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 1: Understand the Rock Salt Structure
In a rock salt structure (like NaCl), the cations and anions are arranged in a face-centered cubic lattice. The distance between the cation and anion is equal to half the edge length of the unit cell.

### Step 2: Given Data
- Edge length (A) = 500 pm
- Radius of cation (r+) = 80 pm

### Step 3: Calculate the Distance Between Cation and Anion
The distance between the cation and anion in the rock salt structure can be expressed as:
\[ r+ + r- = \frac{A}{2} \]
Where:
- \( r+ \) is the radius of the cation.
- \( r- \) is the radius of the anion.
- \( A \) is the edge length.

Substituting the known values:
\[ r+ + r- = \frac{500 \, \text{pm}}{2} = 250 \, \text{pm} \]

### Step 4: Substitute the Known Radius of Cation
Now, substitute the radius of the cation into the equation:
\[ 80 \, \text{pm} + r- = 250 \, \text{pm} \]

### Step 5: Solve for the Radius of Anion
Rearranging the equation to find \( r- \):
\[ r- = 250 \, \text{pm} - 80 \, \text{pm} \]
\[ r- = 170 \, \text{pm} \]

### Conclusion
The radius of the anion (r-) is **170 pm**.

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