Calculate CFSE and Magnetic Moment from d-Electron Count
Both CFSE and magnetic moment reduce to one skill: correctly filling t₂g/eg (or e/t₂ for tetrahedral) with the right number of d-electrons, given the metal's oxidation state and the ligand's field strength.
CFSE & Magnetic Moment Calculations is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Counting unpaired electrons drives paramagnetism
[Cu(H₂O)₄]2+ and [Cu(NH₃)₄]2+ are both Cu²⁺ (d₉) regardless of ligand, so both have exactly 1 unpaired electron and the same spin-only magnetic moment: μ = √(n(n+2)) = √3 = 1.73 BM for both. Choose B. A high-spin d₆ ion with a weak-field ligand keeps more unpaired electrons than the same d₆ ion with a strong-field ligand — ligand strength, not just d-count, decides pairing.
Spin-only formula across common configurations
A high-spin d₅ ion like [FeF₆]3- or [MnCl₆]3- has 5 unpaired electrons (maximum possible for any configuration) and the highest simple spin-only moment among first-row transition ions.
d₈ across three geometries gives three different answers
A d₈ ion's magnetic moment depends entirely on geometry: octahedral d₈ keeps 2 unpaired electrons (2.8 BM), tetrahedral d₈ also keeps 2 unpaired (2.8 BM, since Δt is too small to force pairing), but square planar d₈ pairs completely (0 BM, diamagnetic) — because the dx₂-y₂ orbital is pushed high enough that all electrons pair into the four lower orbitals.
CFSE follows the electron-filling pattern, not just d-count
CFSE magnitude doesn't rise smoothly across a d-electron series for same-charge ions, because half-filled and fully-filled t₂g/eg configurations reset the stabilisation calculation each time.
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- ✓Same metal ion (same d-count) can still have different unpaired-electron counts if ligand field strength differs.
- ✓Spin-only formula: μ = √(n(n+2)) BM — memorise 1.73, 2.83, 3.87, 4.90, 5.92 for n = 1 through 5.
- ✓d₈ is diamagnetic (0 BM) ONLY in square planar geometry; it stays paramagnetic (2.8 BM) in both octahedral and tetrahedral.
- ✓CFSE must be computed by filling t₂g (−0.4Δo each) and eg (+0.6Δo each) according to the actual high-spin/low-spin pattern, not just counted from d-electron total.
Don't assume identical d-electron count means identical magnetic moment — ligand field strength and geometry both change how those electrons actually fill the orbitals. Square planar d₈ is the single most-tested exception (diamagnetic, unlike octahedral/tetrahedral d₈).
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