Number of antibonding electrons in `O_(2)^(-)` molecular ion is :

Options

A. 8
B. 6
C. 7
D. 4

Explanation

To determine the number of antibonding electrons in the molecular ion \( O_2^- \), we can follow these steps:

### Step 1: Determine the Total Number of Electrons
Each oxygen atom has 8 electrons, and since there are two oxygen atoms in \( O_2 \), we start with:
\[ 8 \text{ (from O)} \times 2 = 16 \text{ electrons} \]
However, since we have a negative charge on the ion (\( O_2^- \)), we need to add one more electron:
\[ 16 + 1 = 17 \text{ total electrons} \]

### Step 2: Draw the Molecular Orbital Diagram
In the molecular orbital theory, the molecular orbitals for \( O_2 \) can be arranged as follows:
1. \( \sigma_{1s} \) (bonding)
2. \( \sigma^*_{1s} \) (antibonding)
3. \( \sigma_{2s} \) (bonding)
4. \( \sigma^*_{2s} \) (antibonding)
5. \( \sigma_{2p_z} \) (bonding)
6. \( \pi_{2p_x} \) and \( \pi_{2p_y} \) (bonding)
7. \( \pi^*_{2p_x} \) and \( \pi^*_{2p_y} \) (antibonding)
8. \( \sigma^*_{2p_z} \) (antibonding)

### Step 3: Fill the Molecular Orbitals with Electrons
We fill the molecular orbitals with the 17 electrons according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle:
1. Fill \( \sigma_{1s} \) with 2 electrons
2. Fill \( \sigma^*_{1s} \) with 2 electrons
3. Fill \( \sigma_{2s} \) with 2 electrons
4. Fill \( \sigma^*_{2s} \) with 2 electrons
5. Fill \( \sigma_{2p_z} \) with 2 electrons
6. Fill \( \pi_{2p_x} \) and \( \pi_{2p_y} \) with 4 electrons (2 in each)
7. Fill \( \pi^*_{2p_x} \) and \( \pi^*_{2p_y} \) with 3 electrons (2 in one and 1 in the other)

### Step 4: Count the Antibonding Electrons
Now we can count the number of electrons in the antibonding orbitals:
- \( \sigma^*_{1s} \): 2 electrons
- \( \sigma^*_{2s} \): 2 electrons
- \( \pi^*_{2p_x} \): 2 electrons
- \( \pi^*_{2p_y} \): 1 electron

Adding these gives:
\[ 2 + 2 + 2 + 1 = 7 \text{ antibonding electrons} \]

### Final Answer
The number of antibonding electrons in the \( O_2^- \) molecular ion is **7**.

---