A binary solid ( AB ) has a rock salt structure . If the edge length is 500 pm , and radius of cation is 80 pm , find the radius of anion

Options

A. 100 pm
B. 120 pm
C. 250 pm
D. 170 pm

Answer

To find the radius of the anion in a binary solid (AB) with a rock salt structure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure**: In a rock salt structure, cations (A) and anions (B) are arranged in a face-centered cubic lattice. Each edge of the cube is formed by the touching of the cations and anions.

2. **Identify Given Values**:
- Edge length of the cubic lattice (a) = 500 pm
- Radius of cation (r_A) = 80 pm

3. **Set Up the Relationship**: In a rock salt structure, the edge length (a) can be expressed in terms of the radii of the cation and anion. The relationship is:
\[ a = 2r_A + 2r_B \]
where \( r_B \) is the radius of the anion.

4. **Substitute Known Values**: Substitute the known values into the equation:
\[ 500 = 2(80) + 2r_B \]
Simplifying this gives:
\[ 500 = 160 + 2r_B \]

5. **Solve for the Radius of Anion**:
- Rearranging the equation to isolate \( 2r_B \):
\[ 2r_B = 500 - 160 \]
\[ 2r_B = 340 \]
- Now, divide by 2 to find \( r_B \):
\[ r_B = \frac{340}{2} = 170 \text{ pm} \]

6. **Conclusion**: The radius of the anion (B) is 170 pm.

### Final Answer:
The radius of the anion is 170 pm.

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