# Particle in a Box Experiment

**Topics:**Absorption spectroscopy, Electromagnetic radiation, Absorption

**Pages:**6 (1193 words)

**Published:**August 22, 2013

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 given by:

λ = 8mcL²/h (2ni + 1) ni = p p = #e/2 (3)

Therefore, the Particle in a Box model predicts that the wavelength of the absorption maximum

is a function of chain length (L) and number of p-electrons (N).

The adjustable parameter Lmax can be calculated as:

λ = 8mc/h(2p+1)[(2p-1)Lb + Lext]2 (4)

λmax h/8mc=[2p-1Lb + Lext ]2/ (2p +1) (5)

Procedure:

In this experiment, we used the following dyes.

Dye #1: 3,3-diethyl-thiacyanine iodide (yellow)

Dye #2: 3,3'-diethylthiacarbocyanine iodide (Pink)

Dye #3: 3,3'-diethylthiadicarbocyanine iodide (Blue)

Dye #4: 3,3'-diethylthiatricarbocyanine iodide (Olive)

We placed 0.3 ml of dye solution in the 1- cm cuvette and added 3.00 ml of water and mixed

well. Using the nano drop spectrometer, first cuvette with water was used as a blank and later

second Cuvette with dye solution was inserted and measured the absorbance of the sample.

Once our absorbance of the highest peak was less than 0.5 and the absorption spectrum of each

dye was between 400-800 we collected the data.

Notes On Wavelength:

If only changes in electronic energy accompany absorption of light, a very sharp maximum in absorption should be observed at the characteristic wavelength. Although sharp lines are observed for isolated atoms, broad absorption bands are observed for substances in liquid phases (due to the accompanying vibrational and rotational transitions). In the experiment, we shall assume that the wavelength λmax, the wavelength at which the dyes absorb most strongly, is the wavelength to use in the equation (5).

Data/Result:

A UV-Vis absorbance spectrum (Fig 1) was obtained and used to calculate experimental λmax values for each of the studied cyanine dyes.

Fig 1: UV...

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.

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