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Question:

A solution containing active cobalt-60 (60Co) having activity of 0.8 µCi and decay constant λ is injected in an animal's body. If 1 cm³ 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?

4 litres

5 litres

6 litres

7 litres

Solution:

The activity equation can be written as -dN/dt = λN0e-λt. Given that λN0 = 0.8 µCi. Putting the values, λN0 = 2.96 × 104. Let the volume of the blood flowing be V, the activity would reduce by a factor of 10-6V. Hence λN010-6Ve-λt = 300/60 (Both R.H.S. and L.H.S. are decay/s). Putting the values of e-λt and λN0 we get V = 5 litres