Physics 11–12 · Year 12

Half-life with dice and a decay simulation

Module 8: From the Universe to the Atom (Properties of the Nucleus)

Practical, model not builtLow risk

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The idea

Each unstable nucleus has a fixed chance of decaying per unit time, so a large sample loses a constant fraction in each half-life however many remain.

What you need

200 dice per group and a tray (the NSW Department of Education Module 8 guide activity)
Spreadsheet or graph paper

How to do it

Roll all the dice; remove every die showing a six (it has decayed) and record the number left; repeat until fewer than ten remain.
Plot the number remaining against roll number and read the number of rolls for the count to halve, at several points.
Change the rule (remove ones and twos) and repeat; compare the half-lives.
Compute the decay constant from the rule and compare ln 2 divided by the decay constant with the measured half-life.

What you should see

With a one-in-six rule the count falls to half every 3.8 rolls (ln 2 / ln(6/5)); the curve is exponential and the half-life is the same whether read from 200 to 100 or from 50 to 25. A one-in-three rule halves every 1.7 rolls. Successive halvings take equal numbers of rolls, which is what makes the half-life a property of the rule and not of the starting number.

What changes

What you change: decay rule (probability per roll)
What you measure: number remaining after each roll, half-life in rolls
What you keep the same: same starting number
every die rolled each time

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

After two half-lives nothing is left; a quarter remains.
A nucleus that has survived a long time is due to decay; its chance per second never changes.

Safety card

Low riskLearners carry it out

Hazards

dice on the floor

Controls

roll in a tray

Note

Record the activity in RiskAssess (https://www.riskassess.com.au/) and follow the Science ASSIST risk management information sheet (https://asta.edu.au/resource/ais-risk-management-and-risk-assessment/).

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Physics Stage 6 Syllabus (2017), current: Year 11 until the end of 2026, Year 12 until Term 3 2027PH12-15 PH11/12-5 PH11/12-6
Physics 11-12 Syllabus (2025), not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027, first HSC examination 2028PY-12-04 PY-12WS-04
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

All Concept Studio activities