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Question

A small quantity of solution containing 24Na radionuclide (half life 15 hours) of activity 1.0 microcuric is injected into the blood of a person.A sample of the blood of volume 1cm3 taken after 5 hours shows an activity of 296 disintegrations per minute.Determine the total volume of blood in litre in the body of the person.Assume that the radioactivity solution mixes uniformly in the blood of the person.(1Curie=3.71010 disintegrations per second).

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Solution

λ=0.693T1/3=0.69315×3600=1.283×105/sec
Also, activity is given by A=dNdt=λN0
3.7×104=1.283×105×N0
N0=3.7×1041.283×105=2.883×109
Let the number of radioactive nuclei present after 5 hrs be N1 in 1 sample of blood ,
Then, dNdt=λN1
29660=0.69315×3600N1
N1=3.844×105
Let N10 be the no. of radioactive nuclei in per of sample, then
N1N0=(12)t/T1/2;N10=(2)5/15×N1(2)1/3×3.844×105
=4.878×105
Volume of blood V=N0N10=2.883×1094.878×105=5.916L

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