The two ions `A^+` and `B^-` have radii 40 pm and 120 pm respectively. In the closed packed crystal of compound AB, the coordination number of `A^+` would be

Options

A. 6
B. 8
C. 4
D. 12

Answer

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

### Step 1: Identify the radii of the ions
The radius of ion \( A^+ \) is given as \( 40 \, \text{pm} \) and the radius of ion \( B^- \) is \( 120 \, \text{pm} \).

### Step 2: Calculate the radius ratio
The radius ratio \( \frac{R^+}{R^-} \) can be calculated as follows:
\[ \text{Radius Ratio} = \frac{R^+}{R^-} = \frac{40 \, \text{pm}}{120 \, \text{pm}} = \frac{1}{3} \approx 0.333 \]

### Step 3: Analyze the radius ratio
We need to compare the calculated radius ratio with the standard intervals for coordination numbers:
- \( 0.125 < \frac{R^+}{R^-} < 0.225 \) → Coordination number = 3
- \( 0.225 < \frac{R^+}{R^-} < 0.414 \) → Coordination number = 4
- \( 0.414 < \frac{R^+}{R^-} < 0.732 \) → Coordination number = 6
- \( 0.732 < \frac{R^+}{R^-} < 1 \) → Coordination number = 8

### Step 4: Determine the coordination number
Since our calculated radius ratio \( 0.333 \) falls within the interval \( 0.225 < 0.333 < 0.414 \), the coordination number of \( A^+ \) is 4.

### Final Answer
The coordination number of \( A^+ \) in the closed packed crystal of compound \( AB \) is **4**.

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