A sealed source gives 920 counts/min initially and 220 counts/min after 18 years. Background is 120 counts/min and is assumed constant. (a) Explain why background must be subtracted. [2] (b) Calculate both net count rates and the number of half-lives elapsed. [4] (c) Determine the half-life. [2] (d) Predict the total detector reading after a further 12 years and state two assumptions. [4]

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Net activity falls from 800 to 100 counts/min, a factor of eight or three half-lives in 18 years, so the half-life is 6 years. After 12 more years the predicted total is 25 + 120 = 145 counts/min. (a) The detector records environmental and instrumental background as well as the source. Radioactive decay applies to the source contribution, not to the unchanged background count. (b) Initial net count = 920 − 120 = 800 counts/min; later net count = 220 − 120 = 100 counts/min. (b) The net count falls 800 → 400 → 200 → 100, which is three halvings, so three half-lives have elapsed in 18 years. (c) Half-life = 18/3 = 6 years. (d) A further 12 years is two half-lives, so net count becomes 100/4 = 25 counts/min. Add background back for the detector prediction: 25 + 120 = 145 counts/min. (d) Assumptions include constant detector geometry and efficiency, constant mean background, no contamination or source loss, and a single radionuclide with unchanged decay probability.

Recover half-life from count-rate evidence

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