Question

Consider the hydrated ions of $T{{i}^{2+}} , {{V}^{2+}} , T{{i}^{3+}} and S{{c}^{3+}}$. The order of their spin-only magnetic moment is:

Answer 1

Hint:. Spin magnetic moment is the magnetic moment caused by the spin of elementary particles. Magnetic moments can also be defined in terms of an electric current and the area enclosed by the current loop.

Complete step by step answer:
Angular momentum corresponds to rotational motion while the magnetic moment can be related to the orbital angular momentum of the charge carriers in the constituting current. In magnetic materials the atomic and molecular dipoles have magnetic moments not just because of their quantized orbital angular momentum but also due to the spin of elementary particles between them.
Spin only magnetic moment is represented by µ and can be calculated from the formula
$\mu =\sqrt{n(n+2)}$; where n = number of unpaired electrons
$T{{i}^{2+}}=[Ar]3{{d}^{2}}$; n =2 ; $\therefore \mu =\sqrt{2(2+2)}=\sqrt{8}=2.82$
$T{{i}^{3+}}=[Ar]3{{d}^{1}}$; n =1; $\therefore \mu =1(1+2)=3$
$S{{c}^{3+}}=1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}$; n = 0 ; $\therefore \mu =\sqrt{1(1+2)}=\sqrt{3}=1.73$
${{V}^{2+}}=[Ar]3{{d}^{3}}$; n =3 ; $\therefore \mu =\sqrt{3(3+2)}=\sqrt{15}=3.87$

Note: Hydrated ion can be defined as the solvated ion which consists of an ion in the middle which is surrounded by aligned solvent molecules who surround the ion in a spherical shell when their solvent is water.