What are the coordination number (C.N.) of `Ca^(2+) and F^(-)` ion in calcium fluoride `(CaF_(2))` crystal structure?

Options

A. `"C.N. of "Ca^(2+) = 4 and F^(-)=8`
B. `"C.N. of "Ca^(2+) = 6 and F^(-)=6`
C. `"C.N. of "Ca^(2+) = 8 and F^(-)=8`
D. `"C.N. of "Ca^(2+) = 8 and F^(-)=4`

Answer

To determine the coordination numbers (C.N.) of \(Ca^{2+}\) and \(F^{-}\) ions in calcium fluoride (\(CaF_2\)), we will analyze the crystal structure of \(CaF_2\).

### Step-by-Step Solution:

1. **Understanding the Structure of \(CaF_2\)**:
- Calcium fluoride crystallizes in a face-centered cubic (FCC) structure.
- In this structure, the \(Ca^{2+}\) ions occupy the corners and the face centers of the unit cell, while the \(F^{-}\) ions occupy the tetrahedral voids.

2. **Coordination Number of \(F^{-}\) Ions**:
- The coordination number of an ion is defined as the number of nearest neighbor ions surrounding it.
- Each \(F^{-}\) ion in the tetrahedral void is surrounded by four \(Ca^{2+}\) ions.
- Therefore, the coordination number of \(F^{-}\) is **4**.

3. **Coordination Number of \(Ca^{2+}\) Ions**:
- Each \(Ca^{2+}\) ion at the corner of the unit cell is shared among 8 neighboring unit cells.
- Each \(Ca^{2+}\) ion is surrounded by 8 \(F^{-}\) ions (4 from the tetrahedral voids in its own unit cell and 4 from adjacent unit cells).
- Hence, the coordination number of \(Ca^{2+}\) is **8**.

### Final Answer:
- The coordination number of \(Ca^{2+}\) is **8**.
- The coordination number of \(F^{-}\) is **4**.