In the radii of `A^(+)` and `B^(-)` are 95 pm and 181 pm respectively, then the coordination number of `A^(+)` will be:

Options

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

Explanation

To determine the coordination number of the cation \( A^+ \) given the radii of \( A^+ \) and \( B^- \), we can follow these steps:

### Step 1: Identify the given data
We have the following information:
- Radius of cation \( A^+ \) = 95 pm
- Radius of anion \( B^- \) = 181 pm

### Step 2: Calculate the ratio of the radii
To find the coordination number, we first need to calculate the ratio of the radius of the cation to the radius of the anion:
\[ \text{Ratio} = \frac{R_{A^+}}{R_{B^-}} = \frac{95 \, \text{pm}}{181 \, \text{pm}} \]

### Step 3: Perform the calculation
Calculating the ratio:
\[ \text{Ratio} = \frac{95}{181} \approx 0.524 \]

### Step 4: Analyze the ratio
Next, we need to analyze the value of the ratio \( 0.524 \):
- The coordination number can be determined based on the ratio of the radii.
- The ranges for coordination numbers based on the radius ratio are as follows:
- If \( 0.225 < \text{Ratio} < 0.414 \), coordination number = 4 (tetrahedral)
- If \( 0.414 < \text{Ratio} < 0.732 \), coordination number = 6 (octahedral)
- If \( 0.732 < \text{Ratio} < 1.0 \), coordination number = 8 (cubic)

Since \( 0.524 \) lies between \( 0.414 \) and \( 0.732 \), we conclude that the coordination number is 6.

### Step 5: Conclusion
Thus, the coordination number of \( A^+ \) is 6.

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

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