When a sample of human blood is diluted 200 time its initial volume and microscopically examined in a layer 0.10 mm thick, an average of 30 RBC are found in `100xx100` micrometer square. The number of RBC in 1 `mm^(3)` of undiluted blood is

Options

A. `10^6`
B. `6 xx 10^6`
C. `2xx10^6`
D. `3 xx 10^6`

Answer

To solve the problem step by step, we will follow the process outlined in the video transcript.

### Step 1: Understand the given data
- The blood sample is diluted 200 times.
- The thickness of the layer examined is 0.10 mm.
- The area examined is \(100 \, \mu m \times 100 \, \mu m\).
- The average number of RBCs found in that area is 30.

### Step 2: Calculate the volume of the examined layer
First, we need to convert the area and thickness into consistent units (meters):
- Area in square meters:
\[ 100 \, \mu m = 100 \times 10^{-6} \, m = 10^{-4} \, m \]
Therefore, the area is:
\[ (10^{-4} \, m) \times (10^{-4} \, m) = 10^{-8} \, m^2 \]

- Thickness in meters:
\[ 0.10 \, mm = 0.10 \times 10^{-3} \, m = 10^{-4} \, m \]

- Volume of the examined layer:
\[ \text{Volume} = \text{Area} \times \text{Thickness} = 10^{-8} \, m^2 \times 10^{-4} \, m = 10^{-12} \, m^3 \]

### Step 3: Calculate the concentration of RBCs in the diluted sample
The concentration of RBCs in the diluted sample can be calculated as:
\[ \text{Concentration} = \frac{\text{Number of RBCs}}{\text{Volume}} = \frac{30}{10^{-12} \, m^3} = 30 \times 10^{12} \, \text{RBCs/m}^3 \]

### Step 4: Calculate the concentration in undiluted blood
Since the blood was diluted 200 times, the concentration in the undiluted blood will be:
\[ \text{Concentration in undiluted blood} = 200 \times \text{Concentration in diluted blood} = 200 \times 30 \times 10^{12} \, \text{RBCs/m}^3 \]

### Step 5: Simplify the expression
Calculating the above expression:
\[ = 6000 \times 10^{12} \, \text{RBCs/m}^3 = 6 \times 10^{15} \, \text{RBCs/m}^3 \]

### Step 6: Convert to number of RBCs in 1 mm³
Since \(1 \, mm^3 = 10^{-9} \, m^3\), we can find the number of RBCs in 1 mm³:
\[ \text{Number of RBCs in 1 mm}^3 = 6 \times 10^{15} \, \text{RBCs/m}^3 \times 10^{-9} \, m^3 = 6 \times 10^{6} \, \text{RBCs} \]

### Final Answer
The number of RBCs in 1 mm³ of undiluted blood is \(6 \times 10^{6}\).

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