Question

Oxygen molecules are paramagnetic in nature. What is the paramagnetic content in terms of the magnetic moment in \[{{O}}_2^ - \]?
A) 1.732
B) 3
C) 1.5
D) 2.5

Answer 1

Hint: Molecular orbital theory is used to determine the magnetic behavior of the molecules. If there are unpaired electrons in the molecule, then such a molecule is paramagnetic in nature. If all electrons are paired then the substance or molecule is diamagnetic. The order of the energy of molecular orbitals is important to determine the magnetic nature of the substance. The magnetic moment is used to express the magnetic behavior of the substance which is calculated using the formula given below.

Formula used: The spin only magnetic moment formula is given as follows:
\[{{\mu = }}\sqrt {{{n}}\left( {{{n + 2}}} \right)} \] (i)
Here, the magnetic moment is represented as \[{{\mu }}\]and the number of unpaired electrons is n.

Complete step-by-step answer:
As per the Molecular Orbital Theory the species having total electron 14 or less the order of the molecular orbitals is given as follows:
\[{{(\sigma 1s)(\sigma *1s)(\sigma 2s)(\sigma *2s)(\pi 2px}}{{ = \pi 2py}}{{)(\sigma 2pz}}{{)(\pi *2px}}{{ = \pi *2py}}{{)(\sigma *2pz}}{{)}}\] (ii)
As per the Molecular Orbital Theory the species having total electron greater than 14 or the order of the molecular orbitals is given as follows:
\[{{(\sigma 1s)(\sigma *1s)(\sigma 2s)(\sigma *2s)(\sigma 2pz}}{{)(\pi 2px}}{{ = \pi 2py}}{{)(\pi *2px}}{{ = \pi *2py}}{{)(\sigma *2pz}}{{)}}\]……(iii)
Here, the molecule given is \[{{O}}_2^ - \] which contains are total 17 electrons. Hence, use the second energy order of the molecular orbitals.
Theses 17 electrons are filled in these orbitals as follows:
\[{{(\sigma 1}}{{{s}}^2}{{)(\sigma *1}}{{{s}}^2}{{)(\sigma 2}}{{{s}}^2}{{)(\sigma *2}}{{{s}}^2}{{)(\sigma 2p}}{{{z}}^2}{{)(\pi 2p}}{{{x}}^2}{{ = \pi 2p}}{{{y}}^2}{{)(\pi *2p}}{{{x}}^2}{{ = \pi *2p}}{{{y}}^1}{{)}}\]
It indicates that there is one unpaired electron in \[{{\pi *2py}}\]an orbital.

Now, to determine the magnetic moment use equation number(i),
\[{{\mu = }}\sqrt {{{n}}\left( {{{n + 2}}} \right)} \]
Here, substitute 1 for n.
\[\Rightarrow {{\mu = }}\sqrt {{{1}}\left( {{{1 + 2}}} \right)} \,{{B}}{{.M}}\]
\[\Rightarrow {{\mu = }}\sqrt {{{3}}\,} {{B}}{{.M}}\]
\[\Rightarrow {{\mu = 1}}{{.732}}\,{{B}}{{.M}}\]
Thus, the value of the magnetic moment of \[{{O}}_2^ - \] is \[{{1}}{{.732}}\,{{B}}{{.M}}\].

Hence the correct answer is option ‘C’.,

Note: The magnetic moment is used to express the magnetic behavior of the substance which is calculated using the formula given below. The magnetic moment is represented by the latter \[{{\mu }}\] and it is expressed in units of Bohr magneton.An increase in the number of unpaired electrons increases the value of the magnetic moment and increases is the paramagnetic nature of the substance.