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  • Two ratio active materials  and <img alt="X_{2}" src="https://entrancecorner.oncodecogs.com/gif.lat

Two ratio active materials X_{1} and X_{2} have decay constants 10\lambda and \lambda respectively . If initially they have the same number of nuclei, then the ratio of the number of nuclei of X_{1} to that of X_{2} will be \frac{1}{e} after a time -

Option: 1

\frac{1}{10}\lambda


Option: 2

\frac{1}{11}\lambda


Option: 3

\frac{11}{10}\lambda


Option: 4

\frac{1}{9}\lambda


Answers (1)

Use , N_1=N_0 e^{-10 \lambda} \text { and } N_2=N_0 e^{-\lambda t}

\begin{aligned} & \frac{N_1}{N_2}=\frac{e^{-10 \lambda}}{e^{-\lambda t}} \\ & \frac{N_1}{N_2}=e^{-10 \lambda} \cdot e^{\lambda t}=e^{(-10 \lambda+\lambda t)} \\ & \frac{N_1}{N_2}=e^{-9 \lambda t}-(1) \end{aligned}

but ratio of \frac{N_1}{N_2}=\frac{1}{e}  put in (1)

\begin{aligned} & \frac{1}{e}=e^{-9 \lambda t} \\ & e^{-1}=e^{-9 \lambda t} \\ & t=\frac{1}{9 \lambda} \end{aligned}

Posted by

Sumit Saini

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