INDEX:       Introduction
                 Particle-in-a-box formalism
                 Application to Conjugated Dyes
                 Procedure
                 Data Analysis
                 Discussion
                 Figure 1.
                 Figure 2.
                 Figure 3.

Introduction:

This experiment is a study of the visible spectra of several dye molecules. Absorption of electromagnetic radiation (EMR) in the visible (l range ca. 400-750 nm), ultraviolet (ca. 180-400 nm), and vacuum UV (ca. 10-180 nm) regions is associated with the promotion of a valence electron from its lowest energy (ground state) level to a higher energy level. For most organic molecules the energy spacing, DE, between these levels is greater than about 400 kJ/mole. Using the de Broglie relationship,

                  (1)

The structures, names, and numerical codes of the molecules for this study are shown in Figure 1. These compounds are all intensely colored, many with a bluish tinge, and have been historically called cyanine dyes. Structurally their distinguishing feature is the chain -of alternating double bonds connecting the two nitrogens. As shown in particular (Figure 2) for 1,l'-diethyl-2,2'-carbocyanine cation (dye #2) this is a type of conjugated system. The delocalization of the pi electrons shifts the electronic absorption into the visible region, and, as this experiment will demonstrate, the l_max of the transition increases with the length of the conjugated system.

This system can be treated theoretically by the "free electron" model, as proposed by Kuhn¹. He assumed that the spectral characteristics in the visible region are determined solely by the pi electrons, which are "freely" in motion along the chain. (The electrons in single bonds (sigma electrons) are localized between the connected atoms, and are excited only by EMR in the vacuum UV range.) This is effectively an example of a one-dimensional "particle-in-a-box" system, one of the simplest applications of quantum mechanics.

¹The primary colors of light divide the visible region into three parts: blue, 400-500 nm; green, 500-600 nm; and red, 600-700 nm. The secondary colors are combinations of two of these, with the third primary as the complement: red + green produces yellow, with blue as the complement; red + blue produces magenta (reddish-purple), with green as the complement; green + blue produces cyan, with red as the complement. A cute mnemonic relating the complementary primary/secondary colors is Red Cadillac BYGeneral Motors (Red/Cyan; Blue/Yellow; Green/Magenta).