The number of antibonding electron pairs in `O_(2)^(2-)` molecular ion on the basic of molecular orbital theory is

Options

A. (a) 5
B. (b) 2
C. (c) 4
D. (d) 6

Explanation

To determine the number of antibonding electron pairs in the \( O_2^{2-} \) molecular ion based on molecular orbital theory, we can follow these steps:

### Step 1: Determine the Total Number of Electrons
The atomic number of oxygen is 8, meaning each oxygen atom has 8 electrons. For \( O_2 \), which consists of two oxygen atoms, the total number of electrons is:
\[ 2 \times 8 = 16 \text{ electrons} \]
Since the ion has a \( 2- \) charge, we add 2 more electrons:
\[ 16 + 2 = 18 \text{ electrons} \]

### Step 2: Write the Molecular Orbital Configuration
According to molecular orbital theory, the order of filling the molecular orbitals for \( O_2 \) and its ions is:
1. \( \sigma_{1s} \)
2. \( \sigma^*_{1s} \)
3. \( \sigma_{2s} \)
4. \( \sigma^*_{2s} \)
5. \( \sigma_{2p_z} \)
6. \( \pi_{2p_x} \) and \( \pi_{2p_y} \) (degenerate)
7. \( \pi^*_{2p_x} \) and \( \pi^*_{2p_y} \) (degenerate)
8. \( \sigma^*_{2p_z} \)

### Step 3: Fill the Electrons in the Molecular Orbitals
We fill the molecular orbitals with the 18 electrons:
- \( \sigma_{1s} \): 2 electrons
- \( \sigma^*_{1s} \): 2 electrons
- \( \sigma_{2s} \): 2 electrons
- \( \sigma^*_{2s} \): 2 electrons
- \( \sigma_{2p_z} \): 2 electrons
- \( \pi_{2p_x} \): 2 electrons
- \( \pi_{2p_y} \): 2 electrons
- \( \pi^*_{2p_x} \): 2 electrons
- \( \pi^*_{2p_y} \): 0 electrons (since we have filled 18 electrons)

The filling looks like this:
- \( \sigma_{1s}^2 \)
- \( \sigma^*_{1s}^2 \)
- \( \sigma_{2s}^2 \)
- \( \sigma^*_{2s}^2 \)
- \( \sigma_{2p_z}^2 \)
- \( \pi_{2p_x}^2 \)
- \( \pi_{2p_y}^2 \)
- \( \pi^*_{2p_x}^2 \)
- \( \pi^*_{2p_y}^0 \)

### Step 4: Count the Antibonding Electrons
The antibonding orbitals are:
- \( \sigma^*_{1s} \): 2 electrons
- \( \sigma^*_{2s} \): 2 electrons
- \( \pi^*_{2p_x} \): 2 electrons
- \( \pi^*_{2p_y} \): 0 electrons

Total antibonding electrons:
\[ 2 + 2 + 2 + 0 = 6 \text{ antibonding electrons} \]

### Step 5: Calculate the Number of Antibonding Electron Pairs
Since each pair consists of 2 electrons, the number of antibonding electron pairs is:
\[ \frac{6}{2} = 3 \text{ antibonding electron pairs} \]

### Conclusion
Thus, the number of antibonding electron pairs in \( O_2^{2-} \) is **3**.