This experiment examines the absorption spectra of conjugated dyes using spectroscopy. The objectives are to study how the electronic energy levels of molecules vary with molecular size, and to compare theoretical models to experimental results. Absorption spectra are obtained for several dyes and the maximum wavelength is used to determine the energy difference between the excited and ground states. Theoretical models like the particle in a box model are applied to predict absorption wavelengths, which are then compared to measured values.

1. Running Head: ABSORPTION SPECTRUM OF A CONJUGATED DYE 1
Absorption Spectrum of a Conjugated Dye
Name
Institution

2. Absorption Spectrum of a Conjugated Dye 2
Absorption Spectrum of a Conjugated Dye
Objectives
This experiment main objective is to probe the quantized nature of molecular electronic
states. This probe will be done by spectroscopy. The homologous series of molecules is studied
and the electronic energy levels variation of molecules will be examined during this experiment.
Also, theoretical molecules will be used in studying the way electronic absorption energy of a
molecule alternates with size. Lastly, skills of comparing theoretical values obtained from simple
models with more complicated and robust models will be leant.
Introduction
The interpretation of spectroscopic transitions requires quantum mechanics. This
experiment will employ the use of quantum mechanics in modeling electronic transitional energy
of a molecule between its ground state and its first excited state. Colored compounds such as
cyanine and polymethine when excited results in absorption which occurs in visible region of
spectrum. Absorption spectrum of several dyes will be obtained in this experiment and the
wavelength of the maximum absorption used in determining the energy difference between
excited state and ground state. The experimental results will then be compared with theoretical
results.
Background
The absorption band which is in the visible region of a spectrum corresponding to the
change from molecular state to excited electronic state is 170kj/mole – 300 Kj / mole above the

3. Absorption Spectrum of a Conjugated Dye 3
ground state. Dyes that absorb in the visible spectrum have weakly bound or delocalized
electrons (free radicals or  electrons) in conjugated systems.
Polymethine dyes’ electronic transitions involve the electrons along the polymethine chain. This
chain is conjugated; that is, it contains a string of alternating double and single carbon
bonds. The number of bonds in this string is connoted by the nomenclature, P(#carbon-carbon
bonds) Since wavelength of these bands depend on the spacing of the electronic energy levels,
one must know the transition associated with any given absorption. The simple free-electron
model (Kuhn) is accepted as the most precise model for explaining the energy of the absorption
maxima, max. The free electron model assumes that  electrons are free to move unfettered
along a conjugated carbon system. There is a correlation between the length of the conjugated
system and max. One of the objectives of this laboratory exercise is the elucidation of this
relationship.
The absorbance wavelength is a population average of the absorbance of both structures
according to the Boltzmann distribution equation. The conjugated chain is defined as the shortest
chain from nitrogen to nitrogen and has a length L. Since the accepted value of a C=C is
known, L can be determined for each structure using equation.
The quantum mechanical solution for the energy level of this model is
2 2
h n
En  2
8 mL
(1)

4. Absorption Spectrum of a Conjugated Dye 4
Where m is the mass of the electron and h is the Planck constant. The ground state of a molecule
with N  electrons will have N/2 lowest levels filled. The electron transition is from HOMO to
LUMO where n1 = N/2 and n2 = N/2+1. Thus the energy of transition is related to HOMO and
LUMO by equation (2).
(2) h
2
E  (n 2  n1 )
2 2
2
8 mL
The Particle in a Box model can be applied to conjugated systems, such as a hexatriene
molecule. For hexatriene, there are carbon six carbons in the conjugated system and there are six
pi electrons; 2 per double bond. Observing the Pauli Exclusion Principle, one can distribute the
electrons in the energy levels starting from the lowest as per the Aufbau Principle (See below).
n= 4
S1  S0
n= 3
U (x) ap p rox
n= 2
n= 1
x
Above graphic from Hope College “Absorption Spectra of Conjugated Polyenes”
It can be seen in hexatriene that the S1 ¬ S0 transition relates to n=4 ¬ n=3 change of the particle
in the Box model. The wave functions and energy for this model are
1
 22 nx
n    sin  
(3) a  a 
And the energy of discrete level En

5. Absorption Spectrum of a Conjugated Dye 5
(4) E =h
So 2
8 mc L
 
h N 1
(5)
In case the amount of carbon atoms that are in the chain = p, Then the number of pi electrons in
the system is N = p+3 (remember 2 carbon atoms = double bond, 2 electrons per bond and L
is the length of the conjugated chain plus one bond length. L = (p+3) l (where l is the bond
length between the atoms in the chain. (Remember: a conjugated bond length is an average
between a single and a double bond. A)
l =1.39 A = .139 nm
(p 3)
2
 ( nm )  63 . 7
p4
(6)
If there polarizable groups at eh end of the chain the conjugation of the group lengthens the
chain. This lengthening is the quantity by. If there are no groups attached to the nitrogen then 
= 0. Rangesbetween 0 and 1 and is specific for each constituent.
Experimental
The computer was turned on and allowed to completely boot up. The spectrometer was turned on
and when the amber light turned green, the spectrometer program was opened on the computer
and the both the lamps were turned on. The spectrum range window was then filled in such a
way to display the spectral range from 360 nm to 900nm.
Using 2.5ml graduated pipette, 1.00mLs of the stock solution of the dyes was dispensed to 10Ml
volumetric flask and diluted to mark with the methanol. The visible spectrum of the solution was

6. Absorption Spectrum of a Conjugated Dye 6
then taken using the plastic disposable cuvettes. Aliquots of the solution were diluted similar to
the above manner until an absorbance reading of one was obtained forming the working
concentration.
8 ml 0f the sample was then diluted to 10 ml. The other dyes were also made in the same
manner. The spectra of all the dyes were taken and recorded as spectra overlays.
Results