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Two radioactive materials X₁ and X₂ have decay constants 5λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will be 1/e after a time

1. λ
2. 1 / 2
3. e / λ
4. 1 / λ

Correct answer: 1 / λ

Solution

The number of nuclei remaining after time t is given by N = N₀e^(-λt). For X₁ and X₂, the ratio becomes 1/e when e^(-5λt) / e^(-λt) = 1/e. Simplifying, we get t = 1/λ.

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