Arrange the following complexes in increasing order of their magnetic moment
(A) \( [CoF_6]^{3-} \)
(B) \( [Co(H_2O)_6]^{2+} \)
(C) \( [FeF_6]^{3-} \)
(D) \( [Fe(CN)_6]^{4-} \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (D), (B), (A), (C)
The spin-only magnetic moment depends only on the number of unpaired electrons, n:
\( \displaystyle \mu = \sqrt{n(n+2)}\ \mathrm{BM} \)
The number of unpaired electrons follows from the d electron count of the metal ion and the ligand: a weak field ligand (\( \ce{F-} \), \( \ce{H2O} \)) leaves the electrons unpaired (high spin), while a strong field ligand (\( \ce{CN-} \)) pairs them (low spin).
(A) \( \ce{[CoF6]^3-} \): x + 6(−1) = −3, so Co is +3. Co (Z = 27) is \( \mathrm{[Ar]\,3d^{7}\,4s^{2}} \); \( \ce{Co^{3+}} \) is \( \mathrm{3d^{6}} \). \( \ce{F-} \) is weak field: n = 4, μ = √24 = 4.90 BM.
(B) \( \ce{[Co(H2O)6]^2+} \): Co is +2, \( \mathrm{3d^{7}} \). \( \ce{H2O} \) is weak field: n = 3, μ = √15 = 3.87 BM.
(C) \( \ce{[FeF6]^3-} \): x + 6(−1) = −3, so Fe is +3. Fe (Z = 26) is \( \mathrm{[Ar]\,3d^{6}\,4s^{2}} \); \( \ce{Fe^{3+}} \) is \( \mathrm{3d^{5}} \). \( \ce{F-} \) is weak field: n = 5, μ = √35 = 5.92 BM.
(D) \( \ce{[Fe(CN)6]^4-} \): x + 6(−1) = −4, so Fe is +2, \( \mathrm{3d^{6}} \). \( \ce{CN-} \) is strong field and pairs all six electrons: n = 0, μ = 0 (diamagnetic).
Shortcut: Only the number of unpaired electrons matters, so compare n = 0, 3, 4, 5 directly without working out μ. \( \ce{[Fe(CN)6]^4-} \) (zero) comes first and \( \ce{[FeF6]^3-} \) (five) last: only Option (1).