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 given ionic radii of A^+ and B^-, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ionic Radii**:
- The radius of A^+ (cation) = 96 pm
- The radius of B^- (anion) = 200 pm

2. **Calculate the Radius Ratio**:
- The radius ratio (r+) is calculated using the formula:
\[ \text{Radius Ratio} = \frac{\text{Radius of Cation}}{\text{Radius of Anion}} = \frac{96 \, \text{pm}}{200 \, \text{pm}} \]
- Performing the calculation:
\[ \text{Radius Ratio} = \frac{96}{200} = 0.48 \]

3. **Determine the Structure Using Radius Ratio**:
- We will refer to a table that correlates the radius ratio with the geometry and coordination number of the crystalline structure.
- The ranges for the radius ratio and their corresponding geometries are as follows:
- 0.155 to 0.225: Triangular geometry (Coordination number = 3)
- 0.225 to 0.414: Tetrahedral geometry (Coordination number = 4)
- 0.414 to 0.732: Octahedral geometry (Coordination number = 6)
- 0.732 and above: Cubic geometry (Coordination number = 8)

4. **Locate the Radius Ratio in the Table**:
- The calculated radius ratio of 0.48 falls within the range of 0.414 to 0.732.

5. **Conclude the Structure**:
- Since the radius ratio of 0.48 corresponds to the octahedral geometry, we conclude that the expected structure of the crystalline solid AB is octahedral with a coordination number of 6.

### Final Answer:
The expected structure of the crystalline solid AB will be octahedral.

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