The radii of Na+ and `Cl^(-)` ions are 100 pm and 200 pm respectively. Calculate the edge length of NaCl unit cell.

Explanation

To calculate the edge length of the NaCl unit cell, we will follow these steps:

1. **Identify the radii of the ions**:
- The radius of Na⁺ (sodium ion) is given as 100 pm (picometers).
- The radius of Cl⁻ (chloride ion) is given as 200 pm.

2. **Understand the structure of NaCl**:
- NaCl crystallizes in a face-centered cubic (FCC) structure.
- In this structure, Na⁺ ions occupy the octahedral voids, while Cl⁻ ions are located at the corners and face centers of the cube.

3. **Determine the relationship between edge length and ionic radii**:
- In the FCC structure, the edge length (denoted as 'a') can be calculated using the formula:
\[ a = 2(r_{Na^+} + r_{Cl^-}) \]
- This formula arises because the edge length of the cube is equal to the sum of the radii of the cation and anion along the edge of the cube.

4. **Substitute the values of the ionic radii into the formula**:
- Substitute \( r_{Na^+} = 100 \, \text{pm} \) and \( r_{Cl^-} = 200 \, \text{pm} \):
\[ a = 2(100 \, \text{pm} + 200 \, \text{pm}) \]

5. **Calculate the edge length**:
- First, calculate the sum of the radii:
\[ 100 \, \text{pm} + 200 \, \text{pm} = 300 \, \text{pm} \]
- Now, multiply by 2:
\[ a = 2 \times 300 \, \text{pm} = 600 \, \text{pm} \]

6. **Final result**:
- The edge length of the NaCl unit cell is **600 pm**.