The distance between `Na^(+)` and`Cl^(-)` ion ion NaCI is 281 pm.
What is the edge length of the cube

Options

A. 1405 pm
B. 562 pm
C. 843 pm
D. 281 pm

Explanation

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

### Step-by-Step Solution:

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

2. **Identify the Relationship**: In an FCC lattice, the relationship between the edge length (A) and the distance between the ions can be expressed as:
\[ r_{Na^+} + r_{Cl^-} = \frac{A}{2} \]
where \( r_{Na^+} \) is the radius of the Na⁺ ion and \( r_{Cl^-} \) is the radius of the Cl⁻ ion.

3. **Given Distance**: The distance between Na⁺ and Cl⁻ ions is given as 281 pm. This distance corresponds to the sum of the radii of the ions:
\[ r_{Na^+} + r_{Cl^-} = 281 \text{ pm} \]

4. **Relate to Edge Length**: From the relationship established in step 2, we can substitute the known distance:
\[ 281 \text{ pm} = \frac{A}{2} \]

5. **Solve for Edge Length (A)**: To find the edge length A, we multiply both sides by 2:
\[ A = 281 \text{ pm} \times 2 = 562 \text{ pm} \]

6. **Final Answer**: The edge length of the cube is:
\[ A = 562 \text{ pm} \]