Question

Which of the following has the highest value of magnetic moment?
A) $ F{e^{ + 2}} $
B) $ C{o^{ + 3}} $
C) $ {V^{ + 3}} $
D) $ T{i^{ + 3}} $

Answer 1

Hint: The substances that show magnetic properties show either Paramagnetism or diamagnetism. Most of the transition metal elements are paramagnetic in nature due to the presence of unpaired electrons in the d-subshells. More the no. of unpaired electrons in the substance, more will be the magnetic moment. So in this question, we need to find the no. of unpaired electrons in the respective ions.

Complete Step By Step Answer:
The formula to find the magnetic moment of the substance is: $ m = \sqrt {n(n + 2)} $
Where, m is the magnetic moment and n is the no. of unpaired electrons present in the ion. Let us find the magnetic moment of the given compounds one by one.
 $ F{e^{ + 2}} $ : The electronic configuration of Fe is $ Fe:[Ar]4{s^2}3{d^6} $ . The given ion is a di-cation of Fe, hence the electronic configuration will be $ F{e^{ + 2}}:[Ar]3{d^6} $ . The d shell has 5 orbitals. Hence it will have 4 unpaired electrons. The electronic configuration will be $ m = \sqrt {4(4 + 2)} = \sqrt {24} = 4.89\mu $
 $ C{o^{ + 3}} $ : The electronic configuration of Co is $ Co:[Ar]4{s^2}3{d^7} $ . The configuration of the ion will be $ C{o^{ + 3}}:[Ar]3{d^6} $ . Hence the magnetic moment will be same as above $ m = \sqrt {4(4 + 2)} = \sqrt {24} = 4.89\mu $
 $ {V^{ + 3}} $ : The electronic configuration of V will be $ V:[Ar]4{s^2}3{d^3} $ . The electronic configuration of the ion will be $ {V^{ + 3}}:[Ar]3{d^2} $ . It will have 2 unpaired electrons and the magnetic moment will be $ m = \sqrt {2(2 + 2)} = \sqrt 8 = 2.82\mu $
 $ T{i^{ + 3}} $ : : The electronic configuration of Ti will be $ Ti:[Ar]4{s^2}3{d^2} $ . The electronic configuration of the ion will be $ T{i^{ + 3}}:[Ar]3{d^1} $ . It will have 1 unpaired electron1 and the magnetic moment will be $ m = \sqrt {1(1 + 2)} = \sqrt 3 = 2.44\mu $
Therefore, the highest magnetic moment is found in $ F{e^{ + 2}} $ and $ C{o^{ + 3}} $ .
The correct answer is Option (A) and (B).

Note:
A laboratory method is also used for determining the magnetic moment, which is the Gouy method. In this method the sample is kept in the magnetic field and weighed. Later, it is weighed in the absence of a magnetic field. The difference between the two weights is calculated.