Which of the following molecular orbitals has two nodal planes ?

Options

A. `sigma _(2s) ^(**)`
B. `pi _(2py)^(**)`
C. `pi _(2py)`
D. `pi _(2px)`

Explanation

To determine which molecular orbital has two nodal planes, we need to understand what a nodal plane is. A nodal plane is a region in a molecular orbital where the probability of finding an electron is zero.

### Step-by-Step Solution:

1. **Identify the Molecular Orbitals**: The question mentions several molecular orbitals, including σ* 2s, π* 2py, π 2py, and π 2px.

2. **Analyze σ* 2s Orbital**:
- The σ* 2s is an anti-bonding molecular orbital formed by the destructive interference of two 2s orbitals.
- This orbital has one nodal plane, where the probability of finding an electron is zero.
- **Conclusion**: σ* 2s has 1 nodal plane.

3. **Analyze π* 2py Orbital**:
- The π* 2py is also an anti-bonding molecular orbital formed by the destructive interference of two 2py orbitals.
- This orbital has two nodal planes. The first nodal plane is where the wave functions change sign, and the second nodal plane is perpendicular to the first, resulting in two regions with zero probability of finding an electron.
- **Conclusion**: π* 2py has 2 nodal planes.

4. **Analyze π 2py and π 2px Orbitals**:
- Both π 2py and π 2px are bonding molecular orbitals formed by constructive interference of their respective orbitals.
- Each of these orbitals has one nodal plane, which is the plane where the wave functions of the two orbitals cancel each other out.
- **Conclusion**: Both π 2py and π 2px have 1 nodal plane.

5. **Final Conclusion**:
- Among the given options, the only molecular orbital that has two nodal planes is **π* 2py**.

### Answer:
The molecular orbital that has two nodal planes is **π* 2py**.