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# 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:ln222ln2ln244ln2

A
2ln2
B
ln24
C
ln22
D
4ln2
Solution
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#### Half life of A=ln2t1/2=ℓn2λλA=1at t=0RA=RBNAe−λAT=NBe−λBTNA=NB at t = 0at t= t RBRA=N0e−λtBN0e−λtAe−(λB−λA)t=e−3tλB−λA=3λB=3+λA=4t1/2=ℓn2λB=ℓn24

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