Question

Calculate the magnetic moment of ${\rm{C}}{{\rm{r}}^{{\rm{3 + }}}}$
A. $2.90$
B. $3.57$
C. $4.12$
D. $3.87$

Answer 1

Hint: We know that the electronic configuration of chemical species is necessary for calculating the magnetic moment of any molecule or compound. The atomic orbital used for showing the electronic configuration is s, p, d and f. The formula which can be used for calculating the magnetic moment is ${\rm{\mu }} = \sqrt {{\rm{n}}\left( {{\rm{n}} + {\rm{2}}} \right)} $.

Complete step by step answer:
As we know, the atomic number of chromium is $24$. The electronic configuration of chromium is ${\rm{1}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{6}}}{\rm{3}}{{\rm{s}}^{\rm{2}}}{\rm{3}}{{\rm{p}}^{\rm{6}}}{\rm{3}}{{\rm{d}}^{\rm{5}}}{\rm{4}}{{\rm{s}}^{\rm{1}}}$. This is a stable element because it has a half-filled d orbital. So, in ${\rm{C}}{{\rm{r}}^{{\rm{3 + }}}}$ molecule the removal of three electrons from original chromium molecule take place. So, the electronic configuration of ${\rm{C}}{{\rm{r}}^{{\rm{3 + }}}}$ is ${\rm{1}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{6}}}{\rm{3}}{{\rm{s}}^{\rm{2}}}{\rm{3}}{{\rm{p}}^{\rm{6}}}{\rm{3}}{{\rm{d}}^3}$. It has three unpaired electrons and they are also their valence electrons. The magnetic moment is that tendency which generally is used for identifying the arrangement of the species around the given magnetic field. The formula which can be used for calculating the magnetic moment is shown below.
${\rm{\mu }} = \sqrt {{\rm{n}}\left( {{\rm{n}} + {\rm{2}}} \right)} $
Where, ${\rm{\mu }}$ is the magnetic moment and n is the number of unpaired electrons present in the molecule.
So, the value of unpaired electrons in ${\rm{C}}{{\rm{r}}^{{\rm{3 + }}}}$ is three. Substitute all the respective values in the above equation. We get,
$\begin{array}{c}
{\rm{\mu }} = \sqrt {3\left( {3 + {\rm{2}}} \right)} \\
 = \sqrt {3\left( 5 \right)} \\
 = \sqrt {\left( {15} \right)} \\
 = 3.87
\end{array}$

Hence, the correct answer for this question is D.

Note:
Generally, the magnetic moment is used to show the magnetic strength and the orientation of species in the respective magnetic field.