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A radioactive parent nucleus A has half-life T and transforms into daughter nucleus B. Initially, at t = 0, no B nuclei are present. When the ratio of the number of B nuclei to A nuclei becomes 0.3, the time t is equal to

1. t = T log(1.3)
2. t = T / log(1.3)
3. t = T log 2 / log 1.3
4. t = T log 1.3 / log 2

Correct answer: t = T log 1.3 / log 2

Solution

With N_A = N0 e^(-lt) and N_B = N0(1 - e^(-lt)), N_B/N_A = e^(lt) - 1 = 0.3, so lt = ln(1.3). Since l = ln2/T, t = T ln(1.3)/ln(2) = T log(1.3)/log(2).

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