${}^{131}I$ is an isotope of iodine that decays to an isotope of Xenon with a half-life of 8 days. a small amount of a serum labeled with ${}^{131}I$ is injected into the blood of a person. The activity of the amount of ${}^{131}I$ injected was $2.4 \times 10^{5}$ Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.5 hours, 2.5ml of blood is drawn from person’s body, and gives an activity of 115 Bq. The total volume of blood in the person's body, in litres is approximately
(You may use $e^{x} = 1 + x$ for $| x | < < 1$ and ln 2=0.7)

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answer is 5.

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Detailed Solution

$I^{131} \to X e^{131} + B (T_{\frac{1}{2}} = 8 d a y s)$

$A_{o} = 2.4 \times 10^{5} = λ N_{o}$

At t = 0, Ao = $λ N_{o}$
=2.4 x 105 Bq
At t=11.5 hr
A= $λ N$
After t = 11.5 hr
2.5 ml of blood is drawn from person & gives activity of 15 Bq

$115 = λ (\frac{N}{V} \times 2.5) \Rightarrow V = 5 L$

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