A scientist is monitoring a radioactive isotope used in medical imaging. After 6 hours the count rate has fallen from 800 counts per minute to 100 counts per minute. Explain what this tells us about the half-life of this isotope and how the number of radioactive nuclei in the sample changes over time.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A radioactive isotope used in medical imaging has a count rate of 800 counts per minute at the start of monitoring. After 6 hours, the count rate has fallen to 100 counts per minute.
Model answer (4 marks)
The count rate has fallen from 800 to 100 counts min⁻¹, i.e. to one‑eighth of the initial value. Each half‑life halves the count rate, so 800→400→200→100 shows three half‑lives have elapsed. Therefore the half‑life is 6 h ÷ 3 = 2 h.
The number of radioactive nuclei in the sample therefore decreases by one‑half every 2 h. The decay is exponential, so the rate of decrease slows as the number of nuclei becomes smaller, but the nuclei never reach zero.
The number of radioactive nuclei in the sample therefore decreases by one‑half every 2 h. The decay is exponential, so the rate of decrease slows as the number of nuclei becomes smaller, but the nuclei never reach zero.
Examiner tips
- Use the halving rule to link count rate to half‑lives; calculate half‑life by dividing time by number of halvings.
- Show the exponential decay idea – number halves each half‑life and the rate slows but never reaches zero.
Common mistakes
- Confusing the initial count rate with the half‑life value; writing 800 as the half‑life.
- Failing to explain that the decay rate slows and nuclei never reach zero.
Mark scheme (4 marks)
- The count rate has fallen to half (400) after the first half-life, then halved again to 200, then halved again to 100 — so three half-lives have passed
- The half-life of the isotope is 2 hours (6 hours ÷ 3)
- The number of radioactive nuclei in the sample decreases over time as nuclei decay
- The rate of decrease slows over time / the number of radioactive nuclei never reaches zero
Key terms in this question
half-life · count rate · radioactive nuclei
Related
- All WJEC GCSE Physics (Wales) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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