Question

Match the metal ions given in Column I with the spin magnetic moments of the ions given in Column II and assign the correct code :

Column I		Column II
a.	Co3+	i.	\(\sqrt8\) B.M.
b.	Cr3+	ii.	\(\sqrt{35}\) B.M.
c.	Fe3+	iii.	\(\sqrt3\) B.M.
d.	Ni2+	iv.	\(\sqrt{24}\) B.M.
		v.	\(\sqrt{15}\) B.M.

• A. a-iv, b-v, c-ii, d-i
• B. a-iv, b-i, c-ii, d-iii
• C. a-i, b-ii, c-iii, d-iv
• D. a-iii, b-v, c-i, d-ii

Answer 1

The Correct Option is A

To match the metal ions from Column I to the spin magnetic moments in Column II, we need to calculate the spin magnetic moment for each metal ion using the formula:

\(\mu = \sqrt{n(n+2)}\) B.M.

where n is the number of unpaired electrons.

1. For Co³⁺:
   Electronic configuration of Co is [Ar] 3d⁷ 4s². For Co³⁺, three electrons are removed, giving the configuration [Ar] 3d⁶. It has 4 unpaired electrons (in the high spin state).
   The spin magnetic moment is: \(\mu = \sqrt{4(4+2)} = \sqrt{24}\) B.M.
   Therefore, Co³⁺ corresponds to option iv.
2. For Cr³⁺:
   Electronic configuration of Cr is [Ar] 3d⁵ 4s¹. For Cr³⁺, three electrons are removed, giving [Ar] 3d³. It has 3 unpaired electrons.
   The spin magnetic moment is: \(\mu = \sqrt{3(3+2)} = \sqrt{15}\) B.M.
   Therefore, Cr³⁺ corresponds to option v.
3. For Fe³⁺:
   Electronic configuration of Fe is [Ar] 3d⁶ 4s². For Fe³⁺, three electrons are removed, giving [Ar] 3d⁵. It has 5 unpaired electrons.
   The spin magnetic moment is: \(\mu = \sqrt{5(5+2)} = \sqrt{35}\) B.M.
   Therefore, Fe³⁺ corresponds to option ii.
4. For Ni²⁺:
   Electronic configuration of Ni is [Ar] 3d⁸ 4s². For Ni²⁺, two electrons are removed, giving [Ar] 3d⁸. It has 2 unpaired electrons.
   The spin magnetic moment is: \(\mu = \sqrt{2(2+2)} = \sqrt{8}\) B.M.
   Therefore, Ni²⁺ corresponds to option i.

Thus, the matching of ions to their corresponding spin magnetic moments is as follows:

• a. Co³⁺ - iv. \(\sqrt{24}\) B.M.
• b. Cr³⁺ - v. \(\sqrt{15}\) B.M.
• c. Fe³⁺ - ii. \(\sqrt{35}\) B.M.
• d. Ni²⁺ - i. \(\sqrt{8}\) B.M.

Hence, the correct option is: a-iv, b-v, c-ii, d-i.