Among the following order of energies of molecular orbitals of `O_2` choose the correct one

Options

A. `E(pi2p_x)= E(pi2p_y)ltE(sigma2p_z)lt(Epi^ast2p_x)= E(pi^ast2+-p_y)`
B. `E(pi2p_x)= E(pi2p_y)gtE(sigma2p_z)gt(Epi^ast2p_x)= E(pi^ast2p_y)`
C. `E(pi2p_x)= E(pi2p_y)ltE(sigma2p_z)lt(Epi^ast2p_x)= E(pi^ast2p_y)`
D. `E(pi2p_x)= E(pi2p_y)gtE(sigma2p_z)lt(Epi^ast2p_x)= E(pi^ast2p_y)`

Answer

To determine the correct order of energies of molecular orbitals for the oxygen molecule (O₂), we need to follow these steps:

### Step 1: Determine the Total Number of Electrons
Oxygen (O) has an atomic number of 8, so O₂ has a total of 16 electrons (8 from each oxygen atom).

### Step 2: Understand the Molecular Orbital Theory
In molecular orbital theory, the molecular orbitals are formed by the combination of atomic orbitals. The order of energy levels of these molecular orbitals can vary depending on the number of electrons.

### Step 3: Write the Order of Molecular Orbitals for O₂
For O₂, which has 16 electrons, the order of filling the molecular orbitals is as follows:
1. σ1s
2. σ*1s
3. σ2s
4. σ*2s
5. σ2p (or σ2pz)
6. π2p (or π2px and π2py)
7. π*2p (or π*2px and π*2py)
8. σ*2p

However, for O₂ specifically, the order of energies is:
- σ1s < σ*1s < σ2s < σ*2s < π2px = π2py < σ2pz < π*2px = π*2py < σ*2pz

### Step 4: Fill the Molecular Orbitals
Now, we fill the molecular orbitals with the 16 electrons:
- σ1s (2 electrons)
- σ*1s (2 electrons)
- σ2s (2 electrons)
- σ*2s (2 electrons)
- π2px (2 electrons)
- π2py (2 electrons)
- σ2pz (2 electrons)

This gives us a total of 14 electrons filled. The remaining 2 electrons will occupy the next available orbitals, which are π*2px and π*2py.

### Step 5: Identify the Correct Order of Energies
Based on the filling order and the energy levels, we can summarize the order of energies of the molecular orbitals for O₂ as:
- σ1s < σ*1s < σ2s < σ*2s < π2px = π2py < σ2pz < π*2px = π*2py < σ*2pz

### Conclusion
From the given options, we can identify the correct order of energies of molecular orbitals for O₂. The third option provided matches the order we derived.