The number of octahedral voids in a unit cell of a cubical closest packed structure is:

Options

A. 1
B. 2
C. 4
D. 8

Answer

To determine the number of octahedral voids in a unit cell of a cubical closest packed structure (also known as face-centered cubic or FCC), we can follow these steps:

### Step 1: Understand the Structure of FCC
In a face-centered cubic (FCC) structure, atoms are located at each of the corners and the centers of each face of the cube.

### Step 2: Identify the Location of Octahedral Voids
In an FCC unit cell, octahedral voids are located:
- At the center of the cube (1 body-centered void).
- At the edge centers (12 edge-centered voids).

### Step 3: Calculate the Contribution of Each Octahedral Void
1. **Body-Centered Octahedral Void**:
- There is 1 octahedral void at the body center, and its contribution to the unit cell is 1 (since it is fully contained within the unit cell).

2. **Edge-Centered Octahedral Voids**:
- There are 12 edges in a cube, and each edge contributes 1/4 of an octahedral void to the unit cell (since each edge-centered void is shared by 4 adjacent unit cells).
- Therefore, the total contribution from the edge-centered voids is:
\[ 12 \text{ edges} \times \frac{1}{4} = 3 \]

### Step 4: Total Number of Octahedral Voids
Now, we can sum the contributions from both types of octahedral voids:
\[ \text{Total octahedral voids} = \text{Body-centered void} + \text{Edge-centered voids} = 1 + 3 = 4 \]

### Conclusion
Thus, the total number of octahedral voids in a unit cell of a cubical closest packed structure is **4**.

---