The radius of a divaent cation `A^(2+)` is 94pm and of divalent anion `B^(2-)` is 146pm. The compound AB has:

Options

A. Rock salt structure
B. Zinc blende structure
C. Antifluorite structure
D. CsCl type structure

Answer

To determine the structure of the compound AB formed by the divalent cation \( A^{2+} \) and the divalent anion \( B^{2-} \), we will use the radius ratio rule. Here are the steps to solve the problem:

### Step 1: Identify the given data
- Radius of cation \( A^{2+} \) = 94 pm
- Radius of anion \( B^{2-} \) = 146 pm

### Step 2: Calculate the radius ratio
The radius ratio \( r \) is calculated using the formula:
\[ r = \frac{r_{cation}}{r_{anion}} \]
Substituting the values:
\[ r = \frac{94 \, \text{pm}}{146 \, \text{pm}} \approx 0.644 \]

### Step 3: Determine the type of structure based on the radius ratio
According to the radius ratio rule:
- If \( 0.225 < r < 0.414 \): Tetrahedral structure
- If \( 0.414 < r < 0.732 \): Octahedral structure
- If \( 0.732 < r < 1 \): Cubic structure

Since \( r \approx 0.644 \) lies between 0.414 and 0.732, the structure of the compound AB is octahedral.

### Step 4: Compare with known structures
The octahedral structure is characteristic of several types of compounds. In this case, we can compare it with the known structures:
- Rock salt structure (like NaCl) has an octahedral arrangement.
- Zinc blend and anti-fluoride structures have tetrahedral arrangements.
- Calcium chloride (CaCl₂) has a cubic structure.

Since the radius ratio indicates an octahedral structure, we can conclude that the compound AB has a rock salt type structure.

### Final Conclusion
The compound AB has a rock salt type structure.

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