Question

Which of the following ions has the maximum magnetic moment?
A. \[M{n^{ + 2}}\]
B. \[F{e^{ + 2}}\]
C. \[T{i^{ + 2}}\]
D. \[C{r^{ + 2}}\]

Answer 1

Hint: The elements turn into ions to attain nearest inert or noble gas configuration. These ions have unpaired electrons. The presence of unpaired electrons makes the ions attract or align in presence of a magnetic field. Higher is the number of unpaired electrons the maximum will be the magnetic moment.

Formula used:
\[\mu = \sqrt {n\left( {n + 2} \right)} BM\]
\[\mu \] is magnetic moment
n is number of unpaired electrons
BM is Bohr magnetons which is the unit of magnetic moment

Complete step by step solution:
Given four ions are \[M{n^{ + 2}}\] , \[F{e^{ + 2}}\] , \[T{i^{ + 2}}\], and \[C{r^{ + 2}}\]
\[M{n^{ + 2}}\] has the electronic configuration of \[\left[ {Ar} \right]3{d^5}\] which has the five valence electrons. Substitute the value of \[n = 5\] in the above formula,
\[\mu = \sqrt {5\left( {5 + 2} \right)} BM = 5.9BM\]
Th magnetic moment is \[5.9BM\]
\[F{e^{ + 2}}\]has the electronic configuration of \[\left[ {Ar} \right]3{d^6}\] which has the six valence electrons. out of which four are unpaired electrons. Substitute the value of \[n = 4\] in the above formula,
\[\mu = \sqrt {4\left( {4 + 2} \right)} BM = 4.8BM\]
Th magnetic moment is \[4.8BM\]
\[T{i^{ + 2}}\] has the electronic configuration of \[\left[ {Ar} \right]3{d^2}\] which has two unpaired electrons. Substitute the value of \[n = 2\] in the above formula,
\[\mu = \sqrt {2\left( {2 + 2} \right)} BM = 2.8BM\]
Th magnetic moment is \[2.8BM\]
\[C{r^{ + 2}}\] has the electronic configuration of \[\left[ {Ar} \right]3{d^4}\] which has two unpaired electrons. Substitute the value of \[n = 4\] in the above formula,
\[\mu = \sqrt {4\left( {4 + 2} \right)} BM = 4.8BM\]
Th magnetic moment is \[4.8BM\]
Thus, \[M{n^{ + 2}}\] has the highest magnetic moment compared with all the given ions.
Therefore, Option A is correct.

Note: The presence of completely filled or unfilled electrons in orbitals leads to the formation of diamagnetic substances. The presence of unpaired electrons leads to the formation of paramagnetic substances which shows the magnetic moment. Thus, only unpaired electrons should be counted while calculating the magnetic moment.