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Question #44871

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The Question

Consider the hexaaquacopper(II) complex ion, \ce{[Cu(H2O)6]^{2+}}, in an aqueous medium at 298 K. The experimentally observed effective magnetic moment ( $\mu_{eff}$ ) is approximately 1.95 BM, which is significantly higher than the calculated spin-only value ( $\mu_{so} = 1.73$ BM). Which of the following statements correctly identifies the structural geometry of the complex and the primary quantum mechanical origin of this magnetic deviation?

Options

A.
Tetragonal elongation (Z-out); the deviation is due to unquenched orbital angular momentum arising directly from the asymmetrically filled $e_g$ orbitals.
B.
Tetragonal elongation (Z-out); the deviation is due to spin-orbit coupling mixing the $t_{2g}$ and $e_g$ states, governed by $\mu_{eff} = \mu_{so}(1 - \frac{2\lambda}{\Delta_o})$ with $\lambda < 0$ .
C.
Tetragonal compression (Z-in); the deviation is due to spin-orbit coupling mixing the $t_{2g}$ and $e_g$ states, governed by $\mu_{eff} = \mu_{so}(1 - \frac{2\lambda}{\Delta_o})$ with $\lambda > 0$ .
D.
Perfect octahedral geometry; the deviation is due to the second-order Zeeman effect (Temperature Independent Paramagnetism) dominating at 298 K.

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Magnetic Moment Quenching|Crystal Field Splitting (Octahedral)|Valence Bond Theory Hybridization

Why This Question Is Tricky

Common Mistakes

This question tests the 'Spin-Only' trap and the nuances of Crystal Field Theory.

Students often blindly apply the spin-only formula ( $\mu = \sqrt{n(n+2)}$ ) and assume deviations are mere experimental errors.

The trap forces the recognition that while $e_g$ orbitals in a Jahn-Teller distorted $d^9$ complex have quenched orbital angular momentum, Spin-Orbit Coupling (SOC) mixes the $T_{2g}$ and $E_g$ states.

Furthermore, it tests the critical 'hidden variable' of the sign of the spin-orbit coupling constant ( $\lambda$ ): because $d^9$ is more than half-filled, $\lambda$ is negative, mathematically proving why the magnetic moment increases rather than decreases.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	D and F Block Elements - Class 12
Concept	Magnetic Moment Quenching
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free