A radioactive source used in a school laboratory contains an isotope with a half-life of 6 hours. The initial activity of the source is measured at 3200 Bq. A student says: 'After 24 hours, the source will no longer be radioactive and will be safe to handle without any precautions.' Evaluate the student's statement.

Edexcel A-Level Physics (9PH0) — 6.1 Circular motion and momentum · Evaluate · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Radioactive decay is a random process. Background radiation is present in all environments. The activity of a radioactive source decreases over time as unstable nuclei decay.

Model answer (5 marks)

The source has a half‑life of 6 h, so in 24 h it undergoes 24 ÷ 6 = 4 half‑lives. Each half‑life reduces the activity by ½:
3200 → 1600 → 800 → 400 → 200 Bq after 24 h. The activity is therefore 200 Bq, not zero – the source is still radioactive.
Background radiation (≈ 0.1–0.2 Bq cm⁻² s⁻¹) is always present, so the relative contribution of the source remains significant. Even at 200 Bq the source can add to the background dose and may still pose a risk, especially if handled in large quantities or close to the body. Consequently the student’s claim that the source will be safe after 24 h is incorrect; precautions should still be taken.

Examiner tips

  • Show the calculation of 4 half‑lives and the resulting activity; this earns 2 marks. Explain why the activity is not zero and why precautions remain necessary; this gives 2 marks. Mention background radiation to demonstrate understanding of external exposure; 1 mark.
  • common_mistakes
  • :
  • Assuming the activity becomes zero after a few half‑lives. Ignoring the persistent background radiation. Failing to calculate the exact activity after 24 h.

Mark scheme (5 marks)

  1. Identifies the correct number of half-lives in 24 hours (4 half-lives)
  2. Correctly determines the activity after 4 half-lives is 200 Bq (3200 → 1600 → 800 → 400 → 200 Bq)
  3. States that the activity is not zero / the source is still radioactive after 24 hours
  4. References background radiation as an additional reason precautions are still relevant / the student's comparison is flawed because background radiation is always present
  5. Concludes that the student's statement is incorrect because precautions may still be needed as the source remains radioactive

Key terms in this question

half-life · activity

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