A `0.2 mL` sample of a solution containing `1.0xx10^(-7)` curie of `._(1)^(3)H` is injected to the blood stream of an animal. After sufficient time for circulatory equilibrium to be established, `0.10 mL` of blood is found to have an activity of `20 dp m`. Calculate the volume of blood in animal, assuming no change in activity of sample during circulatory equilibrium.

Options

A. 11110 mL
B. 1110 mL
C. 11010 mL
D. 10110 mL

Answer

To solve the problem step by step, we will follow the given information and apply the necessary calculations.

### Step 1: Convert the initial activity from Curie to DPM
The initial activity of the solution is given as \(1.0 \times 10^{-7}\) Curie. We need to convert this to disintegrations per minute (DPM) using the conversion factor:
\[ 1 \text{ Curie} = 3.7 \times 10^{10} \text{ DPM} \]
Thus, the initial activity \(R_i\) in DPM is:
\[ R_i = 1.0 \times 10^{-7} \text{ Curie} \times 3.7 \times 10^{10} \text{ DPM/Curie} = 3.7 \times 10^{3} \text{ DPM} \]

### Step 2: Set up the relationship between initial and final activity
We know that the activity is proportional to the volume of blood. Therefore, we can set up the following ratio:
\[ \frac{R_i}{R_f} = \frac{V + 0.2 \text{ mL}}{0.1 \text{ mL}} \]
Where:
- \(R_f\) is the final activity, which is given as \(20 \text{ DPM}\).
- \(V\) is the total volume of blood in the animal (in mL).

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ \frac{3.7 \times 10^{3} \text{ DPM}}{20 \text{ DPM}} = \frac{V + 0.2}{0.1} \]

### Step 4: Cross-multiply to solve for \(V\)
Cross-multiplying gives:
\[ 3.7 \times 10^{3} \times 0.1 = 20 \times (V + 0.2) \]
This simplifies to:
\[ 370 = 20V + 4 \]

### Step 5: Solve for \(V\)
Rearranging the equation:
\[ 20V = 370 - 4 = 366 \]
\[ V = \frac{366}{20} = 18.3 \text{ mL} \]

### Step 6: Final result
Thus, the total volume of blood in the animal is approximately:
\[ V \approx 18.3 \text{ mL} \]