`Fe_3O_4` has inverse spinel structure. What is not true about this solid ?

Options

A. `Fe^(3+)` ions are equally distributed between octahedral and tetrahedral voids
B. Tetrahedral voids are equally distributed between `Fe^(2+)` and `Fe^(3+)` ions
C. No. of `O^(-2) gt Fe^(+3) gt Fe^(+2)`
D. Coordination no. of `Fe^(3+)` =8 through out the unit cell

Answer

To determine which statement is not true about the inverse spinel structure of `Fe3O4`, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding the Structure**:
- `Fe3O4` has an inverse spinel structure, which can be represented as `AB2X4`. Here, `A` is the divalent cation (Fe²⁺), `B` is the trivalent cation (Fe³⁺), and `X` is the anion (O²⁻). In this case, `Fe²⁺` and `Fe³⁺` are distributed in the octahedral and tetrahedral voids of the face-centered cubic (FCC) lattice formed by oxide ions.

2. **Analyzing the Options**:
- **Option A**: "Fe³⁺ ions are equally distributed between octahedral and tetrahedral voids."
- **True**: In the inverse spinel structure, half of the Fe³⁺ ions occupy octahedral voids and the other half occupy tetrahedral voids.

- **Option B**: "Tetrahedral voids are equally distributed between Fe²⁺ and Fe³⁺ ions."
- **Not True**: Fe²⁺ ions occupy octahedral voids, while only Fe³⁺ ions occupy tetrahedral voids. Therefore, this statement is incorrect.

- **Option C**: "The number of oxide ions is greater than Fe³⁺ and greater than Fe²⁺."
- **True**: In the structure, there are 32 oxide ions, 8 Fe²⁺ ions, and 16 Fe³⁺ ions, making this statement true.

- **Option D**: "The coordination number of Fe³⁺ is 8 throughout the unit cell."
- **Not True**: The coordination number of Fe³⁺ ions is not consistently 8; it varies depending on whether they occupy octahedral or tetrahedral voids. Therefore, this statement is also incorrect.

3. **Conclusion**:
- The statements that are not true about the solid `Fe3O4` are **Option B** and **Option D**.

### Final Answer:
The statements that are not true about the solid `Fe3O4` are:
- **B**: Tetrahedral voids are equally distributed between Fe²⁺ and Fe³⁺ ions.
- **D**: The coordination number of Fe³⁺ is 8 throughout the unit cell.