Which molecular orbital of `O_(2)` have a nodal plane which is perpendicular to internuclear axis

Options

A. `sigma_(2s)`
B. `sigma^(**)2s`
C. `pi_(2py)`
D. `pi_(2py)^(**)`

Answer

To determine which molecular orbitals of \( O_2 \) have a nodal plane that is perpendicular to the internuclear axis, we can analyze the molecular orbitals formed from the atomic orbitals of the oxygen atoms. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Molecular Orbitals of \( O_2 \)
The molecular orbitals of \( O_2 \) are formed from the combination of atomic orbitals from the two oxygen atoms. The relevant atomic orbitals are the 2s and 2p orbitals.

### Step 2: Identify the Types of Molecular Orbitals
1. **Sigma (σ) and Sigma Star (σ*) Molecular Orbitals**:
- **σ 2s**: Formed by the head-on overlap of the 2s orbitals from each oxygen atom. This orbital has a bonding nature and is symmetric about the internuclear axis.
- **σ* 2s**: Formed by the head-on overlap of the 2s orbitals but with a phase difference (negative overlap), resulting in an antibonding nature. This orbital has a nodal plane that is perpendicular to the internuclear axis.

2. **Pi (π) and Pi Star (π*) Molecular Orbitals**:
- **π 2py**: Formed by the sidewise overlap of the 2p orbitals (specifically 2py) from each oxygen atom. This bonding orbital has electron density above and below the internuclear axis.
- **π* 2py**: Formed similarly to the π orbital but with a phase difference, resulting in an antibonding nature. This orbital also has a nodal plane that is perpendicular to the internuclear axis.

### Step 3: Identify the Nodal Planes
- The **σ* 2s** orbital has a nodal plane perpendicular to the internuclear axis due to its antibonding nature.
- The **π* 2py** orbital also has a nodal plane perpendicular to the internuclear axis due to the sidewise overlap and the nature of the antibonding orbital.

### Conclusion
The molecular orbitals of \( O_2 \) that have a nodal plane perpendicular to the internuclear axis are:
- **Option B: σ* 2s**
- **Option D: π* 2py**