A radioactive source produces a dose rate of 100 arbitrary units at a distance of 1 m when freshly prepared. After exactly two half-lives, determine the minimum distance in metres at which the dose rate becomes 1 unit, assuming dose rate is directly proportional to activity and inversely proportional to the square of distance.
Physics · Nuclear physics · radioactivity and law of decay
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Question

A radioactive source produces a dose rate of 100 arbitrary units at a distance of 1 m when freshly prepared. After exactly two half-lives, determine the minimum distance in metres at which the dose rate becomes 1 unit, assuming dose rate is directly proportional to activity and inversely proportional to the square of distance.

Physics · Nuclear physics · radioactivity and law of decay

G1 Physics · Accepted Answer

After two half-lives, activity becomes A = A₀ ÷ 4. Therefore at 1 m the dose rate becomes 100 ÷ 4 = 25 units. Using inverse-square dependence: Dose rate at distance r = 25 ÷ r². For the safe value 1 unit: 25 ÷ r² = 1. Therefore, r² = 25 and r = 5 m. Hence N = 5.