Explain why two samples of the same radioactive nuclide, one with twice the number of atoms as the other, will have the same half-life but different activities.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
Activity is proportional to the number of undecayed atoms present (A = λN), so the larger sample has a greater activity.
The decay constant λ is a fixed property of the nuclide, independent of the size of the sample.
Half‑life is related to the decay constant by t½ = ln2 / λ, so since λ is identical for both samples, the half‑life is identical.
After one half‑life, each sample retains half its original number of atoms, so the ratio of their activities remains 2:1 throughout — both halve in the same time period.
The decay constant λ is a fixed property of the nuclide, independent of the size of the sample.
Half‑life is related to the decay constant by t½ = ln2 / λ, so since λ is identical for both samples, the half‑life is identical.
After one half‑life, each sample retains half its original number of atoms, so the ratio of their activities remains 2:1 throughout — both halve in the same time period.
Examiner tips
- Use the formula A = λN to link activity to atom number; mention λ is constant. State t½ = ln2/λ and explain λ is the same for both samples. Show that the 2:1 activity ratio persists after each half‑life.
Common mistakes
- Confusing activity with half‑life; writing that the larger sample has a longer half‑life. Forgetting to mention that λ is a property of the nuclide, not the sample size. Not recognising that the activity ratio remains 2:1 after each half‑life.
Mark scheme (4 marks)
- Activity is proportional to the number of undecayed atoms present (A = λN), so the larger sample has a greater activity.
- The decay constant λ is a fixed property of the nuclide, independent of the size of the sample.
- Half-life is related to the decay constant by t½ = ln2 / λ, so since λ is identical for both samples, the half-life is identical.
- After one half-life, each sample retains half its original number of atoms, so the ratio of their activities remains 2:1 throughout — both halve in the same time period.
Key terms in this question
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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