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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=T1T2T1 T2
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B
T=T1+T2T1 T2
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C
T=T1 T2T1+T2
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D
T=T1+T2
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Solution

## The correct option is C T=T1 T2T1+T2 We know that, λ=0.693T ⇒λ∝1T ⇒λ1=ln2T1, λ2=ln2T2, And λ=ln2T Now, dNdt=−λN Total rate of decay is, dNdt=−(λ1+λ2)N=−λeffN ∴λeff=λ1+λ2 ln2T=ln2T1+ln2T2 1T=1T1+1T2 T=T1T2T1+T2 Hence, (C) is the correct answer.

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