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