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Two radioactive materials \mathrm{x_1 } and \mathrm{x_2} have decay constants 10 \lambda and \lambda respectively. If initally they have the same number of nuclei, then the ratio of the number of nuclei of \mathrm{x_1}  to that of \mathrm{ x_2} will be \left (\mathrm{\frac{1}{e}} \right )  after a time -
 

Option: 1

\frac{1}{10\lambda}


Option: 2

\frac{1}{11\lambda}


Option: 3

\frac{11}{10}


Option: 4

\frac{1}{9\lambda}


Answers (1)

best_answer

\begin{aligned} &\mathrm{ \frac{N_{x_1(t)}}{N_{X_2(t)}}=\frac{1}{e} }\\ &\mathrm{ \text { or } \frac{N_0 e^{-10 \lambda t}}{N_0 e^{-\lambda t}}=\frac{1}{e}}\\ \end{aligned}

(Initally both have same number of nuclei say \mathrm{N_0 })

\begin{aligned} &\mathrm{ e=e^{-\lambda t} / e^{-10 \lambda t} \text { or } e=e^{9 \lambda t} }\\ &\mathrm{ 9\lambda t=1 \quad t=\frac{1}{9 \lambda} }\\ \end{aligned}

Posted by

Pankaj Sanodiya

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