A compound `AB_(2)` possesses the `CaF_(2)` type crystal structure. The co-ordination number of `A^(2+)` and `B^(–)` ions is the crystal will be:

Options

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

Answer

To determine the coordination numbers of the ions in the compound \( AB_2 \) with a \( CaF_2 \) type crystal structure, we can follow these steps:

### Step 1: Understand the structure of \( CaF_2 \)
The \( CaF_2 \) structure is characterized by calcium ions (\( Ca^{2+} \)) and fluoride ions (\( F^{-} \)). In this structure:
- Calcium ions are located at the body center of the unit cell.
- Fluoride ions are located at the corners of the unit cell.

### Step 2: Identify the coordination numbers in \( CaF_2 \)
In the \( CaF_2 \) structure:
- Each \( Ca^{2+} \) ion is surrounded by 8 \( F^{-} \) ions, giving it a coordination number of 8.
- Each \( F^{-} \) ion is surrounded by 4 \( Ca^{2+} \) ions, giving it a coordination number of 4.

### Step 3: Relate this to the compound \( AB_2 \)
The compound \( AB_2 \) has a similar structure to \( CaF_2 \):
- Here, \( A^{2+} \) corresponds to \( Ca^{2+} \).
- \( B^{-} \) corresponds to \( F^{-} \).

### Step 4: Assign the coordination numbers for \( AB_2 \)
Based on the \( CaF_2 \) structure:
- The coordination number of \( A^{2+} \) ions in \( AB_2 \) will also be 8.
- The coordination number of \( B^{-} \) ions in \( AB_2 \) will also be 4.

### Conclusion
Thus, the coordination numbers of \( A^{2+} \) and \( B^{-} \) ions in the crystal structure of \( AB_2 \) are:
- Coordination number of \( A^{2+} \): 8
- Coordination number of \( B^{-} \): 4

### Final Answer
The coordination numbers of \( A^{2+} \) and \( B^{-} \) ions in the crystal will be \( 8 \) and \( 4 \), respectively.

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