Half-Life & Heavy Choices
Randomness with a rhythm — and what we owe the atom
What this lesson covers
Why it matters
No nucleus has a calendar. Each one decays at a purely random moment — yet 400 of them together halve on a schedule you can set a clock by. Randomness, averaged, becomes law.
The idea in plain words
The atom's fine print — uses, harms, manners. Tap each.
N = N₀ ÷ 2^(t/t½)
A sample's activity falls to 1/8 of its original in 27 years. Its half-life?
t½ = 9 years
- the good: uses — cancer radiotherapy, carbon-14 dating, thickness gauges, sterilising equipment; fission/fusion for power (E = mc²)
- the danger: harms — ionising radiation damages cells and DNA — dose and exposure time are everything
- the manners: safety — distance, shielding (lead), minimum exposure time, film badges, deep disposal of waste
- perspective: background — cosmic rays, rocks, even bananas — a small natural dose is always around you
- 1/8 = (1/2)³ → three half-lives
- 27 ÷ 3
Predict first
Start with 400 nuclei of half-life 1 hour. After 2 hours, about how many remain?
Each half-life halves whatever REMAINS: 400 → 200 → 100. The pile never cleanly reaches zero — it fades geometrically.
- 100 — halved twice, not gone — correct
- 0 — two half-lives is a whole life
- 200
What you do
Run the dice. Watch 400 random coins produce a curve smoother than any of them knows.
Check yourself
After 3 half-lives, the fraction of the original sample remaining is…
(1/2)³ = 1/8. Halving compounds — it never simply subtracts.
Nuclear fission and fusion both release energy because…
Split heavy or join light nuclei — either way the products weigh slightly less, and c² makes 'slightly' enormous.
The best everyday protections from a radioactive source are…
Radiation follows physics, not biology: intensity falls with distance, lead absorbs, and dose = rate × time.
- 1/8 — correct
- 1/3
- 0
- a tiny mass difference converts to energy: E = mc² — correct
- they burn nuclear fuel chemically
- they release stored electricity
- distance, shielding and minimum exposure time — correct
- washing hands afterwards only
- antibiotics