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A solution containing active cobalt ${}_{27}^{60}Co$ having activity of $0.8\,\mu Ci$ and decay constant $\lambda $ is injected in an animal's body. If $1 \,cm^3$ of blood is drawn from the animal's body after $10\, hrs$ of injection, the activity found was $300\, decays$ per minute. What is the volume of blood that is flowing in the body?..........$litres$ ( $ICi = 3.7 \times 10^{10}$ decay per second and at $t = 10\, hrs$ ${e^{ - \lambda t}} = 0.84$ )
$6$
$7$
$4$
$5$
Solution
Let initial activity $=\mathrm{N}_{0}=0.8\, \mu \mathrm{ci}$
$0.8 \times 3.7 \times 10^{4}\, \mathrm{dps}$
Activity in $1\, \mathrm{cm}^{3}$ of blood at $\mathrm{t}=10\, \mathrm{hr}$
$\mathrm{n}=\frac{300}{60} \mathrm{dps}=5 \,\mathrm{dps}$
$\mathrm{N}=$ Activity of whole blood at timet $=10 \,\mathrm{hr}$ Total volume of the blood in the person, $V$
$=\frac{N}{n}$
$ = \frac{{{N_0}e – \lambda t}}{n} = $ $ \frac{{0.8 \times 3.7 \times {{10}^4} \times 0.7927}}{5} \cong 5\,\,{\mkern 1mu} litre$
