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Question

Two radioactive substances A and B have decay constants 5λ and λ respectively. At t=0, they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e2) after a time:
  1. 4λ
  2. 2λ
  3. 12λ
  4. 14λ

A
4λ
B
12λ
C
2λ
D
14λ
Solution
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Given : (No)A=(No)B=No
Using : Kt=lnNNo where, K is the decay constant
Kt=lnNlnNo

For substance A : λt=lnNAln(No)A
λt=lnNAlnNo .............(1)

For substance B : 5λt=lnNBln(No)B
5λt=lnNBlnNo .............(2)

Subtracting (2) from (1) we get:
λt5λt=lnNANB
4λt=ln1e2
4λt=2
t=12λ

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