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  • A factory produces a radioactive substance A at a constant rate R which decays with a decay constant  to fo

A factory produces a radioactive substance A at a constant rate R which decays with a decay constant \lambda to form a stable substanceThe number of nuclei of A is -

Option: 1

\frac{R}{\lambda}\left(1-e^{-\lambda t}\right)


Option: 2

\frac{R}{\lambda}\left(1+e^{-\lambda t}\right)


Option: 3

\frac{R}{2 \lambda}\left(1-e^{-\lambda t}\right)


Option: 4

\frac{R}{2 \lambda}\left(1+e^{-\lambda t}\right)


Answers (1)

best_answer


let N be the number of nuclei of A at any time t -
\mathrm{\begin{aligned} & \frac{d N}{d t}=R-\lambda N \\ & \int_0^N \frac{d N}{(R-\lambda N)}=\int_0^t d t \\ & \left.\frac{\ln (R-\lambda N)}{(-\lambda)}\right]_0^N=t \\ & R-\lambda N)-\ln R=-\lambda t \\ & N=\frac{R}{\lambda}\left(1-e^{-\lambda t}\right) \end{aligned}} Ans
 

Posted by

jitender.kumar

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