The number of nearest neighbours and next nearest neighbours of an `Na^(o+)` ion in a crystal of `NaCl` are, respectively,

Options

A. `6Na^(o+), 12Cl^(Θ)`
B. `6Cl^Θ, and 12Na^(o+)`
C. `12Cl^(Θ), 12Na^(o+)`
D. `6Cl^(Θ), 6Na^(o+)`

Explanation

To determine the number of nearest neighbors and next nearest neighbors of an \( \text{Na}^+ \) ion in a crystal of \( \text{NaCl} \), we will analyze the structure of \( \text{NaCl} \) and identify the positions of the ions.

### Step-by-Step Solution:

1. **Understanding the Structure of NaCl**:
- \( \text{NaCl} \) crystallizes in a face-centered cubic (FCC) lattice structure, commonly referred to as the rock salt structure.
- In this structure, \( \text{Cl}^- \) ions occupy the corners and face centers of the cube, while \( \text{Na}^+ \) ions occupy the octahedral voids.

2. **Identifying Nearest Neighbors**:
- Each \( \text{Na}^+ \) ion is surrounded by \( \text{Cl}^- \) ions.
- In the rock salt structure, each \( \text{Na}^+ \) ion has 6 \( \text{Cl}^- \) ions as its nearest neighbors. These are located at the positions directly adjacent to the \( \text{Na}^+ \) ion.

3. **Identifying Next Nearest Neighbors**:
- The next nearest neighbors for a \( \text{Na}^+ \) ion are the \( \text{Na}^+ \) ions that are located in the octahedral voids adjacent to the \( \text{Cl}^- \) ions.
- In the case of \( \text{NaCl} \), each \( \text{Na}^+ \) ion has 12 \( \text{Na}^+ \) ions as its next nearest neighbors.

4. **Conclusion**:
- Therefore, the number of nearest neighbors of \( \text{Na}^+ \) is 6 (the \( \text{Cl}^- \) ions), and the number of next nearest neighbors is 12 (the \( \text{Na}^+ \) ions).

### Final Answer:
- The number of nearest neighbors of \( \text{Na}^+ \) is 6, and the number of next nearest neighbors is 12.