Coordination Compounds: Crystal Field Theory at a Glance
A coordination compound’s colour and magnetism are set by its geometry before any splitting diagram is drawn, and most marks are lost in that order of operations.
A topic note mapping the JEE coordination-compound facts — geometry, splitting, magnetic moment, colour — to the crystal field parameters the exam actually uses.
How this actually works
The geometry-first habit
The first thing the JEE asks is not "what colour" but "what geometry", and everything after flows from that. Tetrahedral complexes always pair spins loosely, because Δ_t is four-fifths of the octahedral splitting and is usually too small to force pairing. Octahedral complexes split into t2g and eg, and whether they pair depends on the ligand. Fix the geometry first and the rest of the question is a lookup.
Reading the spectrochemical series
The spectrochemical series orders ligands by the splitting they impose. The JEE version of the table carries only the top half: CN, en, NO₂ on the strong side, and I, Br, Cl, F, H₂O, NH₃ on the weak side. Place the ligand on the line, then decide pairing by comparing Δ against the pairing energy. The trap is to read weak-field ligands as "no splitting" — even the weakest ligand splits, it just splits by less than the pairing energy.
Magnetic moment as a headcount
The magnetic moment is a direct count of unpaired electrons: μ = √(n(n+2)). For octahedral complexes the JEE values that appear are n = 5 (high-spin d⁵), n = 4 (low-spin d⁶), n = 3 (d³), and n = 2 (low-spin d⁷). Match the observed μ to an n, then read geometry and ligand strength off the table. A compound reporting μ = 5.92 BM is a high-spin d⁵ — no geometry needed, and the candidate who starts by guessing geometry has already made the problem harder than it is.
Colour and wavelength
The absorbed wavelength equals the splitting energy, and the observed colour is the complement. The JEE gives you the observed colour and asks which of the options could be correct, so the practical skill is running the complement table in both directions. Once the Δ values are ordered by ligand strength, the ordering of the absorption wavelength follows immediately.
Coordination Compounds: Crystal Field Theory at a Glance: the facts to keep
| Geometry first | Tetrahedral complexes always pair spins loosely, because Delta_t is four-fifths of the octahedral splitting |
|---|---|
| Spectrochemical series | Strong side: CN, en, NO2. Weak side: I, Br, Cl, F, H2O, NH3 |
| The pairing decision | Compare Delta against the pairing energy; a weak ligand still splits, just by less |
| Magnetic moment | mu = sqrt(n(n+2)), so the observed value is a direct count of unpaired electrons |
| Common moments | n = 1 gives 1.73 BM, n = 2 gives 2.83, n = 3 gives 3.87, n = 4 gives 4.90, n = 5 gives 5.92 |
| Colour | The absorbed wavelength equals the splitting energy; the observed colour is its complement |
Questions students ask about this
Why do tetrahedral complexes never pair?
The crystal field splitting in a tetrahedron is four-fifths of the octahedral splitting in the opposite direction, so Δ_t is always smaller than the electron pairing energy. The complex stays high-spin regardless of the ligand.
How do I read a magnetic moment quickly?
Try n = 1 to 6 and see which gives μ² close to the reported value. n = 1 gives 1.73, n = 2 gives 2.83, n = 3 gives 3.87, n = 4 gives 4.90, n = 5 gives 5.92 BM. The nearest match is the unpaired-electron count.