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Question

A radioactive sample can decay by two different processes. The half-life for the first process is T1 and that for the second process is T2. The effective half-life T of the radioactive sample is

A
T=T1+T2
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B
1T=1T1+1T2
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C
T=T1+T2T1T2
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D
T=T1T2T1T2
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Solution

The correct option is B 1T=1T1+1T2
Radioactive decay rate is directly proportional to number of nucleus present at any time

dNdt=λN....(i)

where λ is a constant related to half life as λ=ln2T12 where T12 is half life time of radioactive decay

The total rate of decay is

dNdt=(λ1+λ2)N=λeffectiveN...(ii)

λ1=ln2T1

λ2=ln2T2

λeffective=ln2Teffective

substituting in equation (ii)

(ln2T1 +ln2T2)N =ln2TeffectiveN

1T=1T1+1T2

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