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GATE 2024 CY – Question 12

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

The ground state of $[\mathrm{Cr(H_2O)_6}]^{2+}$ is

  1. $^5E_g$
  2. $^5T_{2g}$
  3. $^6A_{1g}$
  4. $^6A_{2g}$

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Correct answer: (A) $^5E_g$

Explanation

**Cr(II)** is a $d^4$ ion. With the weak-field ligand $H_2O$, the complex is high spin: $t_{2g}^3e_g^1$ with four unpaired electrons.

**Term symbol.** The free-ion ground term of $d^4$ is $^5D$ (spin multiplicity $2S+1=5$). In an octahedral field, $^5D$ splits into two terms: $^5E_g$ and $^5T_{2g}$.

For a $d^4$ configuration (the opposite of $d^6$ in this respect), the ground state is the $^5E_g$ term (the configuration $t_{2g}^3e_g^1$), and the $^5T_{2g}$ lies above it. The $^5E_g$ ground state is orbitally degenerate and is Jahn-Teller active, as expected for high-spin Cr(II).

The ground state is $^5E_g$ (option A).