A binary solid `(A^(+)B^(+))` has a rock sell structure .If the edge length is `400 pm` and radius of cation is 75 pm the radius of amion attion is

Options

A. 100 pm
B. 125 pm
C. 250 pm
D. 325 pm

Answer

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

### Step-by-Step Solution:

1. **Understand the Structure**:
- The rock salt structure (like NaCl) consists of cations (A^+) and anions (B^-). In this case, A^+ corresponds to the cation and B^- corresponds to the anion.

2. **Identify Given Values**:
- Edge length (a) = 400 pm
- Radius of cation (R^+) = 75 pm

3. **Use the Relationship in Rock Salt Structure**:
- In a rock salt structure, the relationship between the edge length (a), the radius of the cation (R^+), and the radius of the anion (R^-) is given by:
\[ a = 2R^+ + R^- \]

4. **Substitute the Known Values**:
- Substitute the known values into the equation:
\[ 400 = 2(75) + R^- \]

5. **Simplify the Equation**:
- Calculate \(2(75)\):
\[ 2(75) = 150 \]
- Now substitute this back into the equation:
\[ 400 = 150 + R^- \]

6. **Solve for R^-**:
- Rearranging the equation to find R^-:
\[ R^- = 400 - 150 \]
- Calculate:
\[ R^- = 250 \text{ pm} \]

### Final Answer:
The radius of the anion (R^-) is **250 pm**.

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