A radioactive material of half-life T was produced at two different instants. The quantity produced the second time was twice the first. If their present activities are A₁ and A₂, find the difference in their ages.
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Question

A radioactive material of half-life T was produced at two different instants. The quantity produced the second time was twice the first. If their present activities are A₁ and A₂, find the difference in their ages.

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G1 Physics · Accepted Answer

Let the two samples initially contain N and 2N nuclei and have ages t₁ and t₂. Activity is A = λN and N(t) = N₀ exp(−λt), with λ = ln2/T. Therefore A₁/A₂ = (1/2)exp[−λ(t₁−t₂)]. Solving, t₁−t₂ = (T/ln2) ln[A₂/(2A₁)]. Correct answer: C.