Spectroscopy: Conjugated Dyes and the Electrons in a Box Model

It seems like a one-dimensional life for some Electrons in a Box. They seem to be stuck in the conjugated bonds of a dye, but they still have energy levels and wave functions. This applet is designed for use with a conjugated dye molecular spectroscopy laboratory.Tes applet shows the energy levels and wave functions for electrons confined to a one-dimensional box. This is a simple model to explain the absorption spectra of conjugated dyes.

A dye will absorb photons having energy equal to the difference between the lowest unoccupied energy level and the highest occupied energy level. Click on the "show excited state" and "show ground state" buttons to see this difference. The red arrows represent electrons in different energy levels.

A dye with longer conjugation is modeled by increasing the box length. Click on the x-axis and drag right or left to change the length of conjugation in the dye.

Exercise. Consider a dye with conjugated bonds as in the figure below.

dye

The dye has 8 pi-electrons that are "free" to move along the -N-C-C-C-C-C-N- skeletal structure. Estimate the length of the conjugated-bond chain assuming carbon-carbon and carbon-nitrogen bond lengths of about 0.14 nm and including a bond length at each end of the chain. Enter these values into the applet below (using the mass of the electron) and determine the wavelength of absorption expected for a molecule with this conjugated component. How does the estimated wavelength of absorption compare to a typical experimental value of 416 nm for this type of molecule?

The Electrons in a Box applet needs a Java-enabled browser.