Biology 11–12 · Year 11
Radiometric dating: dice decay and an age calculator from parent and daughter counts
Module 3: Biological Diversity (Evolution – the Evidence); also Module 4 (Past Ecosystems)
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The idea
Each unstable atom has a fixed chance of decaying in a given time, so a large sample halves at a constant interval and the ratio of parent to daughter atoms gives the age of a fossil or rock.
What you need
- Six-sided dice, 100 per group (or 100 two-colour counters or coins)
- Tray or box lid; results table; graph paper or spreadsheet
How to do it
- Roll all 100 dice at once; remove every die showing a six (these atoms have decayed) and record the number remaining.
- Roll the remaining dice again and repeat, recording after each roll, until fewer than five remain; each roll is one time unit.
- Plot dice remaining against roll number and read the number of rolls for the count to halve, from 100 to 50 and again from 50 to 25.
- Pool the class results and compare the pooled half-life in rolls with the value predicted from a one-in-six chance per roll.
- Use the calculator to convert a measured fraction of parent isotope remaining to an age for carbon-14 and for potassium-40.
- Explain why carbon-14 suits fossils younger than about 50,000 years and potassium-argon suits volcanic layers around much older fossils.
What you should see
With a one-in-six chance of decay per roll the expected fraction remaining after n rolls is (5/6)^n, giving a half-life of 3.80 rolls (computed); single groups scatter around this and the class pool comes close. With the half-life of 5,730 years for carbon-14 given by the USGS page, a sample retaining 25 percent of its carbon-14 is 11,460 years old and one retaining 10 percent is 19,035 years old (computed); with the USGS value of 1.25 billion years for potassium-40, a rock with 25 percent of its original potassium-40 is 2.5 billion years old. The learner knows it worked when successive halvings take about the same number of rolls.
What changes
- What you change
- number of rolls (time)
- What you measure
- number of dice remaining
- What you keep the same
- decay rule (remove sixes)
- starting number
- fair dice
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- After one half-life, the next half-life removes the rest; each half-life halves whatever remains.
- Carbon dating works on dinosaur bones; carbon-14 is exhausted long before 65 million years.
- Decay can be predicted for a single atom; only the average over many atoms is predictable.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No hazards.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Biology Stage 6 Syllabus (2017), current: Year 11 taught to the end of 2026 and Year 12 to Term 3 2027BIO11-10BIO11-11BIO11/12-4
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.