How many formula units are there in the unit cell of sodium chloride ?

Options

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

Answer

To determine how many formula units are there in the unit cell of sodium chloride (NaCl), we need to analyze the arrangement of sodium (Na⁺) and chloride (Cl⁻) ions in the face-centered cubic (FCC) structure of NaCl.

### Step-by-Step Solution:

1. **Identify the Structure**:
Sodium chloride (NaCl) crystallizes in a face-centered cubic (FCC) lattice. In this structure, both Na⁺ and Cl⁻ ions are arranged in a specific manner.

**Hint**: Remember that NaCl adopts an FCC structure, which is crucial for calculating the number of ions in the unit cell.

2. **Count the Na⁺ Ions**:
- In the FCC structure, there are 8 corner atoms and 6 face-centered atoms.
- Each corner atom contributes \( \frac{1}{8} \) of an ion to the unit cell because it is shared among 8 unit cells.
- Each face-centered atom contributes \( \frac{1}{2} \) of an ion to the unit cell because it is shared between 2 unit cells.
- For Na⁺ ions:
- Contribution from corners: \( 8 \text{ corners} \times \frac{1}{8} = 1 \text{ Na⁺} \)
- Contribution from faces: \( 6 \text{ faces} \times \frac{1}{2} = 3 \text{ Na⁺} \)
- Total Na⁺ ions in the unit cell = \( 1 + 3 = 4 \text{ Na⁺} \)

**Hint**: Pay attention to how ions are shared at corners and faces when counting.

3. **Count the Cl⁻ Ions**:
- Similarly, for Cl⁻ ions:
- Contribution from corners: \( 8 \text{ corners} \times \frac{1}{8} = 1 \text{ Cl⁻} \)
- Contribution from faces: \( 6 \text{ faces} \times \frac{1}{2} = 3 \text{ Cl⁻} \)
- Total Cl⁻ ions in the unit cell = \( 1 + 3 = 4 \text{ Cl⁻} \)

**Hint**: Use the same method for counting Cl⁻ ions as you did for Na⁺ ions.

4. **Determine the Formula Units**:
- Since each formula unit of NaCl consists of one Na⁺ ion and one Cl⁻ ion, the total number of formula units in the unit cell can be calculated as follows:
- Total formula units = Minimum of (Number of Na⁺ ions, Number of Cl⁻ ions) = \( \min(4, 4) = 4 \)

**Hint**: The formula unit is defined by the ratio of the cation to anion in the compound.

### Final Answer:
There are **4 formula units** of sodium chloride (NaCl) in the unit cell.

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