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 determine the coordination number of the `A^+` ion in the closed packed crystal of compound `AB`, we can follow these steps:

### Step 1: Identify the radii of the ions.
- The radius of the cation `A^+` is given as 85 pm.
- The radius of the anion `B^-` is given as 200 pm.

### Step 2: Calculate the radius ratio.
- The radius ratio (r) is calculated using the formula:
\[ r = \frac{\text{Radius of cation}}{\text{Radius of anion}} = \frac{85 \text{ pm}}{200 \text{ pm}} \]
- Performing the calculation:
\[ r = \frac{85}{200} = 0.425 \]

### Step 3: Determine the coordination number based on the radius ratio.
- The radius ratio of 0.425 falls within the range of 0.414 to 0.732.
- According to the radius ratio rules for coordination numbers:
- A radius ratio between 0.414 and 0.732 typically corresponds to a coordination number of 6.

### Step 4: Conclusion.
- Therefore, the coordination number of the `A^+` ion in the closed packed crystal of compound `AB` is 6.

### Final Answer:
The coordination number of `A^+` ion is **6**.

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