The number of octahedral voids per lattice site in a lattice is _____ (Rounded off to the nearest integer)

Answer

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

### Step-by-Step Solution

1. **Identify the Lattice Points in FCC Structure:**
- In a face-centered cubic (FCC) lattice, there are atoms located at the corners and the face centers of the unit cell.
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom to the unit cell. Therefore, the total contribution from the corners is:
\[ 8 \times \frac{1}{8} = 1 \text{ atom} \]
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) of an atom to the unit cell. Therefore, the total contribution from the face centers is:
\[ 6 \times \frac{1}{2} = 3 \text{ atoms} \]
- Thus, the total number of lattice points (atoms) in an FCC unit cell is:
\[ 1 + 3 = 4 \text{ atoms} \]

2. **Determine the Number of Octahedral Voids:**
- In an FCC structure, the octahedral voids are located at the body center and at the edge centers.
- There is 1 body center in the unit cell, contributing 1 octahedral void.
- There are 12 edges in the FCC unit cell, and each edge contributes \( \frac{1}{4} \) of an octahedral void (since each edge is shared by 4 unit cells). Therefore, the total contribution from the edges is:
\[ 12 \times \frac{1}{4} = 3 \text{ octahedral voids} \]
- Thus, the total number of octahedral voids in an FCC unit cell is:
\[ 1 + 3 = 4 \text{ octahedral voids} \]

3. **Calculate the Ratio of Octahedral Voids to Lattice Points:**
- Now, we can find the ratio of octahedral voids to lattice points:
\[ \text{Ratio} = \frac{\text{Number of Octahedral Voids}}{\text{Number of Lattice Points}} = \frac{4}{4} = 1 \]

### Final Answer
The number of octahedral voids per lattice site in a lattice is **1** (rounded off to the nearest integer).