Earth and Environmental Science 11–12 · Year 11
Modelling radioactive decay with dice and calculating a radiometric age
Module 1: Earth’s Resources
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The idea
Decay is random for each atom yet exactly predictable for a large number, so the parent-to-daughter ratio in a mineral is a clock.
What you need
- 100 dice per group (or 100 coins, or 100 identical cubes marked on one face)
- a tray with a lip, tally sheet, graph paper or spreadsheet
How to do it
- Throw all 100 dice; remove every die showing a six (a decayed atom) and record how many remain.
- Throw the survivors again; repeat for 12 throws or until fewer than five dice remain.
- Pool the class results and plot survivors against throw number for one group and for the class total.
- Find the throw count at which half remain and compare with the value predicted for a survival probability of 5/6.
- Use the ratio of daughters (removed dice) to parents (remaining dice) to read an age from the clock formula, then repeat for real half-lives in the calculator.
What you should see
Expected survivors after n throws are 100 × (5/6)ⁿ: 83.3, 69.4, 48.2 (n = 4), 23.3 (n = 8) and 11.2 (n = 12); the half-life is ln 2 / ln(6/5) = 3.80 throws. One group scatters around the curve and the pooled class total follows it more closely. Age from the clock t = T½ × log₂(1 + D/P): with uranium-238 (T½ = 4.468 × 10⁹ years, BNL NuDat) a daughter-to-parent ratio of 1 gives 4.47 Ga and a ratio of 0.5 gives 2.61 Ga. For carbon-14 (T½ = 5700 years) the daughter, nitrogen-14, cannot be told from nitrogen already present, so the age comes from the fraction of carbon-14 remaining: a sample with one quarter remaining is 11 400 years old.
What changes
- What you change
- throw number
- What you measure
- number of undecayed dice
- What you keep the same
- same starting number
- same decay rule (a six decays)
- fair dice
- all dice thrown each round
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- After two half-lives nothing is left.
- Each atom decays after exactly one half-life.
- Carbon-14 dates rocks (it dates organic remains younger than about 50 000 years).
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No hazardous chemicals or heat sources: record the activity in the school's RiskAssess risk assessment, following the NSW Department of Education Science safety and compliance page; the Chemical Safety in Schools package is not triggered.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Earth and Environmental Science Stage 6 Syllabus (2017), NESA; current, replaced by the 11–12 Syllabus (2025) from 2028EES11-8EES11/12-3EES11/12-4EES11/12-5
- Earth and Environmental Science 11–12 Syllabus (2025), NESA; to be implemented from 2028, not yet taughtEES-12-01
- Investigating Science Stage 6 Syllabus (2017), NESA; currentINS11-9INS11-10
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.
- www.nsw.gov.au/education-and-training/nesa/curriculum/science/earth-and-environmental-science-stage-6-2017
- www.nsw.gov.au/education-and-training/nesa/curriculum/science/investigating-science-stage-6-2017
- www.ga.gov.au/education/classroom-resources/introduction-to-relative-and-absolute-dating
- www.nndc.bnl.gov/nudat3
- www.earthlearningidea.com/PDF/366_Radioactive_dating.pdf