Ni(en)3^2+ UV-Vis Spectrum Analysis

This solution explains how to correlate the observed absorbance maxima in the UV-visible spectrum of the $[Ni(en)_3]^{2+}$ complex with its specific d-d electronic transitions.

Ni^2+ Configuration and Ground State

The central metal ion is Nickel ($Ni$), with atomic number 28. The $Ni^{2+}$ ion has a $3d^8$ electron configuration. In an octahedral ($O_h$) ligand field, such as that created by the three ethylenediamine (en) ligands in $[Ni(en)_3]^{2+}$, the ground state term symbol for a $d^8$ configuration is $^3A_{2g}$.

Octahedral Electronic Transitions

For a $d^8$ ion in an octahedral field, three spin-allowed d-d electronic transitions typically occur from the $^3A_{2g}$ ground state. These transitions, listed in order of increasing energy, are:

• $^3A_{2g} \to ^3T_{2g}$
• $^3A_{2g} \to ^3T_{1g} (F)$
• $^3A_{2g} \to ^3T_{1g} (P)$

The energy of the lowest transition, $^3A_{2g} \to ^3T_{2g}$, is equal to the ligand field splitting energy, $\Delta_o$. The other transitions occur at higher energies.

Absorbance Maxima Correlation

The observed absorbance maxima ($11200 \text{ cm}^{-1}$, $18350 \text{ cm}^{-1}$, and $29000 \text{ cm}^{-1}$) must be matched with these transitions based on their energy order:

• Lowest energy peak: $11200 \text{ cm}^{-1}$ (a) corresponds to the lowest energy transition, $^3A_{2g} \to ^3T_{2g}$ (ii).
• Intermediate energy peak: $18350 \text{ cm}^{-1}$ (b) corresponds to the intermediate energy transition, $^3A_{2g} \to ^3T_{1g} (F)$ (i).
• Highest energy peak: $29000 \text{ cm}^{-1}$ (c) corresponds to the highest energy transition, $^3A_{2g} \to ^3T_{1g} (P)$ (iii).

Correct Electronic Transition Matches

The correct pairings derived are:

• (a) $11200 \text{ cm}^{-1} \to$ (ii) $^3A_{2g} \to ^3T_{2g}$
• (b) $18350 \text{ cm}^{-1} \to$ (i) $^3A_{2g} \to ^3T_{1g} (F)$
• (c) $29000 \text{ cm}^{-1} \to$ (iii) $^3A_{2g} \to ^3T_{1g} (P)$

These correct pairings correspond to the following numbered options:

• Option 1: (a) $\to$ (ii)
• Option 2: (b) $\to$ (i)
• Option 4: (c) $\to$ (iii)