If the distance between `Na^+` and `Cl^(-)` ions in NaCl crystal is 'a' pm, the edge length of the unit cell is

Options

A. `4 a p m`
B. `a/4 p m`
C. `a/2 p m`
D. `2a p m`

Answer

To find the edge length of the unit cell of NaCl given the distance between the Na⁺ and Cl⁻ ions is 'a' pm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of NaCl**:
- NaCl crystallizes in a face-centered cubic (FCC) structure. In this structure, Na⁺ and Cl⁻ ions alternate in a 3D lattice.

2. **Identify the Position of Ions**:
- In the FCC unit cell of NaCl, Na⁺ ions are located at the corners and the face centers of the cube, while Cl⁻ ions are located at the octahedral sites (the center of the cube and at the edges).

3. **Distance Between Ions**:
- The distance between the Na⁺ and Cl⁻ ions is given as 'a' pm. This distance represents the distance from the center of the Na⁺ ion to the center of the Cl⁻ ion.

4. **Relate Edge Length to Ion Distance**:
- In the FCC structure, the edge length (let's denote it as 'x') is related to the distance between the Na⁺ and Cl⁻ ions.
- The distance between the Na⁺ and Cl⁻ ions can be visualized as spanning from one corner of the cube (Na⁺) to the center of the cube (Cl⁻).

5. **Calculate the Edge Length**:
- The edge length 'x' of the unit cell can be expressed in terms of the distance 'a' as follows:
- The distance from the Na⁺ ion at the corner to the Cl⁻ ion at the center of the cube is equal to the edge length 'x' divided by 2 (since the center of the cube is halfway along the edge).
- Therefore, we have:
\[ x = 2a \]

6. **Final Expression**:
- Thus, the edge length of the unit cell of NaCl is:
\[ x = 2a \text{ pm} \]

### Conclusion:
The edge length of the unit cell of NaCl is \(2a\) pm.