`ThO_(2)` exists in fluorite structure, what is the effective number of bivalent ion in the unit cell of `ThO_(2)`?

Options

A. `2`
B. `4`
C. `1`
D. `8`

Explanation

To find the effective number of bivalent ions in the unit cell of thorium dioxide (ThO₂) which exists in a fluorite structure, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure**:
- Thorium dioxide (ThO₂) has a fluorite structure. In this structure, the cation (Th⁴⁺) and anion (O²⁻) are arranged in a specific manner.

2. **Determine the Coordination**:
- In the fluorite structure, the coordination number of the cations (Th⁴⁺) is 8, while the coordination number of the anions (O²⁻) is 4. This means that each Th⁴⁺ ion is surrounded by 8 O²⁻ ions, and each O²⁻ ion is surrounded by 4 Th⁴⁺ ions.

3. **Calculate the Number of Ions in the Unit Cell**:
- In a face-centered cubic (FCC) unit cell, there are 4 formula units of ThO₂. This is because each corner contributes 1/8 of an ion and each face center contributes 1/2 of an ion. Thus, the total contribution from the corners and faces leads to 4 ThO₂ per unit cell.

4. **Identify the Effective Number of Bivalent Ions**:
- The question specifically asks for the effective number of bivalent ions. In this case, the bivalent ion is O²⁻.
- Since there are 4 ThO₂ units in the unit cell, and each ThO₂ has 2 O²⁻ ions, the total number of O²⁻ ions in the unit cell is:
\[ 4 \text{ (ThO₂ units)} \times 2 \text{ (O²⁻ per ThO₂)} = 8 \text{ O²⁻ ions} \]

5. **Conclusion**:
- Therefore, the effective number of bivalent ions (O²⁻) in the unit cell of ThO₂ is **8**.

### Final Answer:
The effective number of bivalent ions in the unit cell of ThO₂ is **8**.