Explain why the activity of a radioactive sample decreases over time, even though the decay constant of the nuclide remains constant.

IB DP Physics Standard Level (2023 syllabus) — E.3 Radioactive decay · Explain · 4 marks · View as Markdown

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

A freshly prepared sample of a radioactive nuclide has a measured activity of 800 Bq. After several half-lives, the activity is found to be significantly lower.

Model answer (4 marks)

Activity is the number of decays per unit time.

Each decay removes one radioactive nucleus, so the number of undecayed nuclei N falls.

Activity is proportional to N (A = λN). λ is constant, but N decreases.

Therefore λN, and hence activity, decreases exponentially with time.

Examiner tips

Define activity and state A = λN. Show that N decreases because each decay removes a nucleus. Explain that λ is constant, so the decline is due to N. Use the word ‘exponentially’ to match the scheme.

Common mistakes

Confusing activity with decay constant. Forgetting that λ is constant. Not linking the decrease in N to the decrease in activity.

Mark scheme (4 marks)

Activity is defined as the number of decays (disintegrations) per unit time.
Each decay removes one radioactive nucleus from the sample, so the number of undecayed nuclei decreases over time.
Activity is proportional to the number of undecayed nuclei present (A = λN).
Because N decreases while λ remains constant, the product λN decreases, so activity falls exponentially over time.

Key terms in this question

activity · decay constant