A geologist uses a radioactive isotope to determine the age of a rock sample. The isotope has a half-life of 50 million years. The geologist measures the count rate from the sample and finds it is one-eighth of the count rate expected from a freshly formed rock of the same mass. Explain what is meant by the term 'half-life' and use it to determine how many years old the rock sample is.

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)

Half‑life is the time taken for half of the radioactive nuclei in a sample to decay.
After one half‑life the count rate is one‑half of the original.
To reduce the count rate to one‑eighth you need three half‑lives: ½ → ¼ → ⅛.
The rock sample is therefore 3 × 50 million years = 150 million years old.

Examiner tips

  • Define half‑life in terms of decay of nuclei. Show the stepwise reduction of count rate. State the number of half‑lives required. Multiply by the given half‑life to give the age.

Common mistakes

  • Using the wrong fraction (e.g. one‑quarter instead of one‑eighth). Failing to multiply the half‑life by the number of half‑lives. Not explicitly stating the definition of half‑life.

Mark scheme (4 marks)

  1. Half-life is the time taken for half the radioactive nuclei (atoms) in a sample to decay
  2. After one half-life the count rate is one-half of the original
  3. Three half-lives are needed to reduce the count rate to one-eighth (½ → ¼ → ⅛)
  4. The rock sample is 150 million years old (3 × 50 million years)

Key terms in this question

half-life · count rate

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