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?

$(1Ci=3.7\times 1010FcayPerSecondandAtT=10HrsE-\lambda T=0.84)$

Answer 1

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 V

The 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,

$V=5litre$