The total number of tetrahedral voids in the face centred unit cell is

Options

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

Explanation

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

### Step 1: Understand the FCC Unit Cell Structure
In a face-centered cubic (FCC) unit cell, there are atoms located at the corners and the centers of the faces. Specifically, there are:
- 8 corner atoms (each contributes 1/8 to the unit cell)
- 6 face-centered atoms (each contributes 1/2 to the unit cell)

### Step 2: Calculate the Total Number of Atoms (Z)
To find the total number of atoms in the FCC unit cell, we calculate:
- Contribution from corner atoms: \(8 \text{ corners} \times \frac{1}{8} = 1\)
- Contribution from face-centered atoms: \(6 \text{ faces} \times \frac{1}{2} = 3\)

Adding these contributions together gives:
\[ Z = 1 + 3 = 4 \]

### Step 3: Determine the Number of Tetrahedral Voids
In any unit cell, the number of tetrahedral voids is equal to twice the number of atoms present in the unit cell. Therefore, for an FCC unit cell:
\[ \text{Number of tetrahedral voids} = 2 \times Z = 2 \times 4 = 8 \]

### Conclusion
Thus, the total number of tetrahedral voids in a face-centered cubic (FCC) unit cell is **8**.

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