Question

# A solution containing active cobalt 6027Co having activity of 0.8μCi and decay constant λ is injected in an animal's body. If 1cm3 of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? (1Ci=3.7×1010 decay per second and at t=10hrs e−λt=0.84)

A
6 litres
B
7 litres
C
4 litres
D
5 litres
Solution
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#### The activity equation can be written as −dNdt=λNoe−λtgiven thatλNo=0.8μCiPutting the values,λNo=2.96×104 Let the volume of the blood flowing be V,the activity would reduce by a factor of 10−3VHenceλNo10−3Ve−λt=300/60 (Both R.H.S. and L.H.S. are decay/s)Putting the values of e−λt and λNo we getV=5litre

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