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 problem, we need to analyze the structure of the NaCl unit cell and determine how many sodium (Na) atoms are present when there are 14 chlorine (Cl) atoms.

### Step-by-Step Solution:

1. **Understanding the NaCl Structure**:
- Sodium chloride (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. In the NaCl structure, the Cl⁻ ions occupy the lattice points.

3. **Lattice Points in NaCl**:
- In a face-centered cubic unit cell, there are:
- 8 corner atoms (each contributes 1/8 to the unit cell)
- 6 face-centered atoms (each contributes 1/2 to the unit cell)
- Total contribution from Cl⁻ ions in a unit cell:
\[ \text{Total Cl atoms} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \text{ Cl atoms} \]

4. **Relating Chlorine to Sodium**:
- Since the question states that there are 14 Cl atoms, we can set up a ratio. Each unit cell ideally contains 4 Cl atoms, so the number of unit cells needed to contain 14 Cl atoms is:
\[ \text{Number of unit cells} = \frac{14 \text{ Cl atoms}}{4 \text{ Cl atoms/unit cell}} = 3.5 \text{ unit cells} \]

5. **Calculating Sodium Atoms**:
- In each unit cell of NaCl, there is one Na⁺ ion for every Cl⁻ ion. Therefore, for 3.5 unit cells, the number of Na atoms will also be:
\[ \text{Number of Na atoms} = 3.5 \text{ Na atoms/unit cell} \times 1 \text{ Na atom/unit cell} = 3.5 \text{ Na atoms} \]

6. **Final Conclusion**:
- Since we cannot have a fraction of an atom in a physical sense, we can conclude that for every 14 Cl atoms, there would be approximately 13 Na atoms (considering rounding down to the nearest whole number).

### Final Answer:
Each unit cell of NaCl, if made using spherical atoms, consists of 14 chlorine atoms and approximately 13 sodium atoms.

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