At any instant, two elements X1 and X2 have same number of radioactive atoms. If the decay constant of X1 and X2 are 10 λ and λ respectively, then the time when the ratio of their atoms becomes 1/e respectively will be: (a) (1)/(5λ) (b) (1)/(11λ) (c) (1)/(9λ) (d) (1)/(6λ)

Answer: (c). (N₁)/(N₂) = e-10λ te-λ t = e-9λ t. e-9λ t = e⁻¹ ⇒ t = (1)/(9λ). So the answer is (c) (1)/(9λ).

At any instant, two elements X1 and X2 have same number of… | NEET 2022 (Phase 2)

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Law of Radioactive Decay

At any instant, two elements X1 and X2 have same number of radioactive atoms. If the decay constant of X1 and X2 are 10 $\lambda$ and $\lambda$ respectively, then the time when the ratio of their atoms becomes $\frac{1}{e}$ respectively will be:

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Answer: (c)

$\frac{N_1}{N_2} = \frac{e^{-10\lambda t}}{e^{-\lambda t}} = e^{-9\lambda t}$ .
$e^{-9\lambda t} = e^{-1} \Rightarrow t = \frac{1}{9\lambda}$ .
So the answer is (c) $\frac{1}{9\lambda}$ .

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