Which contain at least one `e^(-) "in" sigma 2p` bonding MO

Options

A. `O_(2)`
B. `B_(2)`
C. `C_(2)`
D. `Li _(2)`

Explanation

To determine which molecule contains at least one electron in the sigma 2p bonding molecular orbital, we need to analyze the molecular orbital (MO) electronic configurations of the given molecules. Let's go through each molecule step by step.

### Step 1: Analyze O2
1. **Total Electrons**: Oxygen (O) has 8 electrons, so O2 has \(8 + 8 = 16\) electrons.
2. **Molecular Orbital Configuration**:
- Fill the MOs in the order:
- \(\sigma 1s^2\)
- \(\sigma^* 1s^2\)
- \(\sigma 2s^2\)
- \(\sigma^* 2s^2\)
- \(\sigma 2p_z^2\) (bonding)
- \(\pi 2p_x^2 = \pi 2p_y^2\) (bonding)
- \(\pi^* 2p_x^1 = \pi^* 2p_y^1\) (antibonding)
3. **Filling Electrons**:
- Fill the MOs:
- \(\sigma 1s^2\) (2)
- \(\sigma^* 1s^2\) (2)
- \(\sigma 2s^2\) (2)
- \(\sigma^* 2s^2\) (2)
- \(\sigma 2p_z^2\) (2)
- \(\pi 2p_x^2\) (2)
- \(\pi 2p_y^2\) (2)
- \(\pi^* 2p_x^1\) (1)
- \(\pi^* 2p_y^1\) (1)
4. **Conclusion for O2**: The configuration shows that there are 2 electrons in the sigma 2p bonding MO. Thus, O2 has at least one electron in the sigma 2p bonding MO.

### Step 2: Analyze B2
1. **Total Electrons**: Boron (B) has 5 electrons, so B2 has \(5 + 5 = 10\) electrons.
2. **Molecular Orbital Configuration**:
- Fill the MOs in the order:
- \(\sigma 1s^2\)
- \(\sigma^* 1s^2\)
- \(\sigma 2s^2\)
- \(\sigma^* 2s^2\)
- \(\pi 2p_x^2 = \pi 2p_y^2\) (bonding)
3. **Filling Electrons**:
- Fill the MOs:
- \(\sigma 1s^2\) (2)
- \(\sigma^* 1s^2\) (2)
- \(\sigma 2s^2\) (2)
- \(\sigma^* 2s^2\) (2)
- \(\pi 2p_x^2\) (2)
4. **Conclusion for B2**: There are no electrons in the sigma 2p bonding MO. Thus, B2 does not have any electrons in the sigma 2p bonding MO.

### Step 3: Analyze C2
1. **Total Electrons**: Carbon (C) has 6 electrons, so C2 has \(6 + 6 = 12\) electrons.
2. **Molecular Orbital Configuration**:
- Fill the MOs in the order:
- \(\sigma 1s^2\)
- \(\sigma^* 1s^2\)
- \(\sigma 2s^2\)
- \(\sigma^* 2s^2\)
- \(\pi 2p_x^2 = \pi 2p_y^2\) (bonding)
3. **Filling Electrons**:
- Fill the MOs:
- \(\sigma 1s^2\) (2)
- \(\sigma^* 1s^2\) (2)
- \(\sigma 2s^2\) (2)
- \(\sigma^* 2s^2\) (2)
- \(\pi 2p_x^2\) (2)
- \(\pi 2p_y^2\) (2)
4. **Conclusion for C2**: There are no electrons in the sigma 2p bonding MO. Thus, C2 does not have any electrons in the sigma 2p bonding MO.

### Step 4: Analyze Li2
1. **Total Electrons**: Lithium (Li) has 3 electrons, so Li2 has \(3 + 3 = 6\) electrons.
2. **Molecular Orbital Configuration**:
- Fill the MOs in the order:
- \(\sigma 1s^2\)
- \(\sigma^* 1s^2\)
- \(\sigma 2s^2\)
3. **Filling Electrons**:
- Fill the MOs:
- \(\sigma 1s^2\) (2)
- \(\sigma^* 1s^2\) (2)
- \(\sigma 2s^2\) (2)
4. **Conclusion for Li2**: There are no electrons in the sigma 2p bonding MO. Thus, Li2 does not have any electrons in the sigma 2p bonding MO.

### Final Conclusion
The only molecule that contains at least one electron in the sigma 2p bonding molecular orbital is **O2**.