The fact that is/are true about NaCl crystal's unit cell

Options

A. all `Na^(+)` ions are FCC packed in a typical unit cell
B. the co-ordination number of `Na^(+)` and `Cl^(-)` are 6.6 respectively
C. all `Cl^(-)` ions are FCC packed in a typical unit cell
D. the unit cell formula is `Na_(4)Cl_(4)`

Answer

To answer the question regarding the facts that are true about the NaCl crystal's unit cell, we will analyze the structure and properties of the NaCl crystal step by step.

### 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, chloride ions (Cl-) are arranged in an FCC packing.

**Hint:** Remember that NaCl has a cubic structure, and the arrangement of ions is crucial for understanding its properties.

2. **Identifying the Positions of Ions:**
- In the FCC lattice of NaCl, the Cl- ions occupy the lattice points, while the Na+ ions occupy the octahedral voids created by the Cl- ions.

**Hint:** Visualize the FCC structure to see how the octahedral voids are formed between the Cl- ions.

3. **Calculating the Number of Ions in the Unit Cell:**
- In an FCC unit cell, there are 4 Cl- ions per unit cell (since each corner contributes 1/8 of an ion and each face center contributes 1/2 of an ion).
- Since there are 4 octahedral voids in the FCC structure, there will also be 4 Na+ ions in the unit cell.

**Hint:** Use the formula for the number of ions in an FCC unit cell to confirm the counts.

4. **Determining the Coordination Number:**
- The coordination number (CN) for both Na+ and Cl- in NaCl is 6. This means each Na+ ion is surrounded by 6 Cl- ions and vice versa.

**Hint:** The coordination number can be determined by counting the number of nearest neighbors surrounding an ion.

5. **Verifying the Packing:**
- The Cl- ions are packed in an FCC arrangement, while the Na+ ions occupy the octahedral voids. This confirms that all Cl- ions are indeed FCC packed.

**Hint:** Check the definition of FCC packing to ensure you understand how the ions are arranged.

6. **Conclusion:**
- Based on the analysis, we can conclude the following facts about the NaCl crystal's unit cell:
- The coordination number of Na+ and Cl- ions is 6.
- All Cl- ions are packed in an FCC arrangement.
- Na+ ions are not packed in a typical unit cell but are located in the octahedral voids.

### Summary of True Facts:
- The coordination number of Na+ and Cl- is 6.
- All Cl- ions are FCC packed.
- Na+ ions are present in octahedral voids, not in typical packing.