A count rate is the number of radiation detections per unit time, such as counts per minute. To use it, you correct for background radiation, accept that decay is random, and find the half-life from the corrected values. This lesson in atomic and nuclear models joins the physics idea to a short data calculation.
It helps to know the properties of the radiations first, but the method below works for any source.
What are the three ideas you need?
Random decay. Each unstable nucleus has a fixed chance of decaying in a given time, but no one can say which nucleus will go next. Over a large number of nuclei the pattern is smooth. Over short times the counts jump about.
Background. The detector registers radiation even with no source. Always subtract it, because it is not from your sample.
Half-life. The corrected count rate falls by half in each equal time interval called the half-life.
How do you find a half-life from a table?
- Subtract background from every reading.
- Choose a starting corrected value and find the time at which it has halved.
- Check with a second starting point. The time for the next halving should be the same.
- State the half-life with units.
Averaging repeated readings at each time first reduces the effect of randomness.
Worked example
The following data are invented for practice. A sample gives these measured count rates. The background count rate is 20 counts per minute.
| Time (min) | 0 | 10 | 20 | 30 |
|---|---|---|---|---|
| Measured (counts/min) | 340 | 180 | 100 | 60 |
Step 1, subtract background (measured − 20):
| Time (min) | 0 | 10 | 20 | 30 |
|---|---|---|---|---|
| Corrected (counts/min) | 320 | 160 | 80 | 40 |
Step 2, find the halving time. 320 halves to 160 in 10 min.
Step 3, check. 160 halves to 80 between 10 and 20 min, which is 10 min. 80 halves to 40 between 20 and 30 min, which is 10 min again.
Answer: half-life = 10 minutes.
Prediction. At 50 min there have been 5 half-lives. Corrected rate = 320 ÷ 25 = 320 ÷ 32 = 10 counts/min. A detector would show 10 + 20 = 30 counts/min.
The mistake to watch for
Mistaken answer: “The count rate went from 340 to 180, then 100, then 60. The half-life is about 10 minutes, but it keeps changing, so the sample is not decaying properly.”
The student did not subtract the background. The measured readings fall to 53%, 56% and 60% of the previous value, which drift upward because the constant background becomes a larger share.
After correction, every step is exactly half. Always subtract first, then compare.
A second slip is to treat small differences in repeated counts as a sign the half-life changed. Random scatter around a trend is expected, not a fault.
Check yourself
1. A sample has a half-life of 5 minutes. Its corrected count rate is 800 counts/min at time zero. What is the corrected rate after 15 minutes?
Show answer
15 min is 3 half-lives. 800 → 400 → 200 → 100.
100 counts/min
2. A detector reads 95 counts/min near a source, and the background is 15 counts/min. What is the source’s count rate? What will the corrected rate be after two half-lives?
Show answer
Corrected rate = 95 − 15 = 80 counts/min. After two half-lives: 80 → 40 → 20.
80 counts/min, then 20 counts/min
3. Five counts, each taken over 10 s with the same source, were 5, 8, 6, 9 and 7. Give the average count per 10 s and explain why the readings differ.
Show answer
Total = 5 + 8 + 6 + 9 + 7 = 35, and 35 ÷ 5 = 7 counts per 10 s. The readings differ because decay is random, so the number of nuclei decaying in each interval varies around an average.
Where this leads next
The last lesson in the topic links these results to hazards: separate ionising behaviour from penetration. Then use the mixed practice set, which has count-rate questions with invented data.
If background correction or half-life reasoning keeps slipping under exam pressure, a teacher can work through fresh tables with you in online one-to-one Physics tuition.