In a NaCl structure

Options

A. 6 corners are shared
B. 12 edges are shared
C. 4 comers are shared
D. 8 corners and 6 face are shared

Answer

To solve the question regarding the NaCl structure, let's break down the information step by step.

### Step-by-Step Solution:

1. **Understanding the NaCl Structure**:
- The NaCl (sodium chloride) structure is a type of ionic crystal lattice.
- In this structure, sodium ions (Na⁺) occupy the octahedral voids, while chloride ions (Cl⁻) are located at the face-centered positions of the cubic lattice.

2. **Identifying the Lattice Points**:
- The NaCl structure can be visualized as a face-centered cubic (FCC) lattice for the Cl⁻ ions.
- In an FCC lattice, there are 8 corner atoms and 6 face-centered atoms.

3. **Counting the Shared Atoms**:
- **Corners**: Each corner atom is shared among 8 adjacent unit cells. Since there are 8 corners in total, the contribution from corners is:
\[ \text{Contribution from corners} = 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]
- **Edges**: Each edge atom is shared between 4 adjacent unit cells. There are 12 edges in a cube, so the contribution from edges is:
\[ \text{Contribution from edges} = 12 \text{ edges} \times \frac{1}{4} = 3 \text{ atoms} \]
- **Faces**: Each face-centered atom is shared between 2 adjacent unit cells. There are 6 faces, so the contribution from faces is:
\[ \text{Contribution from faces} = 6 \text{ faces} \times \frac{1}{2} = 3 \text{ atoms} \]

4. **Total Contribution of Atoms**:
- Now, summing up the contributions:
\[ \text{Total Na⁺ ions} = 1 \text{ (from corners)} + 3 \text{ (from edges)} + 3 \text{ (from faces)} = 7 \text{ Na⁺ ions} \]
- However, in the NaCl structure, we typically consider the arrangement of Cl⁻ ions at the face centers and corners, leading to a total of 4 Na⁺ ions per unit cell.

5. **Conclusion**:
- The NaCl structure consists of Na⁺ ions occupying octahedral voids and Cl⁻ ions at the face-centered positions, with the contributions from corners, edges, and faces properly accounted for.