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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/e)² after a time interval

1. 4λ
2. 2λ
3. 1/2λ
4. 1/4λ

Correct answer: 2λ

Solution

The number of nuclei remaining for a radioactive substance is given by N = N₀e^(-λt). For A and B, the ratio of their nuclei is (e^(-5λt))/(e^(-λt)) = e^(-4λt). Setting this equal to (1/e)² gives -4λt = -2, so t = 2λ. Hence, the correct answer is 2λ.

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