If x = radius of `Na^(+) " & " y =` radius of `Cl^(-)` & a is the unit cell edge length for NaCl crystal, then which of the given relation is correct ?

Options

A. `x + y = a`
B. `2x + 2y = a`
C. `x + y = 2a`
D. `x + y = sqrt2a`

Explanation

To solve the problem, we need to understand the relationship between the radii of the ions and the edge length of the NaCl crystal structure.

### Step-by-Step Solution:

1. **Understanding the Crystal Structure**:
- In the NaCl crystal structure, each Na⁺ ion is surrounded by Cl⁻ ions and vice versa. The arrangement is such that the Na⁺ ions and Cl⁻ ions alternate in the lattice.

2. **Identifying the Radii**:
- Let \( x \) be the radius of the Na⁺ ion (cation).
- Let \( y \) be the radius of the Cl⁻ ion (anion).

3. **Determining the Edge Length**:
- The edge length \( a \) of the unit cell in a NaCl crystal can be visualized as the distance between the centers of two adjacent Na⁺ and Cl⁻ ions.
- Since the Na⁺ ion is surrounded by Cl⁻ ions, the edge length can be expressed in terms of the radii of the ions.

4. **Setting Up the Equation**:
- The distance from the center of the Na⁺ ion to the center of the Cl⁻ ion includes the radius of the Na⁺ ion and the radius of the Cl⁻ ion.
- Therefore, the total distance (which is the edge length \( a \)) can be expressed as:
\[ a = 2x + 2y \]
- This equation accounts for the radius of the Na⁺ ion (2x) and the radius of the Cl⁻ ion (2y).

5. **Simplifying the Equation**:
- We can simplify the equation to:
\[ a = 2(x + y) \]

6. **Conclusion**:
- The correct relation that describes the relationship between the radius of Na⁺, the radius of Cl⁻, and the edge length \( a \) of the NaCl crystal is:
\[ a = 2(x + y) \]

### Final Answer:
The correct relation is \( a = 2(x + y) \).