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

Options

A. 4
B. 8
C. twice the number of octahedral voids
D. Four times the number of octahedral voids

Explanation

To determine the number of tetrahedral 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) lattice structure, also known as the rock salt structure.

2. **Determine the Number of Atoms in the Unit Cell**:
- In an FCC lattice, there are 4 atoms per unit cell. This is because each corner atom contributes 1/8th to the unit cell (8 corners) and each face-centered atom contributes 1/2 (6 faces), leading to:
\[ \text{Total atoms} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]

3. **Calculate the Number of Octahedral Voids**:
- In an FCC lattice, the number of octahedral voids is equal to the number of atoms, which is 4. Thus, there are 4 octahedral voids per unit cell.

4. **Calculate the Number of Tetrahedral Voids**:
- The number of tetrahedral voids in a crystal structure is given by the formula:
\[ \text{Number of tetrahedral voids} = 2n \]
- Where \( n \) is the number of octahedral voids. Since we have 4 octahedral voids:
\[ \text{Number of tetrahedral voids} = 2 \times 4 = 8 \]

5. **Conclusion**:
- Therefore, the number of tetrahedral voids per unit cell in NaCl is **8**.

### Final Answer:
The number of tetrahedral voids per unit cell in NaCl crystal is **8**.

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