Predict the close packed struture of an ionic compound ` A^(+) B^(-)` in which the radius of the cation = 148 pm and radius of anion = 195 pm. What is the corrdination number of the cation ?

Answer

To predict the close-packed structure of the ionic compound \( A^{+}B^{-} \) and determine the coordination number of the cation, we will follow these steps:

### Step 1: Calculate the Radius Ratio
First, we need to find the radius ratio of the cation to the anion. The radius of the cation \( A^{+} \) is given as 148 pm and the radius of the anion \( B^{-} \) is given as 195 pm.

\[ \text{Radius Ratio} = \frac{\text{Radius of cation}}{\text{Radius of anion}} = \frac{148 \, \text{pm}}{195 \, \text{pm}} \approx 0.76 \]

### Step 2: Determine the Close-Packed Structure
Based on the radius ratio, we can determine the type of close-packed structure. The radius ratio of \( 0.76 \) falls within the range typically associated with a face-centered cubic (FCC) structure or cubic close packing (CCP).

- For ionic compounds, a radius ratio between \( 0.414 \) and \( 0.732 \) suggests octahedral coordination (coordination number of 6).
- A radius ratio above \( 0.732 \) and up to \( 1.0 \) suggests cubic coordination (coordination number of 8).

Since our calculated radius ratio is approximately \( 0.76 \), we can conclude that the structure is likely to be cubic close packed (CCP).

### Step 3: Identify the Coordination Number of the Cation
In a cubic close-packed structure, each cation is surrounded by anions. The coordination number is defined as the number of nearest neighbor ions surrounding a given ion.

In a CCP structure:
- Each cation is surrounded by 8 anions.

Thus, the coordination number of the cation \( A^{+} \) in this structure is 8.

### Final Answer
The close-packed structure of the ionic compound \( A^{+}B^{-} \) is cubic close packed (CCP), and the coordination number of the cation \( A^{+} \) is 8.

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