If the distance between Na+ and Clions in NaCl crystal is 'a'pm, what is the length of the cell edge ?

Options

A. 2a pm
B. 9/2 pm
C. 4a pm
D. a/4 pm

Answer

To solve the problem, we need to determine the length of the cell edge of the NaCl crystal given the distance between Na⁺ and Cl⁻ ions.

### Step-by-Step Solution:

1. **Understand the Structure of NaCl**:
- NaCl forms a face-centered cubic (FCC) lattice structure.
- In this structure, Na⁺ ions occupy the edge centers and the body center, while Cl⁻ ions occupy the corners and face centers of the unit cell.

2. **Identify the Positions of Ions**:
- In the FCC unit cell, the Na⁺ ions are located at the edge centers and the Cl⁻ ions are located at the corners and face centers.
- The distance between the Na⁺ and Cl⁻ ions is given as 'a' picometers.

3. **Visualize the Unit Cell**:
- The distance between a Na⁺ ion (located at the edge center) and a Cl⁻ ion (located at the corner) can be visualized as the diagonal of a face of the unit cell.

4. **Relate the Distance to the Edge Length**:
- The edge length of the unit cell is denoted as 'x'.
- The relationship between the edge length and the distance between the ions can be established. Since the distance between Na⁺ and Cl⁻ ions is 'a' pm, and this distance spans from the edge center to the corner, the edge length 'x' can be expressed as:
\[ x = 2a \text{ pm} \]
- This is because the distance from the edge center to the corner is half the diagonal of the face, which is equal to 'a' pm.

5. **Conclusion**:
- Therefore, the length of the cell edge (x) is:
\[ x = 2a \text{ pm} \]

### Final Answer:
The length of the cell edge is \( 2a \) pm.

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