A2 Daily A Level Physics question
A sealed gamma source is used to check a counter. At 2.0 m from the source, the counter reads 480 counts per minute (cpm); the laboratory background is 30 cpm and can be treated as constant. The source’s half-life is 6.0 h. Eighteen hours later the source is placed 1.0 m from the counter. Assume the source is effectively point-like and absorption in air is negligible. What is the best estimate of the new reading?
Answer
The correct answer is A.
Correct: A — About 255 counts per minute. Subtract background to get the source rate (480−30=450 cpm); after 18 h (three half-lives) this falls to 450/8≈56 cpm; halving the distance multiplies by 4 to ≈225 cpm; add background back to get ≈255 cpm. B is close but treats the total 480 cpm as all from the source and/or omits adding background at the end, giving 480×(1/8)×4≈240 cpm. C uses only a factor of 2 for halving distance instead of 4, so 450/8≈56 cpm scaled to ≈112 cpm, then plus 30 cpm ≈140 cpm. D ignores decay altogether and only rescales with distance, giving 450×4+30=1830 cpm.