Statement-1 : `O_(2)^(-)` and `O_(2)^(+)` are paramagnetic .
and
Statement-2 : Bond order of `O_(2)^(+)` and `O_(2)^(-)` is same .

Options

A. Statement-1 is True , Statement-2 is True , Statement-2 is a correct explanation for Statement-10
B. Statement-1 is True , Statement-2 is True , Statement-2 is NOT a correct explanation for Statement-10
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To analyze the statements regarding the paramagnetism and bond order of \( O_2^- \) and \( O_2^+ \), we will follow these steps:

### Step 1: Determine the electronic configuration of \( O_2 \)

1. **Identify the number of electrons in \( O_2 \)**:
- Each oxygen atom has 8 electrons, so \( O_2 \) has a total of \( 8 + 8 = 16 \) electrons.

2. **Fill the molecular orbitals**:
- The molecular orbital configuration for \( O_2 \) is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^0 \]
- This results in the following filling:
- Bonding orbitals: \( 10 \) electrons (from \( \sigma_{1s}, \sigma_{2s}, \sigma_{2p_z}, \pi_{2p_x}, \pi_{2p_y} \))
- Antibonding orbitals: \( 6 \) electrons (from \( \sigma^*_{1s}, \sigma^*_{2s}, \pi^*_{2p_x}, \pi^*_{2p_y} \))

### Step 2: Analyze \( O_2^- \) and \( O_2^+ \)

1. **For \( O_2^- \)**:
- It has one extra electron compared to \( O_2 \):
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^2 \pi^*_{2p_y}^0 \]
- Total electrons: \( 17 \)
- Bonding electrons: \( 10 \)
- Antibonding electrons: \( 6 \)

2. **For \( O_2^+ \)**:
- It has one less electron compared to \( O_2 \):
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^0 \]
- Total electrons: \( 15 \)
- Bonding electrons: \( 10 \)
- Antibonding electrons: \( 5 \)

### Step 3: Calculate the bond order for \( O_2^- \) and \( O_2^+ \)

1. **Bond order formula**:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]

2. **For \( O_2^- \)**:
- Bond order = \( \frac{10 - 6}{2} = 2 \)

3. **For \( O_2^+ \)**:
- Bond order = \( \frac{10 - 5}{2} = 2.5 \)

### Conclusion

- **Statement 1**: Both \( O_2^- \) and \( O_2^+ \) are paramagnetic because they have unpaired electrons.
- **Statement 2**: The bond order of \( O_2^- \) (2) and \( O_2^+ \) (2.5) is not the same.

Thus, **Statement 1 is true** and **Statement 2 is false**.