Among the following molecular orbitals how many have at least one nodal plane? `sigma^ast1s`,`sigma2s`,`sigma^ast2p_z`,`pi2p_x`,`pi^ast2p_y`, `sigma 2p_z`

Options

A. 4
B. 5
C. 2
D. 6

Answer

To determine how many of the given molecular orbitals have at least one nodal plane, we need to analyze each molecular orbital provided in the question. 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 molecular orbitals given are:
- \( \sigma^* 1s \)
- \( \sigma 2s \)
- \( \sigma^* 2p_z \)
- \( \pi 2p_x \)
- \( \pi^* 2p_y \)
- \( \sigma 2p_z \)

2. **Analyze Each Molecular Orbital**:
- **\( \sigma^* 1s \)**: This is an antibonding orbital formed from the overlap of 1s orbitals. It has **one nodal plane** due to the nature of antibonding orbitals.
- **\( \sigma 2s \)**: This is a bonding orbital formed from the overlap of 2s orbitals. It has **no nodal planes**.
- **\( \sigma^* 2p_z \)**: This is an antibonding orbital formed from the overlap of 2p orbitals. It has **one nodal plane**.
- **\( \pi 2p_x \)**: This is a bonding orbital formed from the side-on overlap of 2p orbitals. It has **one nodal plane**.
- **\( \pi^* 2p_y \)**: This is an antibonding orbital formed from the side-on overlap of 2p orbitals. It has **two nodal planes**.
- **\( \sigma 2p_z \)**: This is a bonding orbital formed from the overlap of 2p orbitals. It has **no nodal planes**.

3. **Count the Molecular Orbitals with Nodal Planes**:
- \( \sigma^* 1s \): 1 nodal plane
- \( \sigma 2s \): 0 nodal planes
- \( \sigma^* 2p_z \): 1 nodal plane
- \( \pi 2p_x \): 1 nodal plane
- \( \pi^* 2p_y \): 2 nodal planes
- \( \sigma 2p_z \): 0 nodal planes

Now, we count the orbitals with at least one nodal plane:
- \( \sigma^* 1s \) (1)
- \( \sigma^* 2p_z \) (1)
- \( \pi 2p_x \) (1)
- \( \pi^* 2p_y \) (2)

Total = 4 molecular orbitals with at least one nodal plane.

### Final Answer:
The number of molecular orbitals that have at least one nodal plane is **4**.

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