At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio RARB 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:
A
2ln2
B
2ln2
C
4ln2
D
4ln2
Medium
JEE Mains
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Updated on : 2022-09-05
Solution
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Correct option is C)
Half life of A=ln2 t1/2=λℓn2 λA=1 at t=0RA=RB NAe−λAT=NBe−λBT NA=NB at t = 0 at t= t RARB=N0e−λAtN0e−λBt e−(λB−λA)t=e−3t λB−λA=3 λB=3+λA=4 t1/2=λBℓn2=4ℓn2