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)

Explanation

Half-life, `t_(1//2)` = 15 h
Initial activity, `R_(0)=imuCi=10^(-6)xx3.7xx10^(10) `
`" "=3.7xx10^(-4)` dps
At `t`=5h, activity of sample, `R=(360)/(60)` dps,
volume of blood, V= 1 `cm^(3)`
Let initial volume of blood = `V_(0) cm ^(3)`
According to specific activity, `(R)/(V)=(R_(0))/(V_(0))e^(-lamdat)=(R_(0))/(V_(0))e^(((0.693)/(t_(1//2))t))" "(because lamda=(0.693)/(t_(1//2)))`
`" "(360//60)/(1)=(3.7xx10^(4))/(V_(0))e^(((0.693)/(15)xx5))`
`6=(3.7xx10^(4))/(V_(0)xxe^(0.231))`
Volume of the blood, `V_(0)=4894.72 cm^(3) = 4.894` L