Which of the following molecular orbitals has the lowest energy?

Options

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

Explanation

To determine which molecular orbital has the lowest energy, we need to analyze the molecular orbital (MO) diagram and understand the energy levels of the orbitals involved. Here’s a step-by-step solution:

### Step 1: Understand the Molecular Orbital Theory
Molecular Orbital Theory explains how atomic orbitals combine to form molecular orbitals. These molecular orbitals can be bonding or anti-bonding. Bonding orbitals are lower in energy than the original atomic orbitals, while anti-bonding orbitals are higher in energy.

**Hint:** Remember that bonding orbitals stabilize the molecule, while anti-bonding orbitals destabilize it.

### Step 2: Identify the Orbitals Involved
For a diatomic molecule like nitrogen (N2), the relevant atomic orbitals are:
- 1s
- 2s
- 2p (which includes 2px, 2py, and 2pz)

When these orbitals combine, they form molecular orbitals:
- Bonding: σ1s, σ2s, σ2p (π2p)
- Anti-bonding: σ*1s, σ*2s, π*2p

**Hint:** Look for the distinction between bonding and anti-bonding orbitals. Bonding orbitals are typically lower in energy.

### Step 3: Draw the Molecular Orbital Diagram
In the MO diagram:
- The lowest energy orbitals are at the bottom.
- The bonding orbitals (σ1s, σ2s, π2p) are lower than their corresponding anti-bonding orbitals (σ*1s, σ*2s, π*2p).
- The order of energy levels for the molecular orbitals is generally: σ1s < σ*1s < σ2s < σ*2s < π2p < π*2p < σ2p < σ*2p.

**Hint:** Pay attention to the arrangement of orbitals in the diagram; this will help you identify their energy levels.

### Step 4: Compare the Given Molecular Orbitals
From the question, we are given the following molecular orbitals to compare:
- σ2s*
- σ2pz
- π2py
- π2pz

Among these, we need to identify which one has the lowest energy.

**Hint:** Recall that anti-bonding orbitals (indicated by a star) have higher energy than bonding orbitals.

### Step 5: Determine the Lowest Energy Orbital
From the MO diagram and the comparison:
- σ2s* is an anti-bonding orbital and has higher energy.
- σ2pz, π2py, and π2pz are bonding orbitals, with π2p orbitals generally being higher in energy than σ2p orbitals.

Thus, the lowest energy orbital among the options provided is **σ2s** (not listed in the options, but it is the lowest overall). However, if we strictly consider the options given, **σ2pz** would be lower than the anti-bonding orbitals.

**Final Answer:** The molecular orbital with the lowest energy from the provided options is **σ2pz**.