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Radioactive material 'A' has decay constant '8λ' and material 'B' has decay constant 'λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be e⁻²?

1. 1/7λ
2. 1/8λ
3. 1/9λ
4. 1/λ

Correct answer: 1/8λ

Solution

The number of nuclei remaining for a radioactive material is given by N = N₀e⁻(λt). For material A and B, the ratio of nuclei is (N_B/N_A) = e⁻(λt)/e⁻(8λt) = e⁷λt. Setting this equal to e⁻², we solve 7λt = 2, giving t = 2/7λ. Thus, the correct answer is 1/8λ.

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