In the following which of the two are paramagnetic?
a.) \[{N_2}\]
b.) \[CO\]
c.) \[{B_2}\]
d.) \[N{O_2}\]
Correct answer is:
a.) a and c
b.) b and c
c.) c and d
d.) b and d

Hint: To solve this question, we must have a clear concept of molecular orbital theory. We can easily predict if a molecule is paramagnetic or diamagnetic by simply looking at its electronic configuration.

Complete step by step answer:
Perhaps the easiest way to differentiate between paramagnetic and diamagnetic substances is by saying that Paramagnetic molecules are attracted to magnetic field while diamagnetic molecules are repelled by the magnetic field and while paramagnetic compounds have unpaired electrons, diamagnetic compounds the electrons all have paired spins.
While an odd number of electrons can clearly produce a paramagnetic ion, radical or molecule, molecules with an even number of electrons may also be paramagnetic, the most famous example of this is the oxygen molecule.
Now, we should write the electronic configuration in accordance with Molecular Orbital Theory and find out which of these molecules have unpaired electrons.
We see that
\[{N_2} = {(\sigma 1s)^2}{({\sigma ^*}1s)^2}{(\sigma 2s)^2}{({\sigma ^*}2s)^2}{(\pi 2{p_x})^2}{(\pi 2{p_y})^2}{(\sigma 2{p_z})^2}\]
\[CO = {(\sigma 1s)^2}{({\sigma ^*}1s)^2}{(\sigma 2s)^2}{({\sigma ^*}2s)^2}{(\pi 2p)^4}{(\sigma 2p)^2}\]
\[{B_2} = {(\sigma 1s)^2}{({\sigma ^*}1s)^2}{(\sigma 2s)^2}{(\pi 2{p_y})^1}{(\pi 2{p_z})^1}\]
From the periodic table, we know that the atomic number of nitrogen(N) is 7 and that of oxygen(O) is 8.
Hence, the total number of electrons for nitrogen dioxide is:
\[N{O_2} = 7 + 16 = 23\] this is odd, so it is definitely paramagnetic. We can say this without even finding the electronic configuration.
Hence, we can conclude that boron molecules and nitrogen dioxide molecules are paramagnetic.
Therefore, the correct answer is Option (C) c and d.

Additional information:
Electron spin is very important in determining the magnetic properties of an atom. If all of the electrons in an atom are paired up and share their orbital with another electron, then the total spin in each orbital is zero and the atom is diamagnetic.

Note: If we forget the Molecular Orbital Theory there is a way to experimentally determine if a substance is paramagnetic or diamagnetic by using a Gouy balance. It measures the apparent change in the mass of the sample as it is repelled or attracted by the region of high magnetic field between the poles.