Half-life, uses and safety
Counting down
- We cannot say when one nucleus will decay — but a large sample is very predictable.
- That predictability is measured by the half-life.
- It lets us date ancient bones, run smoke alarms, and treat cancer.
Half-life
- The half-life is the time for half the unstable nuclei in a sample to decay.
- After each half-life, the count rate (and the number of unstable nuclei) falls to half.
The half-life of a radioactive isotope is the time taken for:
Each half-life, half of the remaining unstable nuclei decay, so the count rate halves.
Using half-life
- After $n$ half-lives, the count rate has halved $n$ times.
- Example: a source of $800$ counts/min with a half-life of $3$ hours → after $6$ hours (two half-lives): $800 \to 400 \to 200$ counts/min.
- You can read a half-life off a graph: the time for the count rate to fall from any value to half of it.
A source reads $800$ counts/min and has a half-life of $3$ hours. What is the count rate after $6$ hours, in counts/min?
6 hours is two half-lives: $800 \to 400 \to 200$ counts/min.
What fraction of the unstable nuclei remain after 3 half-lives? (Give a decimal.)
Each half-life halves the number: $\left(\tfrac{1}{2}\right)^3 = \tfrac{1}{8} = 0.125$.
Uses of radioactivity
- The choice of isotope depends on its radiation type and half-life:
- Smoke alarms — an alpha source (easily blocked, so safe; long half-life lasts for years).
- Sterilising equipment and food — penetrating gamma kills bacteria through sealed packaging.
- Thickness gauges for paper or metal — a beta source (the amount passing through changes with thickness).
- Finding and treating cancer — gamma rays can pass into (or out of) the body.
Match each radioactive source to its use.
Alpha (easily blocked) suits smoke alarms; beta passes through thin sheets for thickness gauges; penetrating gamma sterilises sealed items.
Why is an alpha source used in a smoke alarm?
Alpha is stopped by a little air or the alarm casing (safe), and a long half-life means it works for years.
Safety
- Ionising radiation harms living cells — it can cause cell death, mutations and cancer.
- Keep the dose low by: less time near the source, more distance from it, and shielding (such as lead).
- Handle sources with tongs, point them away from people, and store them in a lead-lined box.
Select all the ways to reduce the radiation dose you receive.
Less time, more distance and shielding all cut the dose. Handling a source with bare hands does the opposite — always use tongs.
You've got it
- half-life = time for half the nuclei (or the count rate) to halve
- after $n$ half-lives the count rate has halved $n$ times
- uses: α smoke alarms · β thickness gauges · γ sterilising and cancer treatment
- safety: cut the dose with less time, more distance, and shielding