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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 isT=T1+T21T=1T1+1T2T=T1+T2T1T2T=T1−T2T1T2

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

Radioactive decay rate is directly proportional to number of nucleus present at any timedNdt=−λN....(i)where λ is a constant related to half life as λ=ln2T12 where T12 is half life time of radioactive decayThe total rate of decay isdNdt=−(λ1+λ2)N=λeffectiveN...(ii)λ1=ln2T1λ2=ln2T2λeffective=ln2Teffectivesubstituting in equation (ii)(ln2T1 +ln2T2)N =ln2TeffectiveN1T=1T1+1T2

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