The number of octahedral sites per sphere in fcc structure is

Options

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

Explanation

To determine the number of octahedral sites per sphere in a face-centered cubic (FCC) structure, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding FCC Structure**:
- The face-centered cubic (FCC) structure has atoms located at each corner of the cube and at the center of each face.
- Each unit cell of FCC contains a total of 4 atoms.

2. **Identifying Octahedral Sites**:
- In a crystal lattice, octahedral sites are specific locations where an atom can be placed. In FCC, these sites are located at the center of the unit cell and at the edges of the cube.

3. **Counting Octahedral Sites**:
- In an FCC unit cell, there is 1 octahedral site at the center of the cell and 12 edge sites. However, each edge site is shared by 4 adjacent unit cells, so the contribution from the edge sites is:
\[ \text{Number of edge sites} = \frac{12 \text{ edges} \times \frac{1}{4} \text{ (contribution per unit cell)}}{1} = 3 \]
- Therefore, the total number of octahedral sites per unit cell is:
\[ 1 \text{ (from the center)} + 3 \text{ (from the edges)} = 4 \]

4. **Conclusion**:
- The number of octahedral sites per sphere (or per unit cell) in an FCC structure is equal to the number of atoms per unit cell, which is 4.

### Final Answer:
The number of octahedral sites per sphere in FCC structure is **4**.