What it does
An unstable nucleus can decay at any moment, and nothing about its past tells you when. Each one is like a die: at every throw it has the same chance of showing a six. This page gives you hundreds of dice. Each throw, every die that shows a six is removed (it has “decayed”). The number left falls by about one sixth each time, so it halves again and again at a steady rate: a half-life appears out of pure chance. The page plots your counts against the smooth law N = N₀ e^(−λt), measures the half-life from your own throws, and lets you change the number of dice and the chance of removal (coins, ordinary dice, 10-sided and 20-sided dice).
It follows the school topic Class 12 Physics, Nuclei (radioactivity, the law of radioactive decay, decay constant, half-life and mean life). Next, binding energy explains why some nuclei are unstable, decay calculator works with real half-lives, decay chain simulator follows one nucleus decaying into the next, and counting statistics helper handles the randomness of real counts.
How to use it
- Choose how many dice to start with (50 to 1,000) and what removes a die (a coin’s heads, a die’s six, and so on).
- Press Throw once, or Keep throwing to throw every half second (press Stop to pause).
- The grid shows the dice: still in play, just removed, and gone. The graph shows the count after each throw (dots) and the smooth curve.
- Read the half-life from your throws (when half had gone) next to the expected half-life ln 2 / λ.
- Start again to try another run; the result is a little different every time.
Worked example
With 600 ordinary dice, each die has p = 1/6 chance of being removed per throw. The decay constant is λ = −ln(1 − 1/6) = 0.1823 per throw (close to p itself), so the half-life is t½ = 0.6931 / 0.1823 = 3.802 throws. After 4 throws you expect 600 × e^(−0.1823 × 4) = 289.4 dice left; a real run gives a number near that, often within about 12 either way. After 8 throws (about two half-lives) you expect 139.5, roughly a quarter.
With coins (p = 1/2), λ = ln 2 and the half-life is exactly one throw. With 20-sided dice (p = 1/20) it is 13.51 throws.
Check yourself
Five questions, fresh each time: the number left after a few half-lives, the half-life from a decay constant, the fraction left after a time, a coin-throw question, and whether you can predict which die goes next. Nothing is saved.
Tips
- Dice have no memory: a die that has survived ten throws is no more likely to go next time. Nuclei are the same, which is why the curve is exponential.
- The smaller the group, the bigger the wobble around the curve. Real samples hold so many nuclei that their counts follow the curve almost exactly.
- The mean life (average time a die lasts) is 1/λ, about 5.5 throws for a die: longer than the half-life.
FAQ
Why is λ not exactly 1/6? The throws are separate steps. The exact link is (1 − p) = e^(−λ), so λ = −ln(1 − p) = 0.1823; for small p it is very close to p.
Is decay really random? Yes. Quantum physics says there is no hidden clock in a nucleus; only the probability per second is fixed.
Is this from NCERT? No. It is an independent study aid that follows the same school topics, with its own pictures and numbers.
Where the numbers come from
- Radioactive decay law N = N₀ e^(−λt), half-life t½ = ln 2 / λ, and the dice model of decay (each die is removed with chance p per throw, so λ = −ln(1 − p)): standard physics.
- Checked against an independent Python calculation and against the average of 400 simulated runs, written for the tests.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.