Two radioactive materials A and B have decay constants 5λandλ respectively. Initially both A and B have the same number of nuclei. The ratio of the number of nuclei of A to that of B will be 1e after a time

15λ

14λ

54λ

45λ

A

14λ

B

45λ

C

54λ

D

15λ

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Solution

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Using the law of radioactivity, we can write:

N(5λ)N(λ)=N0e−5λte−λt

1e=e−5λte−λt

e−1=e−4λt

−1=−4λt⇒t=14λ

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