Question

According to molecular orbital theory total no of electron pairs in oxygen molecule is
A.16
B.12
C.5
D.8

Answer 1

According to Molecular orbital theory molecular orbitals are formed by combining the atomic orbitals of the atoms in the molecules. Molecular orbital theory uses a linear combination of atomic orbitals (LCMO). Molecular orbits are divided into 3 types of bonding , anti-bonding and non- bonding molecular orbital respectively.

Formula used: In atoms, electrons occupy atomic orbitals but in molecules they occupy molecular orbitals which surround the molecule. Since molecular orbitals are the linear combination of atomic orbitals , which combine to form molecules.
Let us consider two atoms ${{A}}$ and ${{B}}$, which have atomic orbital described by wave function \[\mathop {{\Psi }}\nolimits_{{A}} \] and $\mathop {{\Psi }}\nolimits_{{B}} $ respectively.
If the electron cloud of these two atoms overlaps, we can obtain wave function for the molecule by LCAO. Which can described as
 $\mathop {{\Psi }}\nolimits_{{{MO}}} {{ = }}\,\mathop {{\Psi }}\nolimits_{{A}} {{ \pm }}\,\mathop {{\Psi }}\nolimits_{{B}} $
 When addition of the wave function take place the type of molecular orbital formed are bonding molecular orbital ( $\sigma $ ) .We can represent the wavefunction of bonding molecular orbital by
 $\mathop {{\Psi }}\nolimits_{{{B}}{{.M}}{{.O}}} \,{{ = }}\,\mathop {{\Psi }}\nolimits_{{A}} {{ + }}\,\mathop {{\Psi }}\nolimits_{{B}} $ , it has lower energy than the atomic orbitals involved.
When molecular orbital are formed by the subtraction of wave functions , called as anti- bonding molecular orbitals (${\sigma ^*}$). Hence we can written the wave function of anti-bonding molecular orbital by
 $\mathop {{\Psi }}\nolimits_{{{AMO}}} \,{{ = }}\,\mathop {{\Psi }}\nolimits_{{A}} \,{{ - }}\,\mathop {{\Psi }}\nolimits_{{B}} $ , it has higher energy than the atomic orbitals .
Therefore by the combination of two atomic orbitals , two molecular orbitals are formed , one is bonding molecular orbital with lower energy and other is antibonding molecular orbital with higher energy than the atomic orbitals.

Complete step by step solution:
First we have to learn the main postulates of molecular orbital theory
Atomic orbitals of comparable energy & proper symmetry combine together to form molecular orbitals.
The no.of molecular orbitals formed is equal to the no.of combining atomic orbitals.
When two atomic orbitals combine together two molecular orbitals are formed.In which one molecular orbital forms possess higher energy than corresponding atomic orbitals is called antibonding molecular orbital, and the other has lower energy is called bonding molecular orbital.
Aufbau principle:This principle states that those molecular orbitals which have the lowest energy filled first .
Pauli exclusion principle:According to this principle each molecular orbital can accommodate a maximum of two electrons having opposite spin.
The order of increasing energy of molecular orbitals obtained by combination of atomic orbitals of two atoms can written as
For lighter molecules having electrons $ \leqslant 14$
                 ${{\sigma 1s}}\,\,{{ < }}\,{{{\sigma }}^{{*}}}{{1s}}\,{{ < }}\,{{\sigma 2s}}\,{{ < }}{{{\sigma }}^{{*}}}{{2s}}\,{{ < }}\,{{\Pi 2}}{{{p}}_{{y}}}{{ = \Pi 2}}{{{p}}_{{z}}}{{ < \sigma 2}}{{{p}}_{{x}}}{{ < }}\,{{{\Pi }}^{{*}}}{{2}}{{{p}}_{{y}}}{{ = }}{{{\Pi }}^{{*}}}{{2}}{{{p}}_{{z}}}{{ < }}{{{\sigma }}^{{*}}}{{2}}{{{p}}_{{x}}}$
 For heavier molecules having electrons $ > 14$
      ${{\sigma 1s}}\,{{ < }}{{{\sigma }}^{{*}}}{{1s}}\,{{ < }}\,{{\sigma 2s}}\,{{ < }}{{{\sigma }}^{{*}}}{{2s}}\,{{ < \sigma 2}}{{{p}}_{{x}}}\,{{ < \Pi 2}}{{{p}}_{{y}}}{{ = \Pi 2}}{{{p}}_{{z}}}\,{{ < }}{{{\Pi }}^{{*}}}{{2}}{{{p}}_{{y}}}{{ = }}\,{{{\Pi }}^{{*}}}{{2}}{{{p}}_{{z}}}\,{{ < }}\,{{{\sigma }}^{{*}}}{{2}}{{{p}}_{{x}}}$
 Now we can consider oxygen molecules, Each oxygen atom consists of $8$ electrons .Thus for oxygen molecules contain a total 16 electrons that is 8 pairs of electrons.So here oxygen molecule comes under heavier molecules having no. of electrons higher than 14.
Hence by molecular orbital theory we can written as
${{\sigma 1}}{{{s}}^{{2}}}\,{{ < }}\,{{{\sigma }}^{{*}}}{{1}}{{{s}}^{{{2}}\,}}\,{{ < }}\,{{\sigma 2}}{{{s}}^{{2}}}\,{{ < }}\,{{{\sigma }}^{{*}}}{{2}}{{{s}}^{{2}}}\,{{ < }}\,{{\sigma 2}}{{{p}}_{{x}}}^{{2}}\,{{ < }}\,{{\Pi 2}}{{{p}}^{{2}}}_{{y}}{{ = \Pi 2}}{{{p}}^{{2}}}_{{z}}\,{{ < }}\,{{{\Pi }}^{{*}}}{{2}}{{{p}}^{{1}}}_{{y}}\,{{ = }}\,{{{\Pi }}^{{*}}}{{2}}{{{p}}^{{1}}}_{{z}}$
So the oxygen molecule consists of 8 electron pairs.

So, the correct answer is option D.

Note: By using molecular orbital theory we can calculate bond order of a molecule also magnetic property can be known. Major limitation of molecular orbital theory is it doesn’t give any idea about the geometry and shape of the molecule.