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Question

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 e3t. If the half-life of A is ln2, the half-life of B is:
  1. ln22
  2. 2ln2
  3. ln24
  4. 4ln2

A
2ln2
B
ln24
C
ln22
D
4ln2
Solution
Verified by Toppr

Half life of A=ln2
t1/2=n2λ
λA=1
at t=0RA=RB
NAeλAT=NBeλBT
NA=NB at t = 0
at t= t RBRA=N0eλtBN0eλtA
e(λBλA)t=e3t
λBλA=3
λB=3+λA=4
t1/2=n2λB=n24

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