A `0.20 mL` sample of a solution containing `1.0 xx 10^(-7) Ci` of `._(1)H^(3)` is injected into the blood stream of a laboratory animal. After sufficient time of of a circulatory equilibrium to be established, `0.10 mL` of blood is found to have an activity of 20 dpm. Calculate the blood volume of the animal.

Explanation

In the injected sample the activity is
`(1.0 xx 10^(7) Ci) ((3.7 xx 10^(10) dps)/(Ci)) = 3.7 xx 10^(3) dps`
In the sample withdraw `= (20 dpm)` `(1 "min"//60 s)`
`= 0.33 dps`
The total activity of the entire blood volume is equal to the activity of the sample injected. The ratio of volumes, where `V` is the original body blood volume:
`(3.7 xx 10^(3) dps)/(0.33 dps) = (V + 0.20 mL)/(0.10 mL)`
`V = 1.1 xx 10^(3) mL = 1.1 L`