A radiation detector records 460 counts·s⁻¹ when a radioactive source is present. The background count rate is 10 counts·s⁻¹. The detector efficiency is 25%, meaning only one quarter of all disintegrations are recorded. If the source activity is N Bq, find N.
Physics · Nuclear physics · radioactivity and law of decay
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Question

A radiation detector records 460 counts·s⁻¹ when a radioactive source is present. The background count rate is 10 counts·s⁻¹. The detector efficiency is 25%, meaning only one quarter of all disintegrations are recorded. If the source activity is N Bq, find N.

Physics · Nuclear physics · radioactivity and law of decay

G1 Physics · Accepted Answer

First remove the background count rate: Net recorded count rate = 460−10 = 450 counts·s⁻¹. Detector efficiency is 25%, so recorded rate = 0.25×actual disintegration rate. Therefore, Activity = 450 ÷ 0.25 = 1800 s⁻¹ = 1800 Bq. Hence N = 1800.