Question

How many orbitals are singly occupied in $O_2$ molecule?
A. 2
B. 1
C. 3
D. 4

Answer 1

Hint: An orbital is a three dimensional space, where the probability of finding an electron is high. There are 4 types of orbitals: s, p, d, and f.

Complete step by step answer:
An orbital can be defined as a mathematical function that describes the location and the wave-like behaviour of an electron in an atom.
In this question, we are talking about the molecule of oxygen. So, the molecular orbital theory will come into play. It is a method for describing the electronic structure of the molecules with the help of quantum mechanics. The electrons, in this theory, are treated as moving under the influence of the nuclei in the whole molecule. We draw the molecular orbital diagram for determining the position of the electrons in a molecule. There are some rules according to which the MOD is filled.

Aufbau Principle
You place electrons in the lowest energy orbitals available.

Pauli Exclusion Principle
No orbital may hold more than two electrons, and they must have opposite spin.

Hund's Rule
Every orbital in a subshell must contain only one electron before any orbital can have two electrons. All electrons in singly occupied orbitals must have the same spin.

Each oxygen bonds to the other with its 1s, 2s, and 2p orbitals.
These 5 atomic orbitals combine to form 10 molecular orbitals.
These 10 MOs have capacity to accommodate up to 20 electrons, and each oxygen atom will contribute 8 electrons, so we have 16 electrons to put into the molecular orbitals of O₂.
We put two electrons into each of the $\sigma 1s$, $\sigma 1s$, $\sigma 2s$, $\sigma 2s$, and $\sigma 2p$ (10 electrons).
The next four electrons follow Hund's Rule and go in order into the $\pi x$, $\pi y$, $\pi x$, and $\pi y$ orbitals.
The remaining two electrons follow Hund's Rule and go in order into the ${\pi }^{\ast }x$ and ${\pi }^{\ast }y$ orbitals.
An oxygen molecule has two unpaired electrons.
The way the orbital energies work out, there will be 7 fully occupied MOs (14 electrons), 2 half-occupied MOs (1 electron in each), and 1 empty MO.
Therefore, there are 2 orbitals that are singly filled in $O_2$ molecules. Hence, the correct answer is option (a).

Note: While filling the molecular orbital diagram, keep a note of the bonding and the antibonding electrons in the $O_2$ molecule. This also helps in finding the bond order of the molecules.