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 \(t = 10\, hrs\) \({e^{ - \lambda t}} = 0.84\) )

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Correct Answer

(D) \(5\)

Detailed explanation

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, \(V\)

\(=\frac{N}{n}\)

\( = \frac{{{N_0}e - \lambda t}}{n} = \) \( \frac{{0.8 \times 3.7 \times {{10}^4} \times 0.7927}}{5} \cong 5\,\,{\mkern 1mu} litre\)

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