The ionic radii of `A^(+)` and `B^(-)` are `1.7 Å` and `1.8 Å` respectively . Find the co-ordination number of `A^(+)`

Answer

To find the coordination number of the cation \( A^{+} \) given the ionic radii of \( A^{+} \) and \( B^{-} \), we can follow these steps:

### Step 1: Identify the ionic radii
We are given:
- Ionic radius of \( A^{+} = 1.7 \, \text{Å} \)
- Ionic radius of \( B^{-} = 1.8 \, \text{Å} \)

### Step 2: Calculate the radius ratio
The radius ratio \( \frac{r_{A^{+}}}{r_{B^{-}}} \) can be calculated as follows:
\[ \text{Radius Ratio} = \frac{r_{A^{+}}}{r_{B^{-}}} = \frac{1.7 \, \text{Å}}{1.8 \, \text{Å}} \approx 0.944 \]

### Step 3: Determine the coordination number based on the radius ratio
We can use the radius ratio to determine the coordination number. The general guidelines for coordination numbers based on radius ratios are:
- \( 0.225 \) to \( 0.414 \) → Coordination number = 4
- \( 0.414 \) to \( 0.732 \) → Coordination number = 6
- \( 0.732 \) to \( 0.999 \) → Coordination number = 8
- \( 0.999 \) and above → Coordination number = 12

Since our calculated radius ratio \( 0.944 \) falls between \( 0.732 \) and \( 0.999 \), we can conclude that the coordination number of \( A^{+} \) is 8.

### Final Answer
The coordination number of \( A^{+} \) is **8**.

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