What is the co-ordination number of calcium in `CaF_(2)` ?

Options

A. 6
B. 4
C. 8
D. 2

Explanation

To determine the coordination number of calcium in CaF₂, we can follow these steps:

### Step 1: Identify the Structure of CaF₂
Calcium fluoride (CaF₂) consists of calcium ions (Ca²⁺) and fluoride ions (F⁻). In the crystal structure of CaF₂, calcium ions occupy the cubic close-packed (CCP) lattice, while fluoride ions occupy the tetrahedral voids.

**Hint:** Understand the arrangement of ions in the crystal structure to determine the coordination number.

### Step 2: Analyze the Ion Sizes
The size of the calcium ion (Ca²⁺) is larger than that of the fluoride ion (F⁻). This size difference is crucial as it influences how the ions are arranged in the crystal lattice.

**Hint:** Compare the ionic sizes to understand which ions occupy which positions in the lattice.

### Step 3: Determine the Coordination Number of Fluoride Ions
In the tetrahedral voids, each fluoride ion can coordinate with four calcium ions. Therefore, the coordination number of the fluoride ion is 4.

**Hint:** Recall that in a tetrahedral arrangement, each ion can be surrounded by four others.

### Step 4: Use Charge Ratio to Find Calcium's Coordination Number
The charge ratio between the fluoride ions and calcium ions is 2:1 (since there are two fluoride ions for each calcium ion). Since the coordination number of the fluoride ions is 4, we can use the charge ratio to find the coordination number of calcium.

**Hint:** The coordination number ratio is proportional to the charge ratio of the ions.

### Step 5: Calculate the Coordination Number of Calcium
Given that the coordination number of fluoride ions is 4, and the charge ratio is 2:1, we can set up the following relationship:
- Coordination number of Ca²⁺ : Coordination number of F⁻ = 2 : 1
- Therefore, if the coordination number of F⁻ is 4, the coordination number of Ca²⁺ will be 8.

**Hint:** Set up a proportion based on the charge and coordination numbers to find the unknown.

### Conclusion
Thus, the coordination number of calcium in CaF₂ is 8.

**Final Answer:** The coordination number of calcium in CaF₂ is 8.

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