Which of the following is paramagnetic and HOMO is gerade molecular orbital

Options

A. `O_(2)`
B. `O_(2)^(2-)`
C. `B_(2)`
D. `C_(2)`

Answer

To solve the question of which molecule is paramagnetic and has a Highest Occupied Molecular Orbital (HOMO) that is a gerade molecular orbital, we will analyze the given options step by step.

### Step 1: Analyze O2
- **Electrons in O2**: O2 has a total of 16 electrons.
- **Molecular Orbital Configuration**: The molecular orbital configuration for O2 is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^1 \pi_{2p_y}^1 \]
- **Unpaired Electrons**: The last two electrons occupy the \(\pi_{2p_x}\) and \(\pi_{2p_y}\) orbitals, which are degenerate and are antibonding orbitals. There are 2 unpaired electrons.
- **Magnetic Behavior**: Since O2 has unpaired electrons, it is **paramagnetic**.
- **HOMO**: The highest occupied molecular orbital (HOMO) is \(\pi_{2p_x}\) or \(\pi_{2p_y}\), which are both gerade orbitals.

### Step 2: Analyze O2^2-
- **Electrons in O2^2-**: O2^2- has 18 electrons (2 additional electrons).
- **Molecular Orbital Configuration**: The configuration becomes:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \]
- **Unpaired Electrons**: All orbitals are fully filled, resulting in no unpaired electrons.
- **Magnetic Behavior**: O2^2- is **diamagnetic** and cannot be the answer.

### Step 3: Analyze B2
- **Electrons in B2**: B2 has 10 electrons.
- **Molecular Orbital Configuration**: The configuration is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \]
- **Unpaired Electrons**: All electrons are paired, making B2 **diamagnetic**.
- **Conclusion**: B2 is not the answer.

### Step 4: Analyze C2
- **Electrons in C2**: C2 has 12 electrons.
- **Molecular Orbital Configuration**: The configuration is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^1 \pi_{2p_y}^1 \]
- **Unpaired Electrons**: There are 2 unpaired electrons in the \(\pi_{2p_x}\) and \(\pi_{2p_y}\) orbitals.
- **Magnetic Behavior**: C2 is **paramagnetic**; however, the HOMO is \(\pi_{2p_x}\) or \(\pi_{2p_y}\), which are bonding orbitals, not gerade.

### Conclusion
The only molecule that is both paramagnetic and has a HOMO that is a gerade molecular orbital is **O2**.

### Final Answer
**O2** is the molecule that is paramagnetic and has a HOMO that is a gerade molecular orbital.