The radii of `Na^(+) and Cl^(-)` ions are 95 pm and 181 pm respectively. The edge length of NaCl unit cell is

Options

A. 276 pm
B. 138 pm
C. 552 pm
D. 45 pm

Explanation

To find the edge length of the NaCl unit cell using the given ionic radii, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the ionic radii**:
- The radius of the Na⁺ ion (cation) is given as 95 pm.
- The radius of the Cl⁻ ion (anion) is given as 181 pm.

2. **Understand the relationship between edge length and ionic radii**:
- For NaCl, which forms a face-centered cubic (FCC) structure, the edge length (a) can be calculated using the formula:
\[ a = 2 \times r_{cation} + r_{anion} \]
- Here, \( r_{cation} \) is the radius of the Na⁺ ion and \( r_{anion} \) is the radius of the Cl⁻ ion.

3. **Substitute the values into the formula**:
- Plugging in the values:
\[ a = 2 \times (95 \, \text{pm}) + (181 \, \text{pm}) \]

4. **Calculate the edge length**:
- First, calculate \( 2 \times 95 \):
\[ 2 \times 95 = 190 \, \text{pm} \]
- Now add the radius of the Cl⁻ ion:
\[ a = 190 \, \text{pm} + 181 \, \text{pm} = 371 \, \text{pm} \]

5. **Final answer**:
- The edge length of the NaCl unit cell is \( 371 \, \text{pm} \).

### Summary of the Solution:
The edge length of the NaCl unit cell is calculated to be **371 pm**.