Each unit cell of NaCl if made using spherical atoms consists of 14 chlorine atoms and:

Options

A. 13 Na atoms
B. 14 Na atoms
C. 6 Na atoms
D. 8 Na atoms

Answer

To solve the question regarding the composition of each unit cell of NaCl, we need to analyze the arrangement of sodium (Na) and chloride (Cl) ions in the crystal structure of NaCl.

### Step-by-Step Solution:

1. **Understanding the NaCl Structure**:
- NaCl crystallizes in a face-centered cubic (FCC) lattice structure.
- In this structure, each unit cell contains both Na+ and Cl- ions.

2. **Counting Chlorine Atoms**:
- According to the question, each unit cell consists of 14 chlorine atoms (Cl-).
- In a face-centered cubic unit cell, the contribution of Cl- ions can be calculated as follows:
- There are 8 corners in the cube, and each corner contributes 1/8 of a Cl- ion.
- There are 6 face centers, and each face center contributes 1/2 of a Cl- ion.
- Therefore, the total contribution of Cl- ions is:
\[ \text{Total Cl-} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \text{ Cl- ions} \]
- However, the question states that there are 14 Cl- ions, which suggests that we need to consider the effective number of Cl- ions in the unit cell.

3. **Counting Sodium Atoms**:
- In NaCl, the Na+ ions occupy the octahedral voids.
- Each unit cell of NaCl contains 13 octahedral voids:
- 12 octahedral voids are located at the edge centers (1/4 contribution from each edge) and 1 at the body center (1 contribution).
- Therefore, the total contribution of Na+ ions is:
\[ \text{Total Na+} = 12 \times \frac{1}{4} + 1 = 3 + 1 = 4 \text{ Na+ ions} \]
- However, since the question states that there are 13 Na atoms, we must consider that the octahedral voids are fully occupied by Na+ ions.

4. **Final Composition**:
- From the analysis, we conclude that:
- Each unit cell of NaCl consists of 14 Cl- ions and 13 Na+ ions.
- Therefore, the answer to the question is that each unit cell of NaCl is made using 14 chlorine atoms and 13 sodium atoms.

### Conclusion:
Each unit cell of NaCl consists of 14 chlorine atoms and 13 sodium atoms.