The two ions `A^+' and 'B^-` have radii 85 and 200 pm respectively. In the closed packed crystal of compound AB, the coordination number of `A^+` ion is

Options

A. 3
B. 4
C. 6
D. 8

Answer

To solve the problem, we need to determine the coordination number of the cation \( A^+ \) in the closed-packed crystal structure of the compound \( AB \) based on the given ionic radii.

### Step-by-Step Solution:

1. **Identify the Ionic Radii**:
- The radius of the cation \( A^+ \) is given as \( R^+ = 85 \) pm.
- The radius of the anion \( B^- \) is given as \( R^- = 200 \) pm.

2. **Calculate the Radius Ratio**:
- The radius ratio \( \frac{R^+}{R^-} \) can be calculated as follows:
\[ \frac{R^+}{R^-} = \frac{85 \text{ pm}}{200 \text{ pm}} = 0.425 \]

3. **Determine the Coordination Number**:
- The radius ratio \( 0.425 \) falls within the range of \( 0.414 \) to \( 0.732 \).
- According to the radius ratio rules for ionic compounds:
- If \( 0.414 < \frac{R^+}{R^-} < 0.732 \), the coordination geometry is octahedral.
- In an octahedral geometry, the coordination number is \( 6 \).

4. **Conclusion**:
- Therefore, the coordination number of the cation \( A^+ \) in the closed-packed crystal of compound \( AB \) is \( 6 \).

### Final Answer:
The coordination number of \( A^+ \) ion is \( 6 \).

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