A small quantity of solution containing `Na^24` radio nuclide `(half-life=15 h)` of activity `1.0 microcurie` is injected into the blood of a person. A sample of the blood of volume `1cm^3` 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 person.
(1 curie `=3.7 xx 10^10` disintegrations per second)

Options

A. `5.94 L`
B. 2 L
C. 317 L
D. 1 L

Answer

A

Explanation

(a) `R_(0)=` initial activity = 1microcurice `=3.7xx10^(4)`dps
r= Acitivty in 1`cm ^(3)` of blood at t= 5H
`=(296)/(60)dps=4.93 dps `
R= Activity of whole blood at time t= 5h
total volume should be `V=( R) /( r) =(R_(0) e^(-lamda t))/(r ) `
`=(3.7xx10^(4)xx0.7927)/(4.93)=5.94xx10^(3)cm^(3)=5.94 L `