The correct order of pair regarding nodal surface

Options

A. `sigma 2s gt sigma^(+) 2s `
B. `sigma 2s lt sigma^(**) 2p_(z)`
C. `sigma^(**) 2s gt sigma^(**) 2p_(z)`
D. `sigma^(**) 2p_(z) lt pi 2 px`

Answer

To solve the question regarding the correct order of pairs concerning nodal surfaces, we need to understand the concept of nodal surfaces and how they relate to different molecular orbitals. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand Nodal Surfaces
A nodal surface is a region in an atomic or molecular orbital where the probability of finding an electron is zero. In simpler terms, it is where the wave function (ψ) equals zero, indicating no electron density.

**Hint:** Remember that the number of nodal surfaces increases with the energy of the orbital.

### Step 2: Analyze the Given Molecular Orbitals
We will analyze the nodal surfaces for the following molecular orbitals:
- **σ2s**
- **σ*2s**
- **σ*2pz**
- **π2px**

### Step 3: Determine Nodal Surfaces for Each Orbital
1. **σ2s**: This is a bonding orbital with no nodal surfaces. Therefore, it has **0 nodal surfaces**.
2. **σ*2s**: This is an anti-bonding orbital with one nodal surface. Therefore, it has **1 nodal surface**.
3. **σ*2pz**: This is also an anti-bonding orbital and has one nodal surface. Therefore, it has **1 nodal surface**.
4. **π2px**: This is a bonding orbital and has one nodal surface. Therefore, it has **1 nodal surface**.

### Step 4: Compare the Nodal Surfaces
Now we can compare the nodal surfaces:
- **σ2s (0) < σ*2s (1)**: This means σ2s has fewer nodal surfaces than σ*2s.
- **σ2s (0) < σ*2pz (1)**: This means σ2s has fewer nodal surfaces than σ*2pz.
- **σ*2s (1) = σ*2pz (1)**: Both have the same number of nodal surfaces.
- **σ*2pz (1) = π2px (1)**: Both have the same number of nodal surfaces.

### Step 5: Write the Correct Order
Based on the comparisons:
1. **σ2s < σ*2s**
2. **σ2s < σ*2pz**
3. **σ*2s = σ*2pz**
4. **σ*2pz = π2px**

### Conclusion
The correct order of pairs regarding nodal surfaces is:
- σ2s < σ*2s
- σ2s < σ*2pz
- σ*2s = σ*2pz
- σ*2pz = π2px

Thus, the answer to the question is that the correct order of pairs regarding nodal surfaces is option **B**.

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