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A radioactive specimen has activity R1 at time T1 and activity R2 at time T2. If its half-life is T, then the number of atoms decayed during the interval (T1 - T2) is proportional to

1. R1T1 - R2T2
2. R1 - R2
3. (R1 - R2)/T
4. (R1 - R2)T

Correct answer: (R1 - R2)T

Solution

Number of atoms = R/lambda, so atoms decayed = (R1 - R2)/lambda. Since lambda = ln2/T, this is (R1 - R2)T/ln2, i.e. proportional to (R1 - R2)T.

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