If the radii of `A^+ and B^-` in the crystalline solid AB are 96 pm and 200 respectively. Then expected structure of AB will be

Options

A. trigonal
B. octahedral
C. hexagonal
D. cubic

Answer

To determine the expected structure of the crystalline solid AB based on the radii of the cation \( A^+ \) and the anion \( B^- \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given radii**:
- The radius of the cation \( A^+ \) is \( r_A^+ = 96 \) pm.
- The radius of the anion \( B^- \) is \( r_B^- = 200 \) pm.

2. **Calculate the ratio of the radii**:
- The ratio of the cation radius to the anion radius is given by:
\[ \text{Ratio} = \frac{r_A^+}{r_B^-} = \frac{96 \text{ pm}}{200 \text{ pm}} = 0.48 \]

3. **Determine the structure based on the ratio**:
- We need to compare the calculated ratio \( 0.48 \) with known ranges to determine the expected structure:
- \( 0.154 < \text{Ratio} < 0.225 \) → Triangular structure
- \( 0.225 < \text{Ratio} < 0.414 \) → Tetragonal structure
- \( 0.414 < \text{Ratio} < 0.732 \) → Octahedral structure
- \( 0.732 < \text{Ratio} < 1 \) → Cubic structure

4. **Identify the expected structure**:
- Since \( 0.48 \) falls within the range \( 0.414 < 0.48 < 0.732 \), the expected structure of the crystalline solid AB is **octahedral**.

5. **Determine the coordination number**:
- For an octahedral structure, the coordination number is typically \( 6 \).

### Final Answer:
The expected structure of the crystalline solid AB is **octahedral** with a coordination number of **6**.

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