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Question #44864

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The Question

The hypothetical tetrahedral complex $\ce{[RuCl4]^{2-}}$ ( $4d^6$ ) exhibits a high-spin configuration with a crystal field splitting energy $\Delta_t = 10,000 \text{ cm}^{-1}$ and a pairing energy $P = 13,500 \text{ cm}^{-1}$ . For the isostructural $\ce{[OsCl4]^{2-}}$ ( $5d^6$ ) complex, the lanthanoid contraction results in nearly identical ionic radii. However, due to the greater radial extension of the 5d orbitals, $\Delta_t$ for the Os complex is exactly 50% larger than that of the Ru complex, while its pairing energy $P$ decreases to $12,000 \text{ cm}^{-1}$ . Calculate the expected spin-only magnetic moment ( $\mu_s$ ) and the Crystal Field Stabilization Energy (CFSE, excluding pairing energy) for the $\ce{[OsCl4]^{2-}}$ complex.

Options

A.
$2.83 \text{ B.M.}, -24,000 \text{ cm}^{-1}$
B.
$4.90 \text{ B.M.}, -9,000 \text{ cm}^{-1}$
C.
$4.90 \text{ B.M.}, -6,000 \text{ cm}^{-1}$
D.
$0.00 \text{ B.M.}, -36,000 \text{ cm}^{-1}$

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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

Lanthanoid Contraction cause|Tetrahedral Splitting Patterns

Why This Question Is Tricky

Common Mistakes

This problem targets the rote-memorized rule that 'tetrahedral complexes are always high-spin because $\Delta_t < P$ '.

Students often fall into the trap of assuming that because the Lanthanoid Contraction makes 4d and 5d ionic radii nearly identical, their crystal field splitting energies must also be identical (leading to Distractor C).

The hidden variable is the relativistic radial expansion of 5d orbitals, which significantly increases covalency and $\Delta_t$ , while the larger diffuse orbitals simultaneously lower the pairing energy $P$ .

This unique combination allows 5d elements to form low-spin tetrahedral complexes, completely flipping the expected $e^3 t_2^3$ high-spin configuration to $e^4 t_2^2$ .

Distractor D catches students who incorrectly apply octahedral splitting rules ( $t_{2g}$ lower, $e_g$ higher) to a tetrahedral geometry.

Quick Facts About This Question

Question Information

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