Half-life is the time for half of a radioactive sample to decay, and the count follows N = N0(1/2)^(t/t½). Drag the sliders below to set the half-life and the initial number of atoms, then watch the sample halve, and halve again, in real time.
Radioactive decay does its bookkeeping in fractions, not fixed amounts: each half-life carves away half of whatever remains, so the count steps down by a half, then a quarter, then an eighth, and keeps thinning without ever quite reaching zero. This simulator makes that repeated halving visible. Set the Half-life t½ slider (in seconds) and the Initial atoms N0 slider, then watch Atoms remaining N trace the curve N = N0·(1/2)^(t/t½), equivalently N = N0·e^(-λt).
The readouts pin down why the shape behaves as it does. The decay constant λ is computed straight from the half-life as λ = ln2 / t½, the mean lifetime τ as τ = 1/λ, and the Activity A as A = λN in becquerels. Push t½ higher and decay slows: a bigger half-life yields a smaller λ, a flatter curve, and a lower decay rate, because fewer nuclei break down each second.
Try the sim's own test. The panel reports % remaining and half-lives elapsed, and that percentage depends only on t/t½ — change N0 from a handful to billions and the fraction left after a given number of half-lives is identical. Half-life stays fixed for an isotope no matter the amount, temperature, or chemistry, which is exactly why carbon-14 (t½ ≈ 5730 yr) reliably dates old samples. Put real numbers to it with the half-life calculator, or step through more physics you can tweak by hand in the rest of the simulation library.
Half-life is the time it takes for half of the radioactive nuclei in a sample to decay. After each half-life the amount left halves again, following N = N0·(1/2)^(t/t½).
No — it removes the same fraction (half) of whatever is left, not a fixed number. So the count falls to a half, then a quarter, then an eighth, and so on, approaching but never quite reaching zero.
The fraction remaining depends only on how many half-lives have passed, not on the starting number N0. A bigger sample simply has proportionally more atoms and more decays per second, but the same half-life.
The decay constant is λ = ln2 / t½, and the activity — the number of decays per second, measured in becquerels — is A = λN. A longer half-life means a smaller λ and slower decay. Half-life is fixed for an isotope, unaffected by temperature or chemistry.