Radioactive material ' A ' has decay constant ' 8λ ' and material ' B ' has decay constant ' λ '. Initially they have same number of nuclei. After wha - Physics MCQ NEET 2017 2026 | ExamTest.live

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Radioactive material ' A' has decay constant ' 8 λ' 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 of ' A' will be \frac{1}{e} ?

Solution & Step-by-step Explanation

Let N_{A} and N_{B} be the number of nuclei at time t . N_{A} = N_{0} e^{- 8 λ t} and N_{B} = N_{0} e^{- λ t} .Given ratio \frac{N _{B}}{N _{A}} = \frac{1}{e} . \frac{N _{0} e ^{- λ t}}{N _{0} e ^{- 8 λ t}} = e^{- 1} e^{7 λ t} = e^{- 1} This implies 7 λ t = - 1 .Note: The question likely intended the ratio of A to B or a different exponent. If we solve for magnitude or the ratio \frac{N _{A}}{N _{B}} = \frac{1}{e} : \frac{e ^{- 8 λ t}}{e ^{- λ t}} = e^{- 1} ⟹ e^{- 7 λ t} = e^{- 1} ⟹ 7 λ t = 1 ⟹ t = \frac{1}{7 λ} .

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Radioactive material ' A' has decay constant ' 8 λ' 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 of ' A' will be \frac{1}{e} ?

\frac{1}{λ}

\frac{1}{7 λ}

\frac{1}{8 λ}

\frac{1}{9 λ}

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