$$131I$$ is an isotope of iodine that β decays to an isotope of Xenon with a $$half-life$$ of $$8$$ days. A small amount of a serum labelled with $$131I$$ is injected into the blood of a person. The activity of the amount of $$131I$$ injected was $$2.4$$×$$105$$ 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 $$2.5$$ ml of blood is drawn from the person’s body, and gives an activity of $$115$$ Bq. The total volume of blood in the person’s body, in liters is $$approximately(you$$ may use ex≈$$1+x$$ for x

Question

$$131I$$ is an isotope of iodine that β decays to an isotope of Xenon with a $$half-life$$ of $$8$$ days. A small amount of a serum labelled with  $$131I$$ is injected into the blood of a person. The activity of the amount of  $$131I$$ injected was $$2.4$$×$$105$$ 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 $$2.5$$ ml of blood is drawn from the person’s body, and gives an activity of $$115$$ Bq. The total volume of blood in the person’s body, in liters is $$approximately(you$$ may use ex≈$$1+x$$ for x<<$$1$$ and ln $$2$$≈$$0.7$$ $$)$$.

Infinity Learn · Accepted Answer

$$131I$$→Xe  $$dNdt=$$−λ$$N=2.4$$×$$105$$ i.e. initially.$$N0=2.4$$×$$105$$λ $$N=2.4$$×$$105$$λ×e−λ$$t=2.4$$×$$105$$λe−$$11.5$$×$$0.78$$×$$24$$ For $$2.5$$ ml we get $$115$$ BqSo for  “V” vol. we get $$1152.5V=$$λ$$N115V2.5$$λ$$=2.4$$×$$105$$λ×e−$$11.5$$×$$0.78$$×$$24$$ $$V=0.0521$$×$$105$$×$$0.96=5$$×$$103mL$$ ≈$$5lit$$

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