In the crystals structures of sodium chloride, the arrangement of `Cl^(-)` ions is

Options

A. fcc
B. bcc
C. Both fcc and bcc
D. None of these

Answer

To determine the arrangement of Cl⁻ ions in the crystal structure of sodium chloride (NaCl), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Structure of NaCl**:
- Sodium chloride (NaCl) crystallizes in a face-centered cubic (FCC) lattice structure. In this structure, the Cl⁻ ions occupy specific positions.

2. **Identifying the Arrangement of Cl⁻ Ions**:
- In the NaCl structure, the Cl⁻ ions are arranged in a cubic close-packed (CCP) structure, which is equivalent to the FCC arrangement. This means that Cl⁻ ions are located at the corners and the face centers of the cubic unit cell.

3. **Position of Cl⁻ Ions**:
- The Cl⁻ ions are positioned at:
- 8 corners of the cube (each contributing 1/8 to the unit cell).
- 6 face centers (each contributing 1/2 to the unit cell).
- Therefore, the total contribution of Cl⁻ ions from these positions is:
- From corners: \(8 \times \frac{1}{8} = 1\)
- From face centers: \(6 \times \frac{1}{2} = 3\)
- Total Cl⁻ ions per unit cell = \(1 + 3 = 4\).

4. **Position of Na⁺ Ions**:
- The Na⁺ ions occupy the octahedral voids in the FCC lattice. In the NaCl structure, these octahedral voids are located at:
- The body center of the cube.
- The edge centers of the cube.

5. **Conclusion**:
- Since the Cl⁻ ions occupy the FCC arrangement, we conclude that in the crystal structure of sodium chloride, the arrangement of Cl⁻ ions is indeed face-centered cubic (FCC).

### Final Answer:
The arrangement of Cl⁻ ions in the crystal structure of sodium chloride (NaCl) is **FCC** (Face-Centered Cubic).

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