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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, 2.5ml 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 ex1+x for |x|<<1 and ln20.7).

Solution
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t12=8 days=8×24 hr
R0=2.4×105Bq
Using 0.691t12×t=lnR0R
0.6928×24×11.5=ln2.4×105R
2.4×105R=e0.041=1+0.041
R=2.4×1051.041=2.3×105
115 Bq is in volume=2.5ml
2.3×105Bq is in volume=2.5115×2.3×105
=0.05×105
=5×103ml
=5 litres

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