–14th century — scientists measured the remaining fraction of ¹⁴C activity and applied exponential decay to determine its age.
Exam Focus
Show full working when calculating half-life: derive λ = ln2/t½ first, then substitute — missing this intermediate step is a frequent source of lost marks.
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