A geologist wants to determine the age of a rock sample by analysing the proportion of decayed and undecayed radioactive isotopes it contains. The isotope found in the rock has a half-life of 700 million years. Explain how radioactive decay and the concept of half-life make this method of radioactive dating possible, and why the random nature of radioactive decay does not prevent scientists from using this technique reliably.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Radioactive dating is used by scientists to estimate the age of ancient rocks and fossils. It relies on measuring the ratio of unstable nuclei remaining in a sample compared to the amount originally present.
Model answer (5 marks)
Radioactive decay is the spontaneous emission of radiation from an unstable nucleus, converting it into a more stable form.
The half‑life is the time required for half of the unstable nuclei in a sample to decay.
By measuring the ratio of undecayed to decayed isotopes in the rock, the number of half‑lives that have elapsed can be calculated, and the age of the sample is then found from the half‑life.
Although each nucleus decays at a random instant, the probability of decay is constant, so the fraction of nuclei that survive after a given time follows a predictable exponential law.
Because a rock contains an astronomically large number of atoms, the statistical average (the half‑life) is extremely reliable, allowing scientists to date the rock accurately.
The half‑life is the time required for half of the unstable nuclei in a sample to decay.
By measuring the ratio of undecayed to decayed isotopes in the rock, the number of half‑lives that have elapsed can be calculated, and the age of the sample is then found from the half‑life.
Although each nucleus decays at a random instant, the probability of decay is constant, so the fraction of nuclei that survive after a given time follows a predictable exponential law.
Because a rock contains an astronomically large number of atoms, the statistical average (the half‑life) is extremely reliable, allowing scientists to date the rock accurately.
Examiner tips
- Use the word "half‑life" explicitly; link it to the exponential decay law.
- Show the logical chain: decay → half‑life → ratio → age.
- Mention the statistical nature of large‑number averages to justify reliability.
Common mistakes
- Confusing half‑life with the time for all nuclei to decay.
- Failing to explain why randomness does not affect the average half‑life.
- Using vague terms like "stable” without defining radioactive decay.
Mark scheme (5 marks)
- Radioactive decay is the process by which unstable nuclei emit radiation to become more stable
- Half-life is the time taken for the number of unstable nuclei in a sample to halve
- By comparing the proportion of decayed to undecayed isotopes, the number of half-lives that have passed can be determined, allowing the age to be calculated
- Radioactive decay is random, meaning it is impossible to predict when any one nucleus will decay
- Despite individual decay being random, the half-life of a large sample is constant / reliable because large numbers of nuclei are involved, so statistical averages are consistent
Key terms in this question
radioactive decay · half-life · random nature of radioactive decay · isotopes · radioactive dating
Related
- All OCR A-Level Physics A (H556) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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