A 0.2 mL sample of a solution containing `1.0xx10^(-7)` curie of `._1H^3` is injected to the The bloodstream of an animal. After sufficient time for circulatory equilibrium to be established, 0.10 mL of blood is found to have an activity of 20dpm . Calculate the volume of blood in animal , assuming no change in the activity of the sample during circulatory equilibrium .

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`