In crystal structure of NaCl, total number of `Cl^-` ions in a unit cell is

Options

A. 6
B. 4
C. 8
D. 2

Answer

To determine the total number of Cl⁻ ions in a unit cell of NaCl, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Structure**: NaCl crystallizes in a face-centered cubic (FCC) structure, which is also known as cubic close packing (CCP). In this arrangement, the chloride ions (Cl⁻) occupy the lattice points.

2. **Counting the Corner Ions**: In a unit cell of NaCl, there are 8 corners. Each corner of the cube has one Cl⁻ ion, but since each corner ion is shared among 8 adjacent unit cells, the contribution of the corner ions to the unit cell is:
\[ \text{Contribution from corners} = 8 \text{ corners} \times \frac{1}{8} = 1 \text{ Cl}^- \]

3. **Counting the Face-Centered Ions**: In addition to the corner ions, there are 6 face centers in the unit cell. Each face-centered ion is shared between 2 unit cells, so the contribution from the face-centered ions is:
\[ \text{Contribution from face centers} = 6 \text{ faces} \times \frac{1}{2} = 3 \text{ Cl}^- \]

4. **Total Number of Cl⁻ Ions**: Now, we can add the contributions from the corner and face-centered ions to find the total number of Cl⁻ ions in the unit cell:
\[ \text{Total Cl}^- = \text{Contribution from corners} + \text{Contribution from face centers} = 1 + 3 = 4 \]

5. **Conclusion**: Therefore, the total number of Cl⁻ ions in a unit cell of NaCl is 4.

### Final Answer:
The total number of Cl⁻ ions in a unit cell of NaCl is **4**.

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