Exponential Decay

Radioactive decay is the archetype of exponential processes: every moment, a constant fraction of the remaining atoms transforms, so the quantity follows N(t) = N₀·e^(−λt) with λ = ln 2 / T½. It is memoryless — a sample of 1 g and a sample of 1 kg both decay halfway in exactly one half-life.

The Half-Life in Practice

Half-lives span 23 orders of magnitude — from polonium-214's 164 microseconds to uranium-238's 4.5 billion years. This range is what makes decay so versatile: iodine-131 (8 days) treats thyroid cancer then clears from the body, while carbon-14 (5,730 years) dates archaeology and potassium-40 (1.25 billion years) dates the Earth's rocks.

Decay Chains and Safety

Decay often continues through daughter products — uranium-238 passes through 14 steps before reaching stable lead. The 'ten half-life rule' is the practical safety guideline: after 10 half-lives less than 0.1% of an isotope remains, which is why medical isotopes are chosen with half-lives measured in hours to days.