Half-life and activity
Activity
The activity of a radioactive source is the number of nuclear decays per second.
- Symbol: A. Units: becquerel (Bq). 1 Bq = 1 decay per second.
- Activity is measured by a Geiger–Müller tube and counter.
- Background radiation must be subtracted from the count rate to give the source’s true activity.
Activity always decreases over time because there are fewer undecayed nuclei left.
Half-life
The half-life is the time taken for half the radioactive nuclei in a sample to decay (or, equivalently, for the activity to fall to half its starting value).
- Symbol: t½.
- Each isotope has its own characteristic half-life — from microseconds (some lab isotopes) to billions of years (uranium-238: 4.5 × 10⁹ years).
- After 1 half-life: ½ of nuclei remain. After 2: ¼. After 3: ⅛. After n: (½)ⁿ.
Reading half-life from a graph
A graph of activity vs time is a smooth decay curve. To read off the half-life:
- Pick a starting activity (e.g. 800 Bq at t = 0).
- Find the time at which activity has halved (e.g. 400 Bq at t = 6 hours).
- The half-life is 6 hours.
- Verify by finding when 200 Bq is reached — should be 12 hours from start.
Half-life from a table
Look down the activity column and find a value that is half of an earlier value. The time difference is the half-life. Repeat for several pairs and take a mean — this reduces uncertainty from background radiation.
✦Worked example
A sample has an activity of 640 Bq. After 12 minutes the activity is 80 Bq. Find the half-life.
640 → 320 → 160 → 80 = 3 halvings. 3 × t½ = 12 min, so t½ = 4 minutes.
Contamination vs irradiation
- Contamination — the radioactive substance gets onto or into an object/person. The object continues to be exposed to radiation for as long as the source is there. Especially dangerous if inhaled, ingested or absorbed (alpha emitters then become very harmful inside the body).
- Irradiation — exposure to radiation from outside the body. The object is not made radioactive; once removed from the source the exposure stops.
Precautions: lead aprons, distance, shorter exposure times, sealed sources, protective gloves and masks during handling.
Edexcel exam tip
When reading a half-life off a graph, always show two points on the graph (initial and half value). Also be careful to subtract background count rate before dividing — a frequent dropped mark.
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