If the distance between `Na^(+)` and `Cl^(-)` ions in NaCl crystals is 265 pm, then edge length of the unit cell will be ?

Options

A. 265 pm
B. 795 pm
C. 132.5 pm
D. 530 pm

Explanation

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

### Step-by-Step Solution:

1. **Understand the Crystal Structure**: In NaCl, sodium ions (Na⁺) and chloride ions (Cl⁻) form a face-centered cubic (FCC) lattice. The Cl⁻ ions occupy the corners of the cube, while the Na⁺ ions occupy the octahedral voids.

2. **Identify the Distance Between Ions**: The problem states that the distance between the Na⁺ and Cl⁻ ions is 265 pm (picometers).

3. **Relate the Distance to the Edge Length**: In the NaCl crystal structure, the distance between the Na⁺ and Cl⁻ ions is equal to half the edge length of the unit cell (since one ion is at a corner and the other is at the center of the edge). Therefore, the edge length (a) can be calculated using the formula:
\[ a = 2 \times \text{distance between Na⁺ and Cl⁻} \]

4. **Substitute the Given Distance**: Plugging in the given distance:
\[ a = 2 \times 265 \text{ pm} \]

5. **Calculate the Edge Length**:
\[ a = 530 \text{ pm} \]

6. **Conclusion**: The edge length of the unit cell of NaCl is 530 pm.

### Final Answer:
The edge length of the unit cell of NaCl is **530 pm**.

---