Q47 / 54 · JEE Advanced 2017 (Paper 1) · Physics

 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 litres is approximately (you may use $\mathrm{e}^{\mathrm{x}} \approx 1+\mathrm{x}$ for $|\mathrm{x}|<<1$ and $\ln 2 \approx 0.7$).

Correct answer: 5

Solution

t12=8 days

A=A0 e-λt

eλt 115=A0

A0=1151+λt=115 1+ln2t12×11.5

A0=115×1.042=119.82

A0 ≅120 Bq

120 Bq is the activity of 2.5 ml

∴   2.4×105 Bq  is the activity of 2.5×10-3120×2.4×105

∴    Total volume of blood = 5 litres

Hence, the correct answer is 5.

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