Which of the following `MO's` has zero nodal planes ? .

Options

A. `sigma^(**) 1s`
B. `sigma 1 s`
C. `pi 2p_(x)`
D. `pi^(**) 2p_(z)`

Explanation

To determine which molecular orbital (MO) has zero nodal planes, we will analyze each option step by step.

### Step 1: Understanding Nodal Planes
A nodal plane is a region in a molecular orbital where the probability of finding an electron is zero. The presence of nodal planes indicates the number of nodes in the molecular orbital.

### Step 2: Analyze Each Option

#### Option A: σ* 1s
- **Type**: Anti-bonding molecular orbital (denoted by the star).
- **Formation**: Formed by the head-on overlap of two 1s orbitals.
- **Interference**: Destructive interference occurs.
- **Nodal Plane**: There is one nodal plane present, which is perpendicular to the internuclear axis.

**Conclusion**: This option has one nodal plane.

#### Option B: σ 1s
- **Type**: Bonding molecular orbital.
- **Formation**: Formed by the head-on overlap of two 1s orbitals.
- **Interference**: Constructive interference occurs.
- **Nodal Plane**: There are no nodal planes present.

**Conclusion**: This option has zero nodal planes.

#### Option C: π 2p_x
- **Type**: Bonding molecular orbital.
- **Formation**: Formed by the sidewise overlap of two 2p_x orbitals.
- **Interference**: Constructive interference occurs.
- **Nodal Plane**: There is one nodal plane present.

**Conclusion**: This option has one nodal plane.

#### Option D: π* 2p_z
- **Type**: Anti-bonding molecular orbital.
- **Formation**: Formed by the sidewise overlap of two 2p_z orbitals.
- **Interference**: Destructive interference occurs.
- **Nodal Plane**: There are two nodal planes present.

**Conclusion**: This option has two nodal planes.

### Final Conclusion
After analyzing all the options, we find that the only molecular orbital with zero nodal planes is **Option B: σ 1s**.

### Summary of Steps
1. Define nodal planes and their significance.
2. Analyze each molecular orbital option for nodal planes.
3. Conclude which option has zero nodal planes.