The number of NaCl molecules in unit cell of its crystal is

Options

A. 4
B. 6
C. 2
D. 8

Answer

To determine the number of NaCl molecules in the unit cell of its crystal, we need to analyze the arrangement of sodium (Na⁺) and chloride (Cl⁻) ions in the crystal structure.

### Step-by-Step Solution:

1. **Identify the Crystal Structure**:
NaCl crystallizes in a face-centered cubic (FCC) structure. In this structure, Na⁺ ions occupy the octahedral sites, while Cl⁻ ions are located at the face centers and corners of the unit cell.

2. **Count the Na⁺ Ions**:
- **Body Center Contribution**: There is one Na⁺ ion located at the body center of the unit cell. This contributes fully (100%).
- **Edge Center Contribution**: There are 12 edges in the cube, and each edge center has a Na⁺ ion that is shared among four unit cells. Therefore, the contribution from the edge centers is:
\[ \text{Contribution from edge centers} = 12 \text{ edges} \times \frac{1}{4} = 3 \]
- **Total Na⁺ Ions**: Adding the contributions together gives:
\[ \text{Total Na⁺ ions} = 1 \text{ (from body center)} + 3 \text{ (from edge centers)} = 4 \]

3. **Count the Cl⁻ Ions**:
- **Face Center Contribution**: There are 6 faces in the cube, and each face center has a Cl⁻ ion that is shared between two unit cells. Therefore, the contribution from the face centers is:
\[ \text{Contribution from face centers} = 6 \text{ faces} \times \frac{1}{2} = 3 \]
- **Corner Contribution**: There are 8 corners in the cube, and each corner has a Cl⁻ ion that is shared among eight unit cells. Thus, the contribution from the corners is:
\[ \text{Contribution from corners} = 8 \text{ corners} \times \frac{1}{8} = 1 \]
- **Total Cl⁻ Ions**: Adding these contributions gives:
\[ \text{Total Cl⁻ ions} = 3 \text{ (from face centers)} + 1 \text{ (from corners)} = 4 \]

4. **Determine the Number of NaCl Formula Units**:
- Since there are 4 Na⁺ ions and 4 Cl⁻ ions in the unit cell, they combine to form 4 NaCl formula units. Thus, the number of NaCl molecules in the unit cell is:
\[ \text{Number of NaCl molecules} = 4 \]

5. **Conclusion**:
The number of NaCl molecules in the unit cell of its crystal is **4**.

### Final Answer:
The number of NaCl molecules in the unit cell of its crystal is **4**.

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