Question 44

The correct order of spin only magnetic moments for the following complex ions is

Crystal Field Theory (CFT)

The spin-only magnetic moment ($$\mu$$) depends entirely on the number of unpaired electrons ($$n$$) present in the central metal ion:

$$mu = \sqrt{n(n+2)}$$ B.M
n = no. of unpaired electrons in the central metal ion

Strong Field Ligands (SFL): Like CN−, cause pairing of electrons (Low Spin complexes).
Weak Field Ligands (WFL): Like F− and Br−, do not cause pairing (High Spin complexes).

Step-by-Step Complex Evaluation

Complex Ion	Metal Oxidation State	d-Electron Count	Ligand Type	d-Orbital Arrangement	Unpaired Electrons ($n$)
$$[Fe(CN)_{6}]3^−$$	$$Fe^{3+}$$	$$d^5$$	CN− (SFL)	t2g5 eg0 (Paired)	1
$$[Mn(CN)_{6}]3^−$$	$$Mn^{3+}$$	$$d^4$$	CN− (SFL)	t2g4 eg0 (Paired)	2
$$[CoF_{6}]3^−$$	$$Co^{3+}$$	$$d^6$$	F− (WFL)	t2g4 eg2 (Unpaired)	4
$$[MnBr_{4}]2^−$$	$$Mn^{2+}$$	$$d^5$$	Br− (WFL)	e2 t23 (Tetrahedral)	5

Conclusion Order

Since the magnetic moment increases directly with the number of unpaired electrons ($$n$$):

Correct Option: [Fe(CN)$$_6$$]$$^{3-}$$ < [Mn(CN)$$_6$$]$$^{3-}$$ < [CoF$$_6$$]$$^{3-}$$ < [MnBr$$_4$$]$$^{2-}$$ is Option C

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