A small quantity of solution containing `""^(24)Na` radio nuclide (half-life 15 h) of activity 1.0 micro-curie is injected into the bloof of a person. A sample of the blood of volume 1 `cm^(3)` taken after 5 hours shows an activity of 360 disintegration per minute. Determine the total volume of blood in the body of the person, Assume that the radioactive mixed uniformly in the blood of the person.

Options

A. 5 94 litre
B. 2 litre
C. 317 litre
D. 1 litre

Answer

A

Explanation

`R_(0)= 10^(-6)` Curie `= 3.7 xx 10^(10) xx 10^(-6)` dps
r= Activity in `1cm^(3)` of blood at t= 5 hr
`= (296)/(60)` dps= 4.93 dps
Total volume `V= (R)/(r)= (R_(0)e^(-lamda t))/(r)`
`rArr (3.7 xx 10^(4) xx 0.7927)/(4.93) = 5.94 xx 10^(3) cm^(3)= 5.94` litre