Two ions `A^(o+)` and `B^(Θ)` have radii `88` and `200` pm, respectively. In the close-packed crystal of compound `AB`, predict coodination number of `A^(o+)`.

Explanation

To determine the coordination number of the ion \( A^{o+} \) in the close-packed crystal of compound \( AB \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Radii of the Ions**:
- The radius of ion \( A^{o+} \) is given as \( 88 \) pm.
- The radius of ion \( B^{Θ} \) is given as \( 200 \) pm.

2. **Calculate the Radius Ratio**:
- The radius ratio \( \frac{r_{A^{o+}}}{r_{B^{Θ}}} \) can be calculated using the formula:
\[ \text{Radius Ratio} = \frac{r_{A^{o+}}}{r_{B^{Θ}}} = \frac{88 \text{ pm}}{200 \text{ pm}} \]
- Performing the calculation:
\[ \text{Radius Ratio} = \frac{88}{200} = 0.44 \]

3. **Determine the Coordination Number**:
- According to the radius ratio rule:
- If \( 0.225 < \text{Radius Ratio} < 0.414 \), the coordination number is \( 4 \).
- If \( 0.414 < \text{Radius Ratio} < 0.732 \), the coordination number is \( 6 \).
- Since \( 0.44 \) falls within the range \( 0.414 < 0.44 < 0.732 \), the coordination number of \( A^{o+} \) is \( 6 \).

4. **Final Answer**:
- Therefore, the coordination number of \( A^{o+} \) in the close-packed crystal of compound \( AB \) is \( 6 \).