Question

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)

Answer 1

`t_(1//2) = 15h, A_(0) = 1muCi = 10^(-6) xx 3.7 xx 10^(10)`
`= 3.7 xx 10^(4)dps`
`t = 5h, A = (296)/(60)dps`, volume of blood `V = 1 cm^(3)`
Let initial volume of blood = `V_(0)cm^(3)`
`(A)/(V) = (A_(0))/(V_(0)) e^(-lambdat) = (A_(0))/(V_(0))e^(-(0.693)/(t_(1//2))t)`
`(296//60)/(1) = (3.7 xx 10^(4))/(V_(0)) e^(-(0.693)/(15)xx5)`
`= (3.7xx10^(4))/(V_(0)xxe^(0.231))`
`V_(0) = 5953.17cm^(3)`
`= 5.953` litre