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Atoms and Nuclei question

2017 · Shift 1 · Q48
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Atoms and Nuclei question

2017 · Shift 1 · Q48

JEE AdvancedPhysicsAtoms and NucleiNumerical+3 / −1
131I{}^{131}{\rm I}131I is an isotope of Iodine that BBB decays to an isotope of Xenon with a half-life of 888 days. A small amount of a serum labelled with 131I{}^{131}{\rm I}131I is injected into the blood of a person. The activity of the amount of 131I{}^{131}{\rm I}131I injected was 2.4×1052.4 \times {10^5}2.4×105 Becquerel (Bq).(Bq).(Bq). It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.511.511.5 hours, 2.52.52.5 ml of blood is drawn from person's body, and gives an activity of 115Bq115Bq115Bq. The total volume of blood in the person's body, in liters is approximately (you may use ex≈1+x  {e^x} \approx 1 + x\,\,ex≈1+x for ∣x∣<<1\left| x \right| \lt \lt 1∣x∣<<1 and ln⁡2≈0.7).\ln 2 \approx 0.7).ln2≈0.7).
Numerical answer
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