Radioactive decay with dice: does chance produce an exponential curve?

AA SLAI SLAA HLAI HL Accessible Also in: Modelling, Differential equations

Research question

When 200 dice are rolled repeatedly and every six is removed, does the number remaining follow N = N₀(5/6)ⁿ, and how closely does the experimental half-life match the theoretical one?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

No atom “knows” when to decay, yet a large sample decays exponentially. Rolling dice reproduces this exactly — and the randomness in your results is itself something to analyse.

The mathematics you'll need

Exponential models and half-life
Binomial distribution of the number removed each round
Logarithms to find the experimental decay constant
Expected value and variance; spread between trials

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Roll 200 dice (or simulate with a spreadsheet) and remove sixes; repeat the whole experiment several times.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Derive the expected model from p = 1/6.
Collect several decay runs.
Fit an exponential; compare the decay constant with ln(6/5).
Examine run-to-run variation using the binomial distribution.
Link to carbon dating and real half-lives.

Pitfalls that cost marks

One run only (you cannot discuss randomness).
Confusing the discrete and continuous models.
Fitting without explaining the log transformation.

Showing personal engagement

Try dice with different faces (d4, d20) and predict each half-life.
Compare your class's pooled data with individual runs.
Explain why small samples decay erratically.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Use your model to explain the uncertainty in radiocarbon dating of a small sample.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).