SATHEE: Transition and InnerTransition Elements - Result Question 5

Transition and InnerTransition Elements - Result Question 5

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

(2019 Main, 10 April I)

(a) $S c^{3 +} < T i^{3 +} < T i^{2 +} < V^{2 +}$

(b) $S c^{3 +} < T i^{3 +} < V^{2 +} < T i^{2 +}$

(c) $T i^{3 +} < T i^{2 +} < S c^{3 +} < V^{2 +}$

(d) $V^{2 +} < T i^{2 +} < T i^{3 +} < S c^{3 +}$

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Solution:

The spin only magnetic moment $(μ)$ of each ion can be calculated as :

$μ = \sqrt{n (n + 2)} B M$

$[∵ n =$ No. of unpaired electron(s) $] \Rightarrow μ \propto n$ , i.e. higher the number of unpaired electron, higher will be the value of $μ$ .

Metal ion	$Z$	$n$ (for metal ion)	$M$ (BM)	Nature
$T i^{2 +}$	22	$2 (3 d^{2})$	$\sqrt{8}$	Paramagnetic
$V^{2 +}$	23	$3 (3 d^{3})$	$\sqrt{15}$	Paramagnetic
$T i^{3 +}$	22	$1 (3 d^{1})$	$\sqrt{3}$	Paramagnetic
$S c^{3 +}$	21	$0 (3 d^{0})$	0	Diamagnetic

Thus, the correct order of spin only magnetic moments of given hydrated ions will be

$S c^{3 +} < T i^{3 +} < T i^{2 +} < V^{2 +}$

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