In `Na_2`O, having antifluorite structure

Options

A. oxide ions have a cubic close packed arrangement and `Na^+` occupy all the eight tetrahedral voids
B. oxide ions have a cubic close packed arrangement and `Na^+` occupy all the octahedral voids
C. `Na^+` ions have a cubic close packed arrangement and `O^(2-)` occupy all the octahedral voids
D. `Na^+` ions have a cubic close arrangement and `O^(2-)` occupy all the tetrahedral voids

Answer

To solve the question regarding the antifluorite structure of Na₂O, we will analyze the arrangement of ions in the crystal lattice and determine the correct statements about the structure.

### Step-by-Step Solution:

1. **Identify the Structure**:
Na₂O has an antifluorite structure. In this structure, the oxide ions (O²⁻) form a cubic close-packed (CCP) arrangement.

**Hint**: Recall that the antifluorite structure is characterized by the arrangement of anions and cations in a specific pattern.

2. **Determine the Arrangement of Ions**:
In the antifluorite structure, the oxide ions (O²⁻) occupy the face-centered cubic (FCC) lattice points. In an FCC unit cell, there are 4 oxide ions per unit cell.

**Hint**: Remember that in a face-centered cubic lattice, the number of atoms (or ions) per unit cell is given by Z = 4.

3. **Calculate the Number of Tetrahedral and Octahedral Voids**:
In an FCC structure, there are:
- 8 tetrahedral voids
- 4 octahedral voids

**Hint**: Use the relationship between the number of atoms in the FCC structure to find the number of voids.

4. **Position of Sodium Ions (Na⁺)**:
The sodium ions (Na⁺) occupy the octahedral voids in the antifluorite structure. Since there are 4 octahedral voids in the unit cell, and each Na₂O unit cell contains 4 oxide ions, there will be 8 sodium ions (Na⁺) in total.

**Hint**: Note how the cations (Na⁺) are positioned in relation to the anions (O²⁻) in the crystal lattice.

5. **Final Composition**:
The overall composition of Na₂O can be summarized as:
- 4 O²⁻ ions from the FCC arrangement
- 8 Na⁺ ions occupying the octahedral voids

**Hint**: Confirm that the ratio of sodium to oxide ions aligns with the chemical formula Na₂O.

6. **Conclusion**:
Based on the above analysis, we can conclude that:
- The oxide ions form a cubic close-packed arrangement.
- Sodium ions occupy all the octahedral voids.

Therefore, the correct option regarding the antifluorite structure of Na₂O is option A.

### Summary of Steps:
1. Identify the antifluorite structure.
2. Determine the arrangement of oxide ions in CCP.
3. Calculate the number of tetrahedral and octahedral voids.
4. Identify the position of sodium ions in the structure.
5. Confirm the overall composition of the compound.
6. Conclude with the correct option.