The ionic radii of `A^+` and `B^-` ions are `0.92xx10^(-10)` m and `1.81xx10^(-10)` m . The coordination number of each ion in AB is

Options

A. 2
B. 6
C. 4
D. 8

Explanation

To determine the coordination number of the ions \( A^+ \) and \( B^- \) in the ionic compound \( AB \), we will follow these steps:

### Step 1: Identify the ionic radii
The ionic radii are given as:
- Radius of \( A^+ \) = \( 0.92 \times 10^{-10} \) m
- Radius of \( B^- \) = \( 1.81 \times 10^{-10} \) m

### Step 2: Calculate the radius ratio
The radius ratio is calculated using the formula:
\[ \text{Radius Ratio} = \frac{\text{Radius of cation}}{\text{Radius of anion}} = \frac{r_{A^+}}{r_{B^-}} \]
Substituting the values:
\[ \text{Radius Ratio} = \frac{0.92 \times 10^{-10}}{1.81 \times 10^{-10}} \]

### Step 3: Perform the division
Calculating the radius ratio:
\[ \text{Radius Ratio} = \frac{0.92}{1.81} \approx 0.508 \]

### Step 4: Determine the coordination number
Using the radius ratio to find the coordination number:
- A radius ratio of approximately \( 0.508 \) falls within the range of \( 0.4 \) to \( 0.732 \).
- According to the radius ratio rules, this range corresponds to an octahedral coordination.

### Conclusion
Thus, the coordination number for both \( A^+ \) and \( B^- \) ions in the compound \( AB \) is **6**.

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