GATE 2026 CY – Question 16

Inorganic Chemistry · Transition Metals: Coordination chemistry – structure and isomerism, theories of bonding (VBT, CFT, and MOT). Metal-metal multiple bonds. Energy level diagrams in various crystal fields, CFSE, applications of CFT, Jahn-Teller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, selection rules, Orgel and Tanabe-Sugano diagrams, nephelauxetic effect and Racah parameter, charge-transfer spectra. Magnetic properties of transition metal complexes. Ray-Dutt and Bailar twists, Reaction mechanisms: kinetic and thermodynamic stability, associative, dissociative substitution and redox reactions. · 1 mark · Multiple choice

According to molecular orbital theory, the correct ground-state electronic configuration for $[\mathrm{Co}(\mathrm{NH_3})_6]^{3+}$ is

$a_{1g}^2t_{1u}^6e_g^4t_{2g}^6e_g^{*0}$
$a_{1g}^2t_{1u}^6t_{2g}^6e_g^4e_g^{*0}$
$t_{1u}^6a_{1g}^2e_g^4t_{2g}^6e_g^{*0}$
$a_{1g}^2t_{1u}^6e_g^4t_{2g}^4e_g^{*2}$

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Correct answer: (A) $a_{1g}^2t_{1u}^6e_g^4t_{2g}^6e_g^{*0}$

Explanation

**Ground-state configuration of $[\text{Co(NH}_3)_6]^{3+}$ by MO theory.**

Count the electrons: $\text{Co}^{3+}$ is $d^6$, and the six $\sigma$-donor $\text{NH}_3$ ligands supply 12 electrons. In total, $6+12=18$ electrons.

**Orbital energy order** for an octahedral complex with only $\sigma$ bonding:
- the bonding orbitals, $a_{1g}$ (lowest), $t_{1u}$ and $e_g$, which are mostly ligand in character and take the 12 ligand electrons;
- then the non-bonding $t_{2g}$ (metal $d_{xy},d_{xz},d_{yz}$);
- then the antibonding $e_g^*$.

Ammonia is a strong-field ligand, so the complex is low spin: the six metal $d$ electrons fill $t_{2g}$ completely, and $e_g^*$ stays empty.

$$a_{1g}^2\,t_{1u}^6\,e_g^4\,t_{2g}^6\,e_g^{*0}\quad(\text{option A}).$$