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13.Nuclei
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Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half lives 1 month and 2 months respectively. At time $t=$ 0 , number of nuclei of each $P$ and $Q$ is $x$. Time at which rate of disintegration of $P$ and $Q$ are equal, number of nuclei of $R$ is ........ $x$
A
$1$
B
$1.25$
C
$1.5$
D
$1.75$
Solution
(b)
Let time be $t$
$\lambda_1 \times e^{-\lambda_1 t}=\lambda_2 \times e^{-\lambda_2 t}$
$\lambda_1 e^{-\lambda_1 t}=\lambda_2 e^{-\lambda_2 t}$
$\frac{\lambda_1}{\lambda_2}=e^{\left(\lambda_1-\lambda_2\right) t}$
$\ln \frac{\lambda_1}{\lambda_2}=\left(\lambda_1-\lambda_2\right) t$
$\ln 1-\ln 2=\left(\lambda_1-\lambda_2\right) t$
$0.693=\left(\lambda_1-\lambda_2\right) t$
Standard 12
Physics
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