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Q.(a) What is meant by crystal field splitting energy ? For a d4d^4 ion, write the configuration if

(i) Δo<P\Delta_o < P, and
(ii) Δo>P\Delta_o > P.
(b) Explain why in tetrahedral coordination entities, low spin configurations are rarely observed.
CBSECBSE Class XII Board 2025Subjective· 3mImportance★★★★★
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Crystal field splitting energy (Δ\Delta) is the energy gap between t2gt_{2g} and ege_g orbitals in a complex. For a d4d^4 ion: (i) when Δo<P\Delta_o < P, configuration is t2g3eg1t_{2g}^3 e_g^1 (high spin);

(ii) when Δo>P\Delta_o > P, configuration is t2g4eg0t_{2g}^4 e_g^0 (low spin). Tetrahedral complexes rarely show low spin because Δt\Delta_t is too small to overcome pairing energy PP.

Understanding Crystal Field Splitting

When a transition metal ion sits inside a crystal field created by surrounding ligands, its five dd-orbitals are no longer degenerate. In an octahedral field, the dxyd_{xy}, dyzd_{yz}, and dzxd_{zx} orbitals (the t2gt_{2g} set) point between the ligands and are stabilised, while the dx2−y2d_{x^2-y^2} and dz2d_{z^2} orbitals (the ege_g set) point directly at the ligands and are destabilised. The energy gap between these two sets is called the crystal field splitting energy, denoted Δo\Delta_o (or 10Dq10 Dq).

The key question for any dnd^n configuration is: do electrons prefer to pair up in the lower t2gt_{2g} orbitals, or do they spread out into the higher ege_g orbitals? The answer depends on the competition between Δo\Delta_o and the pairing energy PP — the energy cost of forcing two electrons into the same orbital.

Δo=Energy gap between t2g and eg orbitals in octahedral field\Delta_o = \text{Energy gap between } t_{2g} \text{ and } e_g \text{ orbitals in octahedral field}


(a) Configuration for a d4d^4 ion

For a d4d^4 ion, we have four electrons to place in the dd-orbitals. The first three electrons go into the three t2gt_{2g} orbitals, one each, with parallel spins (Hund's rule). The fourth electron faces a choice.

Case (i): Δo<P\Delta_o < P — The splitting is small, so it costs less energy to promote the electron to the ege_g level than to pair it up in the t2gt_{2g} set. The fourth electron goes into the higher energy ege_g orbital with parallel spin. This gives the high-spin configuration:

t2g3eg1t_{2g}^3 e_g^1

All four electrons are unpaired — the complex is paramagnetic with four unpaired electrons.

Case (ii): Δo>P\Delta_o > P — The splitting is large, so it costs less energy to pair the fourth electron in the t2gt_{2g} set than to promote it to ege_g. The fourth electron pairs up with one of the t2gt_{2g} electrons. This gives the low-spin configuration:

t2g4eg0t_{2g}^4 e_g^0

Now only two electrons are unpaired (since one t2gt_{2g} orbital contains a pair).

Watch out

A common mistake is to write t2g4eg0t_{2g}^4 e_g^0 as having four unpaired electrons. Remember: four electrons in three orbitals means one orbital must contain a pair — so only two electrons are unpaired, not four.


(b) Why low spin is rare in tetrahedral complexes

In a tetrahedral crystal field, the splitting pattern is inverted compared to octahedral. The ee set (dx2−y2d_{x^2-y^2} and dz2d_{z^2}) is lower in energy, and the t2t_2 set (dxyd_{xy}, dyzd_{yz}, dzxd_{zx}) is higher. The splitting energy Δt\Delta_t is related to Δo\Delta_o by:

Δt≈49Δo\Delta_t \approx \frac{4}{9} \Delta_o

This is a much smaller gap — typically only about 40–50% of the octahedral value. Meanwhile, the pairing energy PP remains roughly the same (it depends on the metal ion, not the geometry). …

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