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# 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 time15λ14λ54λ45λ

A
14λ
B
45λ
C
54λ
D
15λ
Solution
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#### Using the law of radioactivity, we can write: N(5λ)N(λ)=N0e−5λte−λt1e=e−5λte−λte−1=e−4λt−1=−4λt⇒t=14λ

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