Which of the following has unpaired electron in antibonding MO?

Options

A. `C_2`
B. `N_2`
C. `O_2`
D. Both `C_2` and `N_2`

Explanation

To determine which of the given molecules has unpaired electrons in an antibonding molecular orbital (MO), we will analyze the molecular orbital configurations of the molecules provided. Let's go through the steps systematically.

### Step 1: Identify the molecules
We need to analyze the molecular orbital configurations for the following molecules:
1. C2
2. N2
3. O2

### Step 2: Write the electronic configuration for each molecule
- **C2**: Each carbon atom has an electronic configuration of 1s² 2s² 2p². Therefore, for C2, the total number of electrons is 2 (from each carbon's 1s) + 2 (from each carbon's 2s) + 4 (from both carbons' 2p) = 8 electrons.

- **N2**: Each nitrogen atom has an electronic configuration of 1s² 2s² 2p³. Therefore, for N2, the total number of electrons is 2 (from each nitrogen's 1s) + 2 (from each nitrogen's 2s) + 6 (from both nitrogens' 2p) = 14 electrons.

- **O2**: Each oxygen atom has an electronic configuration of 1s² 2s² 2p⁴. Therefore, for O2, the total number of electrons is 2 (from each oxygen's 1s) + 2 (from each oxygen's 2s) + 8 (from both oxygens' 2p) = 16 electrons.

### Step 3: Fill the molecular orbitals
Now we will fill the molecular orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

1. **C2**:
- 1s: 2 electrons (bonding)
- 1s*: 2 electrons (antibonding)
- 2s: 2 electrons (bonding)
- 2s*: 2 electrons (antibonding)
- 2p: 4 electrons (2 in bonding π and 2 in antibonding π*)
- Total: 2 (σ1s) + 2 (σ*1s) + 2 (σ2s) + 2 (σ*2s) + 2 (π2p) + 2 (π*2p) = 8 electrons
- **Result**: No unpaired electrons in antibonding orbitals.

2. **N2**:
- 1s: 2 electrons (bonding)
- 1s*: 2 electrons (antibonding)
- 2s: 2 electrons (bonding)
- 2s*: 2 electrons (antibonding)
- 2p: 6 electrons (2 in bonding σ, 2 in bonding π, and 2 in antibonding π*)
- Total: 2 (σ1s) + 2 (σ*1s) + 2 (σ2s) + 2 (σ*2s) + 2 (π2p) + 2 (π*2p) = 14 electrons
- **Result**: No unpaired electrons in antibonding orbitals.

3. **O2**:
- 1s: 2 electrons (bonding)
- 1s*: 2 electrons (antibonding)
- 2s: 2 electrons (bonding)
- 2s*: 2 electrons (antibonding)
- 2p: 8 electrons (2 in bonding σ, 2 in bonding π, 2 in antibonding π*, and 2 in antibonding σ*)
- Total: 2 (σ1s) + 2 (σ*1s) + 2 (σ2s) + 2 (σ*2s) + 2 (π2p) + 4 (π*2p) = 16 electrons
- **Result**: There are 2 unpaired electrons in the antibonding π* orbital.

### Conclusion
The molecule that has unpaired electrons in antibonding molecular orbitals is **O2**.