What is the coordination number of `Th^(4+)` in `ThO_(2)`?

Options

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

Explanation

To determine the coordination number of \( \text{Th}^{4+} \) in \( \text{ThO}_2 \), we can follow these steps:

### Step 1: Understand the Structure of \( \text{ThO}_2 \)
- \( \text{ThO}_2 \) adopts a fluorite structure. In this structure, the cations and anions are arranged in a specific way.

### Step 2: Identify the Positions of Ions
- In the fluorite structure, the \( \text{O}^{2-} \) ions occupy all the tetrahedral voids, while the \( \text{Th}^{4+} \) ions are located at the face-centered cubic (FCC) lattice points.

### Step 3: Determine the Number of Ions in the Unit Cell
- In a unit cell of the fluorite structure:
- The effective number of \( \text{Th}^{4+} \) ions is 4.
- The effective number of \( \text{O}^{2-} \) ions is 8.

### Step 4: Calculate the Coordination Number
- The coordination number is defined as the number of nearest neighbor ions surrounding a central ion.
- Since each \( \text{Th}^{4+} \) ion is surrounded by 8 \( \text{O}^{2-} \) ions, the coordination number of \( \text{Th}^{4+} \) in \( \text{ThO}_2 \) is 8.

### Final Answer
- The coordination number of \( \text{Th}^{4+} \) in \( \text{ThO}_2 \) is **8**.

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