In which of the following oxyanions the oxidation state of central atom is not same as that of its group number in periodic table?

Options

A. `MnO_(4)^(-)`
B. `Cr_(2)O_(7)^(2-)`
C. `VO_(4)^(3-)`
D. `FeO_(4)^(2-)`

Answer

To solve the question regarding which oxyanion has a central atom whose oxidation state is not the same as its group number, we will analyze each given oxyanion step by step.

### Step 1: Analyze MnO4⁻ (Permanganate Ion)
- **Central Atom**: Manganese (Mn)
- **Oxidation State Calculation**:
Let the oxidation state of Mn be \( x \).
\[ x - 4 \times 2 = -1 \quad (\text{since there are 4 O atoms, each with a -2 charge}) \]
\[ x - 8 = -1 \implies x = +7 \]
- **Group Number**: Manganese is in Group 7.
- **Comparison**: Oxidation state (+7) = Group number (7).

### Step 2: Analyze Cr2O7²⁻ (Dichromate Ion)
- **Central Atom**: Chromium (Cr)
- **Oxidation State Calculation**:
Let the oxidation state of Cr be \( x \).
\[ 2x - 7 \times 2 = -2 \quad (\text{since there are 7 O atoms}) \]
\[ 2x - 14 = -2 \implies 2x = +12 \implies x = +6 \]
- **Group Number**: Chromium is in Group 6.
- **Comparison**: Oxidation state (+6) = Group number (6).

### Step 3: Analyze VO4³⁻ (Vanadate Ion)
- **Central Atom**: Vanadium (V)
- **Oxidation State Calculation**:
Let the oxidation state of V be \( x \).
\[ x - 4 \times 2 = -3 \]
\[ x - 8 = -3 \implies x = +5 \]
- **Group Number**: Vanadium is in Group 5.
- **Comparison**: Oxidation state (+5) = Group number (5).

### Step 4: Analyze FeO4²⁻ (Ferrate Ion)
- **Central Atom**: Iron (Fe)
- **Oxidation State Calculation**:
Let the oxidation state of Fe be \( x \).
\[ x - 4 \times 2 = -2 \]
\[ x - 8 = -2 \implies x = +6 \]
- **Group Number**: Iron is in Group 8.
- **Comparison**: Oxidation state (+6) ≠ Group number (8).

### Conclusion
The oxyanion where the oxidation state of the central atom is not the same as that of its group number is **FeO4²⁻**.

### Final Answer
**FeO4²⁻**