Modern Physics 3 Question 41

40. A small quantity of solution containing Na24 radio nuclide (half-life =15h ) of activity 1.0 microcurie is injected into the blood of a person. A sample of the blood of volume 1cm3 taken after 5h shows an activity of 296 disintegrations per minute. Determine the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person.

(1994,6 M)

(1 curie =3.7×1010 disintegrations per second )

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Solution:

  1. λ= Disintegration constant

0.693t1/2=0.69315h1=0.0462h1

Let R0= initial activity =1 microcurie

=3.7×104 disintegrations per second.

r= Activity in 1cm3 of blood at t=5h

=29660 disintegration per second

=4.93 disintegration per second, and

R= Activity of whole blood at time t=5h

Total volume of blood should be

V=Rr=R0eλtr

Substituting the values, we have

V=3.7×1044.93e(0.0462)(5)cm3V=5.95×103cm3 or V=5.95L



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