1. 1/7λ 2. 1/8λ 3. 1/9λ 4. 1/λ

Answer: 1. 1/7λ Key idea: N=N₀e^(-λ t) for each material, and take the ratio of the two. N_A=N₀e^(-8λ t) , N_B=N₀e^(-λ t) . Then N_A/N_B=e^(-7λ t) . Setting this equal to 1/e gives 7λ t=1 , so t=1/7λ . Note: B decays slower, so strictly it is the ratio A to B that equals 1/e . The official answer 1/7λ follows from this ratio.

Topic: Composition and size of nucleus, atomic masses· Atoms and Nuclei

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 1/e ?

1. \(\frac{1}{7\lambda}\)

2. \(\frac{1}{8\lambda}\)

3. \(\frac{1}{9\lambda}\)

4. \(\frac{1}{\lambda}\)

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Answer: 1. \(\frac{1}{7\lambda}\)

Key idea: \(N=N_0e^{-\lambda t}\) for each material, and take the ratio of the two.

\(N_A=N_0e^{-8\lambda t}\), \(N_B=N_0e^{-\lambda t}\). Then \(\dfrac{N_A}{N_B}=e^{-7\lambda t}\).

Setting this equal to \(\dfrac1e\) gives \(7\lambda t=1\), so \(t=\dfrac{1}{7\lambda}\).

Note: B decays slower, so strictly it is the ratio A to B that equals \(1/e\). The official answer \(1/7\lambda\) follows from this ratio.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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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 1/e ?

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