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What you will learn
- Radioactive decay is random for each nucleus.
- Large samples follow an exponential trend.
- Half-life is a statistical property, not a countdown for one nucleus.
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Atomic Physics · reward round
Half-Life Heist
A vault of unstable nuclei, each decaying at random with the true probability 1 − e^(−λ·dt) per tick. Drag the marker to the moment you think the survivors will hit the target count, lock the call, and watch: the smooth ghost is N₀e^(−λt), the jagged line is what the dice actually did. Your score is how few half-lives you missed by.
Score0best 0 · streak 0× · within 0.15 T½ = +3
Your call12.0s1.50 half-lives of T½ = 8 s
Sample64leftof 64 · target 32 · level 1/5
Score 0 · level 1/5 · 64 nuclei, T½ = 8 s. Call the moment 32 remain.
How the physics works
Every surviving nucleus is rolled independently each tick: it decays with probability p = 1 − e^(−λ·dt), where λ = ln 2 / T½ is the decay constant. Nothing in the code draws an exponential — the smooth curve emerges from the statistics, which is exactly how nature does it.
The dashed ghost is the expectation N₀e^(−λt); the jagged line is one particular history. With 64 nuclei the two hug each other; by the deep-tail levels, where only a handful survive, single decays visibly kink the trace — the scatter in a count of N is about √N, so small samples are loud. That is why your call is scored in half-lives: it measures your miss against the only clock the nucleus owns.
The two-isotope level is a preview of real decay chains: a short half-life means a steep dive and an early quiet grid, a long one means a slow burn. Same law, different λ — and no nucleus, fast or slow, ever gets old. Its odds per second never change.
Game 24 · Atomic Physics learning guide
Turn the playthrough into a physics lesson.
Learning objectivePredict when a stochastic radioactive sample will reach a target count and compare a single run with the smooth decay law.
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How to play
- Read the isotope, initial count, half-life, and target count.
- Drag the time marker to make a prediction from the smooth decay curve.
- Lock the call and compare the jagged simulated result with the expected trend.
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Quick classroom check
After three half-lives, what fraction of a large original sample is expected to remain?
Suitable forUpper-secondary physics · radioactivity and exponential decay
Continue this topic
Move from play to explanation and exam-style practice.
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