Physics A2 · Nuclear physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Radioactive decay is spontaneous: it is not affected by temperature, pressure or anything else outside the nucleus. It is also random: we cannot say which nucleus will decay next or when, only the probability that a nucleus decays in a given time. The small fluctuations in a measured count rate are the evidence for this.
That probability per unit time is the decay constant λ. The activity of a sample is the number of nuclei decaying per unit time, so it is proportional to the number of undecayed nuclei left.
The result is exponential decay. The number of undecayed nuclei, the activity and the count rate all halve in each half-life.
Students forget to subtract the background count rate before using the decay equation, or mix time units. λ and t must use matching units, for example s−1 with s.
Answer: About 610 Bq (2.4 half-lives, so between one quarter and one eighth of 3200 Bq).
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