The big idea: Hold a Geiger counter near a fresh radioactive sample and it clicks like mad; come back tomorrow and the clicks have thinned out — decay is random, you can't say when one nucleus will go, but on average a sample gets weaker with time.
The half-life is the time it takes for half the radioactive nuclei to decay.
In that same time the activity and the count rate also halve.
New words, plainly: Activity = how many nuclei decay each second, measured in becquerel (Bq), where 1 Bq = 1 decay per second.
Count rate = how many of those decays a detector actually records each second (clicks per second).
Half-life = the time for the activity (or count rate) to fall to half.
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Halving keeps going: Every half-life that passes, you halve again — not subtract a fixed amount.
So after 1, 2, 3 half-lives the count rate is 1/2, 1/4, 1/8 of the start. It flattens but never reaches zero.
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At SL you only deal with whole numbers of half-lives, so you never need the exponential equation. You just halve, halve, halve, once for each half-life that has passed.
The rule (learn this — it is NOT in the data booklet): After n whole half-lives, the count rate (or activity) is the start value multiplied by (1/2)ⁿ.
Work out n = total time ÷ half-life, then halve that many times.
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Watch the graph build step by step in study mode.
| Half-lives passed | Fraction of original left | Count rate from 80 s⁻¹ |
|---|---|---|
| 0 | 1 (all of it) | 80 s⁻¹ |
| 1 | 1/2 | 40 s⁻¹ |
| 2 | 1/4 | 20 s⁻¹ |
| 3 | 1/8 | 10 s⁻¹ |
| n | (1/2)ⁿ | 80 × (1/2)ⁿ |
Subtract the background FIRST: A detector always records some background radiation (from rocks, cosmic rays, etc.) even with no source.
The true count rate from the source = measured count rate − background count rate. Correct for background before you start halving.
A fresh source gives a measured count rate of 204 counts per second. The background count rate is 4 counts per second. The source has a half-life of 6.0 hours. Find the MEASURED count rate 12 hours later.
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How this is tested — a classic Paper 1A one-step calculation that also turns up in Paper 2:
Paper 1A
- Halve over whole half-lives: find the count rate / activity after a whole number of half-lives.
- Correct for background: subtract it before halving (add it back for the measured value).
- Ratios: two samples with the same half-life keep the same ratio as both halve together.
Paper 2
- Use the activity to work out an effect, such as an ionisation current.
The classic trap: Forgetting the background, or subtracting a fixed amount each half-life instead of halving.
Ratios stay put: If two sources have the same half-life, after the same time both have halved the same number of times.
The ratio of their activities is unchanged — e.g. 5 : 1 stays 5 : 1.
A radioactive sample has an initial activity of 6.4 × 10⁶ Bq and a half-life of 8.0 days. Determine its activity after 24 days.
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Two samples X and Y have the SAME half-life. Right now sample X is four times as active as sample Y. State the ratio of their activities after two half-lives, and explain your answer.
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