With a source present, a detector gives (time in h, count/min) readings (0, 820), (2, 430), (4, 235), (6, 138), (8, 89). Background is 40 counts/min. (a) Correct the readings and determine half-life. (b) Predict measured rate at 12 h. (c) Explain scatter and a reliable method. (d) Distinguish irradiation from contamination and state precautions.

Question

Accepted Answer

Corrected rates 780, 390, 195, 98, 49; half-life ≈2.0 h; predicted 12 h measured rate ≈52 counts/min. Subtract background to obtain 780, 390, 195, 98 and 49 counts/min. The small rounding later is compatible with random decay statistics. Corrected rate halves from 780 to 390 in 2 h and to about 195 after another 2 h, so half-life is approximately 2.0 h. From 8 h to 12 h is two half-lives: corrected rate ≈49/4 = 12.25. Add background to predict about 52 counts/min. Decay is random, so finite counts scatter. Count longer, repeat equal intervals and average while keeping geometry fixed to reduce fractional uncertainty. Irradiation is external exposure and stops when source is removed; contamination is radioactive material present and can spread. Minimise time, maximise distance, shield appropriately and use tongs/storage protocols.

Half-life from count-rate data

What a complete response should do

Count-rate decay

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Count-rate decay — supplied values
Time / h	Count rate / min⁻¹
0	820
2	430
4	235
6	138
8	89