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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 _______.


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Solution

Given:
Half life, t1/2=8 days=8×24 hr

R0=2.4×105 Bq

We know that for half life,

t1/2=ln 2λ=0.693λ(1)

Also, RR0=eλt

On rearranging it can be written as

lnR0R=λt(2)

Using (1) and (2), we get

0.693t1/2×t=lnR0R

0.6928×24×11.5=ln2.4×105R

2.4×105R=e0.041=1.042

R=2.4×1051.041=2.3×105 Bq

Given that,
115 Bq is in volume = 2.5 ml

2.3×105 Bq is in volume

=2.5115×2.3×105=5000 ml

Volume of blood=5 liters

Hence, 5 is the correct answer.


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