the number of octahedral voids per unit cell in NaCl crystal is ………… .

Options

A. 4
B. 8
C. twice the number of tetrahedral voids
D. four times the number of tetrahedral voids.

Answer

To determine the number of octahedral voids per unit cell in a NaCl crystal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure of NaCl**:
- NaCl crystallizes in a face-centered cubic (FCC) structure.

2. **Understand the Arrangement of Atoms**:
- In an FCC unit cell, there are atoms located at the corners and at the face centers of the cube.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell, and each face-centered atom contributes \( \frac{1}{2} \) of an atom.

3. **Calculate the Total Number of Atoms per Unit Cell (Z)**:
- There are 8 corner atoms and 6 face-centered atoms in the FCC unit cell.
- The contribution from corner atoms: \( 8 \times \frac{1}{8} = 1 \)
- The contribution from face-centered atoms: \( 6 \times \frac{1}{2} = 3 \)
- Therefore, the total number of atoms per unit cell (Z) is:
\[ Z = 1 + 3 = 4 \]

4. **Determine the Number of Octahedral Voids**:
- In an FCC structure, the number of octahedral voids is equal to the number of atoms per unit cell (Z).
- Thus, the number of octahedral voids in NaCl is:
\[ \text{Number of octahedral voids} = Z = 4 \]

5. **Conclusion**:
- Therefore, the number of octahedral voids per unit cell in NaCl crystal is **4**.

### Final Answer:
The number of octahedral voids per unit cell in NaCl crystal is **4**.