Which of the following orderof energies of molecular orbitals of `N_(2)` is correct?

Options

A. `(pi 2p_(y)) lt (sigma 2p_(z)) lt (pi^(***)2p_(x))approx(pi^(***)2p_(y))`
B. `(pi2p_(y)) gt (sigma2p_(z)) gt (pi^(***)2p_(x)) approx(pi^(***)2p_(y))`
C. `(pi 2 p_(y)) lt (sigma2p_(z)) gt (pi^(***)2p_(x)) approx(pi^(***)2p_(y))`
D. `(pi 2p_(y)) gt (sigma2p_(z)) lt (pi^(***)2p_(x)) approx(pi^(***)2p_(y))`

Explanation

To determine the correct order of energies of molecular orbitals for nitrogen (N₂), we will follow these steps:

### Step 1: Understand Molecular Orbital Theory
Molecular Orbital (MO) Theory explains how atomic orbitals combine to form molecular orbitals. These molecular orbitals can be bonding or antibonding, and their energy levels depend on the atomic orbitals involved.

### Step 2: Identify the Molecular Orbitals for N₂
For diatomic molecules like nitrogen, the molecular orbitals are formed from the combination of atomic orbitals. The relevant molecular orbitals for nitrogen (N₂) are:
- σ1s
- σ*1s (antibonding)
- σ2s
- σ*2s (antibonding)
- π2px
- π2py (degenerate orbitals)
- σ2pz
- π*2px (antibonding)
- π*2py (antibonding)
- σ*2pz (antibonding)

### Step 3: Establish the Energy Order for N₂
According to MO theory, the energy order of these molecular orbitals for nitrogen is as follows:
1. σ1s
2. σ*1s
3. σ2s
4. σ*2s
5. π2px = π2py (degenerate)
6. σ2pz
7. π*2px = π*2py (degenerate)
8. σ*2pz

### Step 4: Analyze the Given Options
We need to check the given options against the established energy order. The correct order should reflect that:
- π2px and π2py have lower energy than σ2pz.
- σ2pz has lower energy than π*2px and π*2py.

### Step 5: Verify the Correct Answer
From the analysis, we find that the order of energies should be:
- π2py < σ2pz < π*2px = π*2py

If the given option matches this order, it is the correct answer.

### Conclusion
After analyzing the options, we conclude that the correct order of energies of molecular orbitals for nitrogen (N₂) is represented by option A.

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