A radioactive sample has a half-life of 20 years. Explain what is meant by the term 'half-life' and describe how the count rate of the sample changes over a period of 60 years.

WJEC GCSE Physics (Wales) — 2.8 Half-life · Explain · 4 marks · View as Markdown

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

Model answer (4 marks)

A half‑life is the time required for the number of radioactive nuclei in a sample, or its activity (count rate), to decrease to one‑half of its initial value.

After 20 years (one half‑life) the count rate is ½ of the original.
After 40 years (two half‑lives) the count rate is ¼ of the original.
After 60 years (three half‑lives) the count rate is ⅛ of the original.

Examiner tips

  • Define half‑life in terms of nuclei or activity. Show the successive halving for 20, 40 and 60 years. Use the fractions ½, ¼, ⅛ to demonstrate the change.
  • common_mistakes
  • :
  • Saying the count rate stays the same. Using the wrong fractions (e.g. ½, ⅓, ⅙). Forgetting to link the time periods to the number of half‑lives.

Mark scheme (4 marks)

  1. Half-life is the time taken for the number of radioactive nuclei (or activity/count rate) in a sample to halve
  2. After 20 years (one half-life) the count rate falls to half its original value
  3. After 40 years (two half-lives) the count rate falls to one quarter of its original value
  4. After 60 years (three half-lives) the count rate falls to one eighth of its original value

Key terms in this question

half-life · count rate

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