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 litres
B. 2 litres
C. 317 litres
D. 1 litres

Answer

A

Explanation

(a) `R_0` = Initial activity = `1` micro curie `= 3.7 xx 10^4 dps`
`r` = Activity in `1 cm^3` of blood at `t = 5 hrs`
=`(296)/(60) dps = 4.93 dps`
`R` = Activity of whole blood at time `t = 5 hr`,
Total volume should be `V = ( R)/( r) = (R_0 e^(- lamda t))/( r)`
=`(3.7 xx 10^4 xx 0.7927)/(4.93) = 5.94 xx 10^3 cm^3 = 5.94 litres`.