A radioactive sample decays in two modes. In one mode its half life is t1 and in the other mode its half life is t2. Find the overall half life
t1+t22
t1+t2
t1t2t1−t2
t1t2t1+t2
A
t1t2t1+t2
B
t1+t22
C
t1t2t1−t2
D
t1+t2
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Solution
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Let the decay rate of two processes be λ1=ln2/t1 and λ2=ln2/t2.
So the decay rate of quantity N is given by:
−dN(t)/dt=Nλ1+Nλ2
⇒N(t)=Noe−(λ1+λ2)t
⇒N(t)=Noe−(t1+t2t1t2)ln2t
So overall half life is t1t2t1+t2
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