`Fe^(III) (Fe^(II) Fe^(III))O_(4)` represent an inverse `2 : 3` spinel structre.True/False.

Explanation

To determine whether the statement "Fe^(III) (Fe^(II) Fe^(III))O_(4) represents an inverse 2:3 spinel structure" is true or false, we can follow these steps:

### Step 1: Understand the Inverse Spinel Structure
An inverse spinel structure is generally represented as \( A^{2+}B^{3+}_2O_4 \). In this structure, the \( A^{2+} \) cations occupy the tetrahedral voids, and the \( B^{3+} \) cations occupy both tetrahedral and octahedral voids.

### Step 2: Identify the Components in the Given Formula
The formula given is \( Fe^{III} (Fe^{II} Fe^{III})O_4 \). This can be interpreted as:
- \( Fe^{II} \) = \( Fe^{2+} \)
- \( Fe^{III} \) = \( Fe^{3+} \)
- \( O \) = \( O^{2-} \)

### Step 3: Analyze the Cation Distribution
In the inverse spinel structure:
- The \( Fe^{3+} \) ions will occupy both tetrahedral and octahedral sites.
- The \( Fe^{2+} \) ions will occupy the tetrahedral sites.

### Step 4: Count the Cations
In the formula \( Fe^{III} (Fe^{II} Fe^{III})O_4 \):
- There are 2 \( Fe^{3+} \) ions and 1 \( Fe^{2+} \) ion.
- This gives a total of 3 \( Fe^{3+} \) ions and 1 \( Fe^{2+} \) ion, which fits the \( A^{2+}B^{3+}_2O_4 \) format.

### Step 5: Confirm the Structure
In the structure:
- The \( Fe^{3+} \) ions will occupy 1/8 tetrahedral and 1/4 octahedral voids.
- The \( Fe^{2+} \) ions will occupy the remaining tetrahedral voids.

### Conclusion
Since the distribution of cations matches the characteristics of an inverse spinel structure with a ratio of 2:3 (where 2 are \( Fe^{3+} \) and 1 is \( Fe^{2+} \)), the statement is **True**.