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

IB DP Physics Higher 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 iodine-131 has an initial activity of 8.0 × 10⁵ Bq. After several weeks, the activity is measured to be significantly lower.

Model answer (4 marks)

Activity is the number of disintegrations per second, A = λN.

Each decay removes one undecayed nucleus, so N falls as time passes.

Because λ is constant but N decreases, the product λN – the activity – also falls.

The decline follows an exponential law: N = N₀e^(−λt) or A = A₀e^(−λt).

Examiner tips

Use the definition A = λN to link activity to N.
Show that λ is constant and explain that the decrease comes from N.
Mention the exponential decay equation to demonstrate understanding.

Common mistakes

Confusing decay constant with activity; writing λ = A/N incorrectly.
Failing to state that N decreases because each decay removes a nucleus.
Omitting the exponential form or giving the wrong sign in the exponent.

Mark scheme (4 marks)

Activity is defined as the number of disintegrations (decays) per unit time, or A = λN.
Each decay event removes one undecayed nucleus from the sample, so the number of undecayed nuclei N decreases over time.
Since λ is constant but N decreases, the product λN (and therefore the activity) decreases over time.
The decrease in N (and hence activity) follows an exponential pattern, described by N = N₀e^(−λt) or A = A₀e^(−λt).

Key terms in this question

activity · decay constant