At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio RBRA of their activities after time t itself decays with time t as e−3t. If the half-life of A is ln2, the half-life of B is:

ln22

2ln2

ln24

4ln2

A

2ln2

B

ln24

C

ln22

D

4ln2

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Solution

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Half life of A=ln2 t1/2=ℓn2λ λA=1 at t=0RA=RB NAe−λAT=NBe−λBT NA=NB at t = 0 at t= t RBRA=N0e−λtBN0e−λtA e−(λB−λA)t=e−3t λB−λA=3 λB=3+λA=4 t1/2=ℓn2λB=ℓn24

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