Describe how the activity of a radioactive source decreases over a period…

The idea

Radioactive decay is random: you cannot predict which nucleus decays next or when. But a large sample behaves predictably overall, because each undecayed nucleus has a fixed chance of decaying per unit time. As nuclei decay, fewer undecayed nuclei remain, so the number of decays per second — the activity — falls. The activity halves in each successive half-life, giving an exponential decrease: after one half-life the activity is half its starting value, after two half-lives one quarter, after three one eighth. A decay curve plotted as activity against time therefore falls steeply at first and then flattens, never quite reaching zero. The count rate measured by a detector follows the same pattern, after subtracting background radiation.

What earns the marks

• States that radioactive decay is random, so individual decay events cannot be predicted.
• Explains that the activity decreases because the number of undecayed nuclei in the sample falls over time.
• Describes the activity halving in each successive half-life, giving an exponential decrease.
• Recognises that the activity approaches zero but does not reach it in a finite time on the decay curve.

Common mistakes and how to put them right

• Claims that the activity decreases steadily in equal steps.

  Put it right by stating that it halves in each half-life, so the fall is exponential.

• Assumes the activity of a single nucleus can be predicted.

  Put it right by stating that decay is random and only large samples show a predictable pattern.

• Forgets to subtract background count rate.

  Put it right by subtracting the background before comparing count rates with activity.

Exam tips

• Learn the halving sequence: 1, ½, ¼, ⅛ of the initial activity after 1, 2 and 3 half-lives.
• Sketch the decay curve falling steeply then flattening, and label the half-life on the time axis.
• Read the question carefully to see whether it asks about activity, count rate or number of undecayed nuclei — all follow the same halving pattern.