A solution containing active cobalt `60/27` Co having activity of `0.8 muCi` and decay constant `lambda` is injected in an animal's body. If `1cm^(3)` of blood is drawn from the animal's body after 10hrs of injection , the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body ? (`1 Ci = 3.7 xx 10^(10)` decays per second and at `t = 10` hrs `e^(-lambdat) = 0.84`)

Options

A. 8 litres
B. 7 litres
C. 4 litres
D. 5 litres

Answer

D

Explanation

Let initial activity = No = `0.8 mu` ci
`0.8 xx 3.7 xx 10^(4)` dps
Activity in `1 cm^(3)` of blood at t = 10 hr , `n = (300)/(60)` dps = 5 dps
N = Activity of whole blood at time t = 10 hr .
Total volume of the blood in the person `V = (N)/(n)`
`= (N_(0) e - lambda t)/(n) = (0.8 xx 3.7 xx 10^(4) xx 0.7927)/(5) = 5` litres