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=3.7∗1010 disintegrations per second).

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Solution

## λ=0.693T1/3=0.69315×3600=1.283×10−5/secAlso, activity is given by A=dNdt=λN03.7×104=1.283×10−5×N0N0=3.7×1041.283×10−5=2.883×109Let the number of radioactive nuclei present after 5 hrs be N1 in 1㎤ sample of blood ,Then, dNdt=λN129660=0.69315×3600N1N1=3.844×105Let N10 be the no. of radioactive nuclei in per ㎤of sample, thenN1N0=(12)t/T1/2;N10=(2)5/15×N1(2)1/3×3.844×105=4.878×105Volume of blood V=N0N10=2.883×1094.878×105=5.91ℓ≈6L

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