Question

For a blood sample, 15 g of Hb is present per deciliter (dl) of the blood and there are 5 x 1012 RBC's per liter of the blood. The mean cell haemoglobin is

• A. 29 pg
• B. 30 pg
• C. 39 pg
• D. 60 pg

Hint:

Ensure all units are consistent before calculating clinical indices.
Converting $\text{g/dl}$ to $\text{g/L}$ is done by multiplying by 10.
The resulting unit is in picograms ($10^{-12}\text{ g}$).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given:
- Hemoglobin (Hb) concentration = $15\text{ g/dl}$
- Red Blood Cell (RBC) count = $5 \times 10^{12}\text{ cells/L}$
We need to find the Mean Cell Hemoglobin (MCH), which is the average mass of hemoglobin contained in a single red blood cell.

Step 2: Key Formula or Approach:
The formula for Mean Cell Hemoglobin (MCH) is:
\[ \text{MCH} = \frac{\text{Hemoglobin concentration in g/L}}{\text{RBC count in cells/L}} \]

Step 3: Detailed Explanation:

• First, convert the hemoglobin concentration from grams per deciliter ($\text{g/dl}$) to grams per liter ($\text{g/L}$):
Since $1\text{ L} = 10\text{ dl}$:
\[ \text{Hemoglobin} = 15\text{ g/dl} \times 10\text{ dl/L} = 150\text{ g/L} \]
• Next, write the RBC count per liter of blood:
\[ \text{RBC count} = 5 \times 10^{12}\text{ cells/L} \]
• Substitute these values into the MCH formula:
\[ \text{MCH} = \frac{150\text{ g/L}}{5 \times 10^{12}\text{ cells/L}} \] \[ \text{MCH} = 30 \times 10^{-12}\text{ g} \]
• Since $1\text{ picogram (pg)} = 10^{-12}\text{ grams}$, we get:
\[ \text{MCH} = 30\text{ pg} \]

Step 4: Final Answer:
The mean cell hemoglobin is 30 pg.