Which of the following has highest number of formula units per unit cell ?

Options

A. NaCl type structure
B. `Na_2O` type structure
C. `CaF_2` type structure
D. All have same number of formula unit

Answer

To determine which of the given structures has the highest number of formula units per unit cell, we will analyze each structure step by step.

### Step 1: Analyze NaCl Structure
- **Structure Type**: NaCl has a face-centered cubic (FCC) structure.
- **Ionic Positions**: In NaCl, Na⁺ ions occupy all the octahedral voids of Cl⁻ ions.
- **Number of Ions**: In an FCC unit cell, the number of Cl⁻ ions is 4 (since Z = 4 for FCC).
- **Octahedral Voids**: The number of octahedral voids is equal to the number of Cl⁻ ions, which is also 4.
- **Formula Units**: Therefore, in one unit cell of NaCl, there are 4 formula units of NaCl.

### Step 2: Analyze Na2O Structure
- **Structure Type**: Na2O has an anti-fluoride type structure.
- **Ionic Positions**: In this structure, O²⁻ ions are at the FCC lattice points, while Na⁺ ions occupy all the tetrahedral voids.
- **Number of Ions**: The number of O²⁻ ions is 4 (since Z = 4 for FCC).
- **Tetrahedral Voids**: The number of tetrahedral voids in an FCC unit cell is 8 (which is twice the number of lattice points).
- **Formula Units**: Thus, in one unit cell of Na2O, there are 4 formula units of Na2O.

### Step 3: Analyze CaF2 Structure
- **Structure Type**: CaF2 has a fluoride type structure.
- **Ionic Positions**: In this structure, Ca²⁺ ions form a FCC lattice, and F⁻ ions occupy all the tetrahedral voids.
- **Number of Ions**: The number of Ca²⁺ ions is 4 (since Z = 4 for FCC).
- **F⁻ Ions**: The number of F⁻ ions is 8 (since there are 2 F⁻ ions for each Ca²⁺ ion).
- **Formula Units**: Therefore, in one unit cell of CaF2, there are also 4 formula units of CaF2.

### Conclusion
After analyzing all three structures:
- NaCl: 4 formula units
- Na2O: 4 formula units
- CaF2: 4 formula units

All three structures have the same number of formula units per unit cell, which is 4.

### Final Answer
**All have the same number of formula units per unit cell (4 formula units).**

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