In `O_2^-, O_2 ` and `O_2^(-2)` molecular species, the total number of antibonding electrons respectively are

Options

A. 7,6,8
B. 1,0,2
C. 6,6,6
D. 8,6,8

Explanation

To determine the total number of antibonding electrons in the molecular species \( O_2^- \), \( O_2 \), and \( O_2^{2-} \), we will follow these steps:

### Step 1: Determine the number of electrons in each species
- **For \( O_2 \)**: Each oxygen atom has 8 electrons, so \( O_2 \) has \( 8 + 8 = 16 \) electrons.
- **For \( O_2^- \)**: This species has one extra electron, so it has \( 16 + 1 = 17 \) electrons.
- **For \( O_2^{2-} \)**: This species has two extra electrons, so it has \( 16 + 2 = 18 \) electrons.

### Step 2: Fill the molecular orbitals according to the Molecular Orbital Theory (MOT)
The molecular orbitals for \( O_2 \) are filled in the following order:
1. \( \sigma_{1s} \)
2. \( \sigma_{1s}^* \)
3. \( \sigma_{2s} \)
4. \( \sigma_{2s}^* \)
5. \( \sigma_{2p_z} \)
6. \( \pi_{2p_x} \)
7. \( \pi_{2p_y} \)
8. \( \pi_{2p_x}^* \)
9. \( \pi_{2p_y}^* \)
10. \( \sigma_{2p_z}^* \)

### Step 3: Count the antibonding electrons for each species
- **For \( O_2 \)** (16 electrons):
- Filling order: \( 2 \) in \( \sigma_{1s} \), \( 2 \) in \( \sigma_{1s}^* \), \( 2 \) in \( \sigma_{2s} \), \( 2 \) in \( \sigma_{2s}^* \), \( 2 \) in \( \sigma_{2p_z} \), \( 4 \) in \( \pi_{2p_x} \) and \( \pi_{2p_y} \).
- Antibonding electrons: \( 2 \) in \( \sigma_{1s}^* \) and \( 0 \) in \( \pi_{2p_x}^* \) and \( \pi_{2p_y}^* \).
- Total antibonding electrons in \( O_2 \): **2**.

- **For \( O_2^- \)** (17 electrons):
- Filling order: Same as above, but with one additional electron filling the next available orbital.
- Antibonding electrons: \( 2 \) in \( \sigma_{1s}^* \) and \( 1 \) in \( \pi_{2p_x}^* \) or \( \pi_{2p_y}^* \).
- Total antibonding electrons in \( O_2^- \): **3**.

- **For \( O_2^{2-} \)** (18 electrons):
- Filling order: Same as above, but with two additional electrons filling the next available orbitals.
- Antibonding electrons: \( 2 \) in \( \sigma_{1s}^* \) and \( 2 \) in \( \pi_{2p_x}^* \) and \( \pi_{2p_y}^* \).
- Total antibonding electrons in \( O_2^{2-} \): **4**.

### Final Answer
The total number of antibonding electrons in \( O_2^- \), \( O_2 \), and \( O_2^{2-} \) are **3, 2, and 4**, respectively.