Question

A solution containing active cobalt $2760$ co having activity of $0.8\mu ci$and decay constant $\lambda$ is injected into an animal's body. If $1cm3$ of blood is drawn from the animal's body after $10hrs$ of injection, the activity found was $300$ decays per minute. What is the volume of blood that is flowing in the body?$\left(1Ci=3.7×1010FcayPerSecondandAtT=10HrsE-\lambda T=0.84\right)$

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Solution

The activity equation can be written as$\begin{array}{l}\frac{dN}{dt}=\lambda {N}_{o}{e}^{-\lambda t}\end{array}$Substituting the values, we get:$\begin{array}{l}\lambda {N}_{o}=0.8\mu {C}_{i}\end{array}$Substituting the values, we get:$\begin{array}{l}\lambda {N}_{o}=2.96\ast {10}^{4}\end{array}$Let the volume of the blood flowing be VThe activity would reduce by a factor of$\begin{array}{l}\frac{{10}^{-3}}{V}\end{array}$Therefore,$\begin{array}{l}\frac{\lambda {N}_{o}{10}^{-3}}{V}{e}^{-\lambda t}=300/60.\end{array}$Now substituting the values of$\begin{array}{l}{e}^{-\lambda t}and\lambda {N}_{o},\end{array}$we get,$V=5litre$

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