How many number of tetrahedral voids in the face centred unit cell are present?

Options

A. 12
B. 8
C. 10
D. 6

Explanation

To determine the number of tetrahedral voids in a face-centered cubic (FCC) unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Face-Centered Cubic (FCC) Structure**:
- In an FCC unit cell, atoms are located at each of the corners of the cube and at the centers of each face.
- There are 8 corner atoms and 6 face-centered atoms.

2. **Calculating the Effective Number of Atoms (Z)**:
- Each corner atom contributes \( \frac{1}{8} \) to the unit cell (since it is shared by 8 unit cells).
- Each face-centered atom contributes \( \frac{1}{2} \) to the unit cell (since it is shared by 2 unit cells).
- Therefore, the total number of atoms per unit cell (Z) can be calculated as:
\[ Z = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]

3. **Calculating the Number of Tetrahedral Voids**:
- The number of tetrahedral voids in a crystal structure is given by the formula:
\[ \text{Number of Tetrahedral Voids} = 2 \times Z \]
- Substituting the value of Z we found:
\[ \text{Number of Tetrahedral Voids} = 2 \times 4 = 8 \]

4. **Conclusion**:
- Therefore, the total number of tetrahedral voids in a face-centered cubic unit cell is **8**.

### Final Answer:
The number of tetrahedral voids in the face-centered unit cell is **8**.

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