Select the correct statement (s) for the rock -salt structure (NaCl) :

Options

A. (a) The tetrahedral voids are smaller than the octahedral sites
B. (b) The octahedral voids are occupied by cations and the tetrahedral sites are empty
C. (c) The radius ratio `(r_(c)//r_(a))` is 0.225
D. (d) The radius ratio `(r_(c)//r_(a))` is 0.732

Answer

To solve the question regarding the rock-salt structure of NaCl, we will analyze the statements provided and determine their correctness based on the properties of the NaCl crystal structure.

### Step-by-Step Solution

1. **Understanding the Rock-Salt Structure**:
- NaCl crystallizes in a rock-salt structure, which is a type of face-centered cubic (FCC) lattice.
- In this structure, the chloride ions (Cl⁻) occupy the cubic close-packed (CCP) positions, while the sodium ions (Na⁺) occupy the octahedral voids.

2. **Determining the Number of Atoms per Unit Cell (Z)**:
- In a CCP structure, there are 4 formula units of NaCl per unit cell.
- Therefore, the number of Na⁺ ions is 4, and the number of Cl⁻ ions is also 4, leading to Z = 4.

3. **Analyzing the Void Types**:
- In a crystal lattice, there are two types of voids: octahedral and tetrahedral.
- The radius ratio (r_cation/r_anion) for octahedral voids is between 0.414 and 0.732.
- The radius ratio for tetrahedral voids is between 0.225 and 0.414.

4. **Evaluating Each Statement**:
- **Statement 1**: "The tetrahedral voids are smaller than that of octahedral sites."
- This statement is **incorrect**. Octahedral voids are indeed larger than tetrahedral voids.

- **Statement 2**: "The octahedral voids are occupied by cations and tetrahedral sites are empty."
- This statement is **correct**. Na⁺ occupies the octahedral voids, while the tetrahedral voids remain unoccupied in NaCl.

- **Statement 3**: "The radius ratio that is the ratio of cation to that of anion is 0.225."
- This statement is **incorrect**. The radius ratio for octahedral voids must be between 0.414 and 0.732, and 0.225 does not fall within this range.

- **Statement 4**: "The radius ratio of the ratio of cation and ratio of anion is 0.732."
- This statement is also **incorrect**. The radius ratio for NaCl is less than 0.732.

5. **Conclusion**:
- The only correct statement regarding the rock-salt structure of NaCl is **Statement 2**.

### Final Answer:
The correct statement for the rock-salt structure of NaCl is:
- **Statement 2**: The octahedral voids are occupied by cations and tetrahedral sites are empty.