Science 7–10 · Year 9

Radioactive dating with dice: half-life as a rule, not a clock

Science understanding: Chemical sciences (ACARA Year 9 radioactive decay, applied here to dating rocks; NSW Stage 5 focus area: Reactions, content group Nuclear reactions; the Stage 4 focus area Change covers only relative dating by superposition)

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

Each unstable atom has a fixed chance of decaying in a given time, so the number left halves every half-life; counting the parent left in a mineral against the daughter formed gives the rock's age.

What you need

100 six-sided dice per group (or 100 coins, or 50 washers painted on one side as in the SERC model)
a tray with a lid; a results table; graph paper or a spreadsheet

How to do it

Roll all 100 dice; remove every die showing a 1 (a decayed atom becomes a daughter) and record the number left.
Roll the remaining dice again; repeat until fewer than 5 remain, recording the count after every roll.
Plot dice remaining against roll number and read the number of rolls for the count to halve from 100 to 50 and from 50 to 25.
Pool the class results to smooth the curve and compare with the theoretical curve in the simulation.
Use the Earthlearningidea dating questions: a rock with 25 percent parent and 75 percent daughter for an element of half-life 200 million years is two half-lives old, 400 million years; one sixteenth parent with a 180 million year half-life is four half-lives, 720 million years.

What you should see

With a decay chance of 1 in 6 per roll the count falls by about one sixth each roll, and halves every 3.80 rolls (ln 0.5 / ln (5/6) = 3.80); a single group's curve is ragged, the pooled class curve lies close to 100 x (5/6) to the power n. With coins the half-life is exactly one toss. The worked dating answers are 400 million years and 720 million years. The learner knows it worked when the pooled curve halves near roll 4 and again near roll 8.

What changes

What you change: number of rolls (time)
What you measure: number of undecayed dice
What you keep the same: decay rule (a 1 decays)
starting number

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.
Decay happens on a schedule for each atom; each atom's decay is random and only the population is predictable.
Sedimentary rocks can be dated directly by radioactivity; their grains formed earlier, so igneous and some metamorphic rocks are dated instead, as the Earthlearningidea notes.

Safety card

Low riskLearners carry it out

Hazards

No hazard is listed.

Controls

No control is listed.

Note

No hazardous chemical and no flame or heating apparatus: a generic classroom risk assessment (CSIS 1.7 or RiskAssess) covers trips, spills, warm lamps and sharp edges.

Curriculum references

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

Science 7-10 Syllabus (2023), NSW Education Standards Authority (implemented from 2026; outcome code and content read at the focus-area content page on 22 September 2026); Stage 5 focus area Reactions (content group Nuclear reactions: the half-life of a radioactive isotope)SC5-RXN-01
Science 7-10 Syllabus (2023), NSW Education Standards Authority (implemented from 2026; outcome codes read at the outcomes page on 22 September 2026); Stage 5 Working scientificallySC5-WS-05 SC5-WS-06
Australian Curriculum v9AC9S9U06AC9S9I04AC9S9I05

Sources

The pages the author read to write this activity.

All Concept Studio activities