If the distance between `Na^+` and `Cl^-` ions of sodium chloride crystal is 'x' pm, then length of the edge of the unit cell is

Options

A. 2x pm
B. 4x pm
C. x/2 pm
D. x/4 pm

Answer

To solve the problem of finding the length of the edge of the unit cell of sodium chloride (NaCl) given the distance between Na⁺ and Cl⁻ ions is 'x' picometers, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Structure of NaCl**:
- Sodium chloride crystallizes in a face-centered cubic (FCC) lattice structure. In this arrangement, the Cl⁻ ions are located at the corners and the centers of the faces of the cube, while the Na⁺ ions occupy the octahedral voids.

2. **Identifying the Position of Ions**:
- In the NaCl unit cell, the Cl⁻ ions are positioned at the corners of the cube and at the center of each face. The Na⁺ ions are located at the center of the cube and at the center of each edge.

3. **Distance Between Ions**:
- The distance between a Na⁺ ion and a Cl⁻ ion is given as 'x' picometers. This distance represents the distance from the center of a Cl⁻ ion (located at the face center) to a Na⁺ ion (located at the edge center).

4. **Determining the Edge Length**:
- The edge length of the unit cell can be visualized as the distance that spans from one Cl⁻ ion at a face center to the corresponding Na⁺ ion at the edge center. Since the distance from the center of the Cl⁻ ion to the Na⁺ ion is 'x', and this distance spans half the edge length of the cube, we can conclude that the edge length (L) of the unit cell is twice this distance.
- Therefore, the edge length \( L = 2x \) picometers.

5. **Final Answer**:
- The length of the edge of the unit cell is \( 2x \) picometers.

### Summary:
The edge length of the unit cell of sodium chloride, given the distance between Na⁺ and Cl⁻ ions is 'x' pm, is \( 2x \) pm.