Question

In order to determine the volume of blood in an animal, a $1.0mL$ sample of solution of ${10}^{3}dpm$ of ${}_1{H}^3$ is injected into the animal blood stream. After sufficient time for circulatory equilibrium to be established, $2mL$ of blood is found to have activity to $10dpm$. The volume of blood in animal is:

• A. $199mL$
• B. $198mL$
• C. $200mL$
• D. $20mL$

Answer 1

The correct option is A $199mL$

Let V ml be the volume of blood in animal.
When 1.0 ml sample is added, total volume becomes $V+1.0ml$. Its activity is 1000 dpm.
After equilibrium, 2.0 ml of the sample had activity of 10 dpm.
Hence, after equilibrium, the activity of V+1.0 ml of blood sample will be $\frac{10}{2}(V+1.0ml)=1000dpm$
Hence, $V=199ml$.