In aqueous solution of K 4[Fe(CN) 6], the allowed transition(s) is (are)

GATE 2024 CY – Question 50

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. · 2 marks · Multiple select

In aqueous solution of $\mathrm{K_4[Fe(CN)_6]}$, the allowed transition(s) is (are)

$^5T_{2g}$ to $^3E_g$
$^1A_{1g}$ to $^1T_{1g}$
$^1A_{1g}$ to $^1T_{2g}$
$^5T_{2g}$ to $^5E_g$

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Correct answer: (B) $^1A_{1g}$ to $^1T_{1g}$; (C) $^1A_{1g}$ to $^1T_{2g}$

Explanation

In $\text{K}_4[\text{Fe(CN)}_6]$, Fe(II) is a **low-spin $d^6$** ion ($t_{2g}^6$) in an octahedral field. The ground state is a spin-singlet, $^1A_{1g}$.

**Spin selection rule:** only transitions with $\Delta S=0$ are allowed. From a singlet ground state, the allowed transitions go to **singlet** excited states.

**$^5T_{2g}\to{}^3E_g$:** starts from a quintet state, which is not the ground state here, and changes spin. ✗
**$^1A_{1g}\to{}^1T_{1g}$:** singlet to singlet, spin-allowed (and Laporte-allowed as a vibronically allowed $d$-$d$ band). ✓
**$^1A_{1g}\to{}^1T_{2g}$:** singlet to singlet, spin-allowed. ✓
**$^5T_{2g}\to{}^5E_g$:** the initial state is not the ground state of this complex. ✗

Answer **B and C**.