The oxoanion in which the oxidation state of the central atom is same as its group number in the periodic table is:

Options

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

Answer

To determine the oxoanion in which the oxidation state of the central atom is the same as its group number in the periodic table, we will analyze each option given.

### Step-by-Step Solution:

1. **Identify the Options:**
We have four oxoanions to analyze:
- A) SO2^2-
- B) VO2^-
- C) MnO4^2-
- D) Cr2O7^2-

2. **Analyze Option A: SO2^2-**
- The central atom is sulfur (S).
- Atomic number of sulfur = 16, which places it in group 16.
- To find the oxidation state (X) of sulfur:
\[ X + 2(-2) = -2 \quad \text{(since there are 2 oxygen atoms with -2 charge each)} \]
\[ X - 4 = -2 \implies X = +2 \]
- The oxidation state of sulfur (+2) is not equal to its group number (16). Thus, this option is incorrect.

3. **Analyze Option B: VO2^-**
- The central atom is vanadium (V).
- Atomic number of vanadium = 23, which places it in group 5.
- To find the oxidation state (X) of vanadium:
\[ X + 2(-2) = -1 \quad \text{(since there are 2 oxygen atoms with -2 charge each)} \]
\[ X - 4 = -1 \implies X = +3 \]
- The oxidation state of vanadium (+3) is not equal to its group number (5). Thus, this option is incorrect.

4. **Analyze Option C: MnO4^2-**
- The central atom is manganese (Mn).
- Atomic number of manganese = 25, which places it in group 7.
- To find the oxidation state (X) of manganese:
\[ X + 4(-2) = -2 \quad \text{(since there are 4 oxygen atoms with -2 charge each)} \]
\[ X - 8 = -2 \implies X = +6 \]
- The oxidation state of manganese (+6) is not equal to its group number (7). Thus, this option is incorrect.

5. **Analyze Option D: Cr2O7^2-**
- The central atom is chromium (Cr).
- Atomic number of chromium = 24, which places it in group 6.
- To find the oxidation state (X) of chromium:
\[ 2X + 7(-2) = -2 \quad \text{(since there are 7 oxygen atoms with -2 charge each)} \]
\[ 2X - 14 = -2 \implies 2X = 12 \implies X = +6 \]
- The oxidation state of chromium (+6) is equal to its group number (6). Thus, this option is correct.

### Conclusion:
The oxoanion in which the oxidation state of the central atom is the same as its group number in the periodic table is **Cr2O7^2-**.