Radioactive Decay & Half-Life Simulator

The half-life (T½) of a radioactive isotope is the time it takes for half of the undecayed nuclei in a sample to decay. It is a fixed property of each isotope and does not depend on how much you start with: after one half-life half the nuclei remain, after two half-lives a quarter, after three an eighth, and so on. The simulator marks these N₀/2, N₀/4, N₀/8 levels on the decay curve.

For a large sample the number of undecayed nuclei falls exponentially: N(t) = N₀·e^(−λt), where N₀ is the starting number and λ is the decay constant. The decay constant is linked to the half-life by λ = ln2 / T½, and the mean lifetime of a nucleus is τ = 1/λ = T½/ln2. At n whole half-lives this reduces to the simple result N = N₀/2ⁿ, which is exactly what the curve shows.

Activity is the rate at which nuclei are decaying, measured in becquerel (Bq, one decay per second). It is proportional to how many undecayed nuclei are left: A = λN. Because both N and A share the factor e^(−λt), the activity falls off with the same half-life as the number of nuclei — so an old source is both smaller in count and quieter in activity. The simulator plots A(t) alongside N(t) to make that proportionality visible.

Whether any single nucleus decays in the next second is genuinely random and cannot be predicted. But with a very large number of nuclei, the average behaviour is extremely smooth — like flipping millions of coins at once — and that average follows the exponential N₀·e^(−λt) precisely. This tool shows that deterministic average curve for a single isotope; it is the large-sample limit of the underlying random process.

It models a single radioactive isotope with the deterministic exponential decay law and its half-life, matching the Cambridge IGCSE 0625 radioactivity content and the IB E.3 decay law. A nucleus-by-nucleus stochastic (Monte-Carlo) simulation and decay chains with daughter products — where one isotope decays into another that then decays itself — are deliberately out of scope, the same way this tool keeps to the clean, examinable single-isotope case.

Half-life questions reward a clear routine — read the half-life off a decay curve, halve repeatedly, or use N = N₀/2ⁿ and the exponential law when the time is not a whole number of half-lives. A GetYourTutors physics specialist who comes to your home in Dubai can work through past-paper decay-curve and activity questions with your child, connect λ, T½ and τ, and clear up the common confusion between count, activity and fraction remaining.