Safety boundary
Use coin/dice half-life models, simulations, and trusted lifecycle datasets only. Do not use radioactive sources or hazardous materials.
Explicit chemistry instruction
Half-life is the time for the expected number of undecayed nuclei in a large sample to decrease by half.
Individual nuclei decay unpredictably, but large populations show stable statistical patterns.
After n half-lives, the expected remaining fraction is (1/2)^n.
Vocabulary: half-life; radioactive decay; exponential; probability; population.
Worked example
After three half-lives, expected remaining fraction is 1/8=12.5%.
Guided question
What fraction remains after five half-lives?
Independent work
- Solve four half-life fraction problems.
- Graph remaining fraction versus half-lives.
- Explain why individual decay time is unpredictable.
Instructional depth extension · half-life as exponential change
Radioactive decay is stochastic for individual nuclei but predictable statistically for large populations. After each half-life, the expected undecayed amount is multiplied by one-half; equal time intervals therefore produce equal fractional change, not equal absolute change.
Worked example: a 160 mg sample with a 3-day half-life is expected to have 80 mg after 3 days, 40 mg after 6 days, and 20 mg after 9 days. The amount lost each interval changes, but the fraction remaining is consistent.
Use N=N₀(1/2)t/t½ when the elapsed time is not an exact whole number of half-lives. Measurement uncertainty and background counts should remain visible when interpreting real decay data.
Misconception check
Half-life does not mean every nucleus survives exactly half the stated time.
Formative check
What fraction remains after one half-life?
Reveal response
One-half of the original population, on average.
Mentor evidence conference
Ask Archaemenes to audit mechanism, quantitative evidence, tradeoffs, and uncertainty.
Teacher guidance
Foundation: Use halving tables.
Core: Solve half-life models.
Extended: Fit/interpret exponential-decay data.