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Two radio active materials \mathrm{x_1 } and \mathrm{x_2} have decay constants \mathrm{10 \lambda} and \mathrm{\lambda }respectively. If Initially they have the same number of nuclei, thew the ratio of the number of nuclei of \mathrm{ x_1 } to that of \mathrm{ x_2}  will be \mathrm{ \frac{1}{e}} after a time -
 

Option: 1

\frac{1 }{10 \lambda}\frac{1 }{10 \lambda}


Option: 2

\frac{1 }{11 \lambda}


Option: 3

\frac{1 1}{10 \lambda}


Option: 4

\frac{1 }{9 \lambda}


Answers (1)

best_answer

\begin{aligned} &\mathrm{Use, N_1=N_0 e^{-10 \lambda}~ and ~N_2=N_0 e^{-\lambda t}}\\ &\mathrm{ \frac{N_1}{N_2}=\frac{e^{-10 \lambda}}{e^{-\lambda t}} }\\ &\mathrm{ \frac{N_1}{N_2}=e^{-10 \lambda} \cdot e^{\lambda t}=e^{(-10 \lambda+\lambda t)} }\\ &\mathrm{ \frac{N_1}{N_2}=e^{-9 \lambda t}-(1)}\\ &\mathrm{but ~ratio ~of~ \frac{N_1}{N_2}=\frac{1}{e} ~put~ in ~(1) }\\. &\mathrm{ \frac{1}{e}=e^{-9 \lambda t} }\\ &\mathrm{ e^{-1}=e^{-9 \lambda t} }\\ &\mathrm{ t=\frac{1}{9 \lambda} }\\ \end{aligned}

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Sanket Gandhi

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