Chapter 15, Problem 15.4P

Interpretation Introduction

Interpretation:

The approximate energy difference between the HOMO and LUMO is to be calculated for the given UV-vis spectrum.

Concept introduction:

UV-vis spectrum of a particular compound is a plot of relative absorbance against wavelength. The peak in the spectrum is called ${\text{λ}}_{\max }$ (lambda-max), which shows the absorbance at the maximum wavelength. When electromagnetic radiations behave as a particle, radiation exists as photons. Each photon possesses a characteristic energy that depends only on its frequency (or wavelength) and is given by the equation:

${\text{E}}_{\text{photon}}{\text{ = h×ν}}_{\text{photon}}{\text{= (h×c)/ λ}}_{\text{photon}}$. In UV–vis spectroscopy, the absorption of a photon typically corresponds to the promotion of an electron from an occupied MO (HOMO) to an unoccupied one (LUMO). The HOMO-LUMO transition requires the least energy, so it corresponds to the longest-wavelength UV-vis absorption. In other words, the longest-wavelength UV–vis absorption band corresponds to the HOMO–LUMO transition of the organic compound.