A hospital disposes of radioactive waste from a medical procedure. The waste contains a radioactive isotope with a half-life of 8 days. A radiation protection officer states that after 32 days the waste will be safe to dispose of in normal refuse. Explain what is meant by the term 'half-life' and use it to justify the officer's statement.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
A half‑life is the time taken for the activity (or count rate) of a radioactive source to fall to half its original value.
The waste has a half‑life of 8 days. 32 days is 32÷8 = 4 half‑lives.
After each half‑life the activity halves, so after 4 half‑lives the activity has been halved four times.
Therefore the activity is (1/2)^4 = 1/16 of the original value – a very small fraction, so the waste is effectively safe for normal disposal.
The waste has a half‑life of 8 days. 32 days is 32÷8 = 4 half‑lives.
After each half‑life the activity halves, so after 4 half‑lives the activity has been halved four times.
Therefore the activity is (1/2)^4 = 1/16 of the original value – a very small fraction, so the waste is effectively safe for normal disposal.
Examiner tips
- Define half‑life clearly; include activity or count rate. Show the calculation 32÷8=4. Explain the successive halving and the 1/16 result. Use words like ‘negligible’ or ‘safe’ to justify the statement.
Common mistakes
- Confusing half‑life with decay constant or half‑life with half‑life time. Giving the wrong number of half‑lives (e.g., 3 instead of 4). Failing to state the final activity as 1/16 of the original.
Mark scheme (4 marks)
- Half-life is the time taken for the activity (or count rate / number of radioactive nuclei) of a radioactive source to fall to half its original value
- 32 days represents 4 half-lives (32 ÷ 8 = 4)
- After each half-life the activity halves, so after 4 half-lives the activity has halved four times
- After 4 half-lives the activity is 1/16 of the original value, so the level of radioactivity is much lower / negligible / safe
Key terms in this question
Related
- All WJEC GCSE Physics (Wales) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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