Particle in a Box Experiment
Absorption Spectra of Conjugated Dyes
04-21-2103
Introduction: The visible absorption bands or conjugated dye arise from electron transitions involving the electrons in the conjugated and they are free to move along the chain and are not attached to any atom. An example of such a dye is 3,3-diethyl-thiacyanine iodide. The cation has two resonance forms causing each of the bonds in the conjugated chain to have an order of 1.5 and have a length similar to the C--‐C bond length in benzene. We will assume that the potential energy is constant along the chain and sharply rises to infinity at the ends. Therefore, we can replace the electron
system by free electrons moving in a one dimensional box of length .
Objective:
The purpose of this experiment is to obtain the visible spectra of several cyanine dyes and then
interpret them to a simple model of the electronic structure of the π system: the Particle in a
Box.
Theoretical Model “Particle in a Box”
In the Particle in a Box model, all potential energy interactions are assumed to be zero
(constant) along the chain except at ends of the chain where the potential energy abruptly goes
to +. If a particle moving freely along the length of the box the energy can be calculated as : E = n2h28mL2 + V n = 1, 2, 3 … (1)
where n is an integer positive quantum number, h is Planck’s constant, m is the mass of the
particle and L is the length of the box. If we assume that the most intense band in the
experimentally observed spectrum can be interpreted as absorption of electromagnetic radiation
by an electron as it is promoted from the HOMO to the LUMO, we can derive the following
expression for the energy absorption E.
E =h2 [2ni+ 1]/ (8mL²) (2)
the absorption wavelength for the HOMO _ LUMO transition is
04-21-2103
Introduction: The visible absorption bands or conjugated dye arise from electron transitions involving the electrons in the conjugated and they are free to move along the chain and are not attached to any atom. An example of such a dye is 3,3-diethyl-thiacyanine iodide. The cation has two resonance forms causing each of the bonds in the conjugated chain to have an order of 1.5 and have a length similar to the C--‐C bond length in benzene. We will assume that the potential energy is constant along the chain and sharply rises to infinity at the ends. Therefore, we can replace the electron
system by free electrons moving in a one dimensional box of length .
Objective:
The purpose of this experiment is to obtain the visible spectra of several cyanine dyes and then
interpret them to a simple model of the electronic structure of the π system: the Particle in a
Box.
Theoretical Model “Particle in a Box”
In the Particle in a Box model, all potential energy interactions are assumed to be zero
(constant) along the chain except at ends of the chain where the potential energy abruptly goes
to +. If a particle moving freely along the length of the box the energy can be calculated as : E = n2h28mL2 + V n = 1, 2, 3 … (1)
where n is an integer positive quantum number, h is Planck’s constant, m is the mass of the
particle and L is the length of the box. If we assume that the most intense band in the
experimentally observed spectrum can be interpreted as absorption of electromagnetic radiation
by an electron as it is promoted from the HOMO to the LUMO, we can derive the following
expression for the energy absorption E.
E =h2 [2ni+ 1]/ (8mL²) (2)
the absorption wavelength for the HOMO _ LUMO transition is
Cited: http://homepages.gac.edu/~anienow/CHE-372/Labs/Example.pdf http://homepages.gac.edu/~anienow/CHE-372a/Labs/Conjugated%20Dyesa.pdf Freeman,W.H. “Experimental Physical Chemistry: A Laboratory Textbook.” Eds.Joan.Mims, 201.Print.