Question

How many molecular orbitals are in ${{O}_{2}}$ ?

Answer 1

Hint : We know that an orbital is a three dimensional space, where the probability of finding an electron is high. There are four types of orbitals: $s,\text{ }p,\text{ }d,$ and $f.$ ${{O}_{2}}$ has an infinite number of molecular orbitals, but only nine of them are occupied in the ground state.

Complete Step By Step Answer:
An orbital can be defined as a mathematical function that describes the location and the wave-like behavior 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.
Pauli Exclusion Principle: No orbital may hold more than two electrons, and they must have opposite spin and Aufbau’s Principle: We place electrons in the lowest energy orbitals available. ${{O}_{2}}$ has an infinite number of molecular orbitals, but only nine of them are occupied in the ground state.
Each $O$ atom contributes eight electrons to the ${{O}_{2}}$ molecule. We use the Pauli Exclusion Principle and Hund's Rule to add the $16$ electrons to the molecular orbitals in an Aufbau’s process. The molecule then has five fully occupied bonding molecular orbitals, two fully occupied antibonding orbitals, and two half-filled molecular orbitals.
Therefore, there are $10$ molecular orbitals each oxygen bond to the other with its $1s,\text{ }2s$ , 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 ${{O}_{2}}$ .

Note :
While filling the molecular orbital diagram, keep a note of the bonding and the antibonding electrons in the molecule. This also helps in finding the bond order of the molecules. Each oxygen bonds to the other with its $1s,\text{ }2s,$ and $2p$ orbitals. These 5 atomic orbitals combine to form $10$ molecular orbitals.