Radioactive Decay Simulator
Watch atoms decay one by one, at random, and see the half-life emerge from chance — for real isotopes, decay chains such as radon and its products, or the classroom dice and coin experiment.
At a glance
- Simulates 100 to 10,000 atoms. Each atom draws the exact moment it decays from the exponential distribution, so the result does not depend on the frame rate or the speed you choose.
- Pick any of 67 isotopes with their NUBASE2020 half-lives — from polonium-214 (164 microseconds) to uranium-238 (4.463 billion years) — and set how much time one second on screen stands for.
- Shows the counted atoms against the expected curve with a ±1 standard deviation band, and measures the half-life back from the run.
- Three real decay chains: strontium-90 → yttrium-90 (secular equilibrium), tellurium-132 → iodine-132 (transient equilibrium) and radon-222 with its short-lived products; or make your own parent and daughter. Expected numbers come from the Bateman equations.
- A dice and coins mode recreates the classroom experiment: remove every die that shows a six and the half-life is 3.8 throws; with coins it is exactly one toss.
- Optional Geiger counter clicks, an activity view, a log scale and a CSV download of every count for your own graphs.
Step by step
How to use the radioactive decay simulator
- 1
Choose what to simulate
Pick An isotope, A decay chain, or Dice or coins for the classroom version.
- 2
Choose the isotope and atoms
Select an isotope such as Ba-137m or I-131, and the number of atoms — more atoms give a smoother curve.
- 3
Start the clock
Press Start. Each square changes colour when its atom decays; set the Speed to show more or less time per second.
- 4
Compare with theory
Watch the counted line against the dashed expected curve. Switch the chart to Activity or a Log scale — on a log scale decay is a straight line.
- 5
Measure and download
Read the half-life measured from your run, then download the numbers as a CSV file.
Features
Everything you need, nothing you don’t
Randomness you can see
No atom knows when it will decay, yet thousands of them halve on schedule. The flashing squares and the wobbling line show both at once.
Exact, not stepped
Decay times are drawn for each atom, so a fast or slow speed, or a slow computer, never changes the physics.
Decay chains and equilibrium
See a daughter isotope build up until it decays as fast as it is made — the idea behind radon in homes and medical isotope generators.
The classroom experiment
Run the dice, coin or 20-sided-dice experiment with up to 1,000 objects, throw by throw, with the table a worksheet asks for.
Real data
Half-lives, decay modes and daughters come from NUBASE2020, the international evaluation published by the IAEA.
Data to take away
Download every count as a CSV file and plot it in a spreadsheet, or fit the half-life yourself.
Why decay is random but predictable
A radioactive nucleus has a fixed chance of decaying in any second, the decay constant λ, and nothing — not its age, temperature or neighbours — changes it. Which atom goes next is pure chance. But with many atoms the law of large numbers takes over: in each half-life about half of those left decay, and the count follows N = N₀ × (½)^(t ÷ T½).
The smaller the sample, the larger the wobble. The typical difference from the expected number is √(N₀ × p × (1 − p)), where p is the fraction expected to be left — about 16 atoms out of 1,000 after one half-life, but only 1.6 % of the sample instead of 5 % with ten times fewer atoms.
The decay chains
| Chain | What it shows |
|---|---|
| Strontium-90 (28.91 years) → yttrium-90 (64.05 hours) → zirconium-90 | secular equilibrium: after about a month the two activities are equal |
| Tellurium-132 (3.204 days) → iodine-132 (2.295 hours) → xenon-132 | transient equilibrium: iodine-132 settles 3 % above its parent’s activity and falls with it |
| Radon-222 (3.8215 days) → polonium-218 → lead-214 → bismuth-214 → polonium-214 → lead-210 | the short-lived products of radon reach equilibrium in about three hours |
| Your own parent and daughter | try a daughter that lives longer than its parent: then no equilibrium forms |
Dice and coins as atoms
The half-life in throws is ln 2 ÷ −ln(1 − p), where p is the chance of removal in one throw.
| Object | Removed when | Chance per throw | Half-life |
|---|---|---|---|
| Coin | it lands heads | 1 in 2 | 1 throw |
| Six-sided die | it shows a six | 1 in 6 | 3.80 throws |
| 20-sided die | it shows a 20 | 1 in 20 | 13.5 throws |
FAQ
Frequently asked questions
Can you predict when a single atom will decay?
Why does my simulation not match the curve exactly?
What is secular equilibrium?
How does the dice experiment model radioactive decay?
Is the simulation accurate for real isotopes?
Can I use the results for homework?
Keep going
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