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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
- a. $Co^{3+}$
- b. $Cr^{3+}$
- c. $Fe^{3+}$
- d. $Ni^{2+}$
Column II
- i. $\sqrt{8}$ BM
- ii. $\sqrt{35}$ BM
- iii. $\sqrt{3}$ BM
- iv. $\sqrt{24}$ BM
- v. $\sqrt{15}$ BM
Correct answer: a → iv, b → v, c → ii, d → i
Explanation
Use $\mu = \sqrt{n(n+2)}$ BM with n unpaired electrons.
Detailed Solution
$Co^{3+} = [Ar]\,3d^6$, unpaired $e^-$ (n) = 4; spin magnetic moment $= \sqrt{4(4+2)} = \sqrt{24}$ BM
$Cr^{3+} = [Ar]\,3d^3$, unpaired $e^-$ (n) = 3; spin magnetic moment $= \sqrt{3(3+2)} = \sqrt{15}$ BM
$Fe^{3+} = [Ar]\,3d^5$, unpaired $e^-$ (n) = 5; spin magnetic moment $= \sqrt{5(5+2)} = \sqrt{35}$ BM
$Ni^{2+} = [Ar]\,3d^8$, unpaired $e^-$ (n) = 2; spin magnetic moment $= \sqrt{2(2+2)} = \sqrt{8}$ BM
Correct match: a-iv, b-v, c-ii, d-i.