LEC 07.03 Excitation of molecules - Phywe

Related concepts
Wave mechanics atomic model; model of electrons in a unidimensional
potential box; ground and excitation states of molecules;
electron excitation spectroscopy (UV-visible spectrometry),
spectroscopical energy and adsorption measurement;
chemical theory of colour; Lambert-Beer’s Law; photometry;
chromatography.
Principle
The position of the longest wavelength p - p*-absorption band
in the UV-visible spectrum of organic compounds which have
chromophoric systems can be approximately calculated by various
methods. For dyes with extended conjugated p-systems,
the model of the electron in a unidimensional potential box (confinement
region) supplies results that agree sufficiently well with
experimental results.
Tasks
Plot the absorption spectrum of carotene, a polyene dye, in the
visible range of electromagnetic radiation. Compare the wavelength
of the absorption maximum determined from this with the
value calculated from the representation of the electron in a unidimensional
box. Discuss this comparison.
Equipment
Spectrophotometer 190 - 1100 nm 35655.97 1
Cells for spectrophotometer 35664.02 1
Retort stand, h = 750 mm 37694.00 1
Fig. 1. Experimental set-up.
Excitation of molecules
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Right angle clamp 37697.00 1
Universal clamp 37715.00 1
Suction filter, d = 70 mm 32707.00 2
Circular filter, d = 70 mm 32977.02 1
Filter flask, 250 ml 34418.01 1
Rubber gaskets, conical 39265.00 1
Glass beaker, 50 ml, tall 36001.00 5
Petri dish, d = 150 mm 64757.00 1
PP stopper, IGJ 19/26 47506.00 1
Security bottle with manometer 34170.88 1
Water jet pump 02728.00 1
Rubber tubing, vacuum, d i = 6 mm 39286.00 2
Spoon 33398.00 1
Knife 33476.00 1
Thermometer, -10… +50°C 38034.00 1
Pasteur pipettes 36590.00 1
Rubber bulbs 39275.03 1
Wash bottle, 500 ml 33931.00 1
Sea sand, purified, 1000 g 30220.67 1
Acetone, chemical pure, 250 ml 30004.25 1
Aluminium oxide S, acidic, 250 g 31084.25 1
Water, distilled, 5 l 31246.81 1
Kitchen grater
Carrot
Set-up and procedure
The spectrophotometer that is required for this experiment is
shown in Fig. 1.
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen P3070301 1

Prepare the carotene dye that is to be used as follows: Scrape a
carrot clean with the knife and use the grater to finely grate it into
the Petri dish. Position a water-wetted circular filter in the suction
filter and transfer the pulp onto it. Press the pulp with the
stopper while sucking the juice through the filter with the water
jet pump. Isolate carotene from the juice by column chromatography
as follows: Position a water-wetted circular filter in the
second suction filter, half-fill the suction filter with aluminium
oxide (acidic) and cover this with a not too thin layer of sea sand.
Carefully pour about 10 ml of the collected juice onto the sea
sand and suck it in if necessary with a gentle water jet pump
vacuum. Carotene, which is only sparingly soluble in water, is
adsorbed to the stationary phase. Following this, fix the suction
filter to a stand and carry out elution by pouring on about 50 ml
of acetone in small portions. Discard the turbid eluate that is first
collected. The subsequent clear eluate contains a mixture of a-,
b- and g-carotene isomers (approx. 15% : 85% : 0.1% respectively).
If the concentration of the dye is too high, dilute the eluate
with acetone until it has an extinction at 450 nm of between
0.8 and 1.0 against acetone as reference. Record the absorptions
spectrum of the solution in the visible range, from 400 to
600 nm, at a slow recording speed. Read off and record pairs of
wavelength and extinction values from the spectrum displayed
on the screen, between 500 and 600 nm in steps of 2 nm;
between 500 and 600 nm in steps of 5 nm. Plot a graph of the
pairs of values.
Theory and evaluation
In the spectral range of 200 to 800 nm that is covered by UV/visible
spectrophotometry, the reciprocal action of electromagnetic
radiation rich in energy on the structures examined causes transitions
from the electron ground state to the electron excitation
state with accompanying rotational and vibrational excitation
(electron excitation spectroscopy).
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Fig. 2: Potential energy E pot of an electron along the conjugated
p-system (box length L in the b-carotene molecule)
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With successful reciprocal action, the radiation energy absorbed
hn is equal to the difference ∆E between the energy states of the
ground state (E A ) and the excited state (E B ).
∆E = EB -EA = hn = h · c · n (1)
h c
l
where
h Planck’s quantum of action (= 6.626 · 10-34 J·s)
c Velocity of light (= 2.998 · 108 m·s-1) n, n
, l Frequency, wave number or wavelength of the electromagnetic
radiation
In UV-visible spectroscopy, the degree of absorption is customarily
defined by the (concentration dependent) extinction E l that
is defined by Lambert-Beer’s law
E l lg I 0
I e i c i d
where
I0 , I Intensity of the radiation before and after passage
through an absorbing medium of layer thickness d
El ei Extinction at wavelength l
Decadic molar extinction coefficient of the substance i
at wavelength l
ci d
Concentration of the substance examined i
Layer thickness in the cell
or the (concentration independent) extinction coefficient ei or the
logarithm of this. The graph of the absorbed energy (E) as a
function of the incident energy (n, n
, l) gives the absorption
spectrum (Fig. 3), from which the relevant coordinates of the
absorption maximums (lmax , ei,max ) can be taken.
Fig. 3: Absorption spectrum of carotene in acetone.
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
(2)

For systems with conjugated p-bonds, the position of the
longest wavelength absorption band in the UV/visible spectrum
can be estimated using various empirical methods and theoretical
model representations. According to the model of the electron
in a unidimensional box (Fig. 2), an electron can move freely
in the low energy box with the length L that is determined by the
spread of the conjugated system. The character of De Broglie
waves can so be ascribed to the electron, and these are reflected
at the walls with higher potential energy E pot , whereby standing
waves are formed following interference. For the quantized
wavelength and energy E , the following relationships are
valid solutions of the Schrödinger equation:
and
E
where:
me Mass of the electron (= 9.109 · 10-31 kg)
n Quantum number (= 1, 2, 3,...)
The quantum numbers n that are contained in the equations (3)
and (4) correspond to quantized energy states that are, for multielectron
systems, occupied in pairs by electrons according to
the corresponding construction principle and Pauli exclusion
principle. The longest wavelength, and so energy poorest electron
transition, with light absorption therefore occurs according
to the selection rule, from the highest occupied energy level (n A )
to the lowest unoccupied energy level (n B = n A + 1). The following
relationship is then obtained from equation (4) for the excitation
energy ∆E
¢E
2 L
n
h 2
8 m e L 2 · n2 E pot
h2
8 m e L 2 1n2 B n 2 A2
Excitation of molecules
(3)
(4)
(5)
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The position of the absorption band belonging to this can be
expressed as the corresponding frequency, wave number or
wavelength using equation (1).
Data and Results
The polyene dye b-carotene has 22 p-electrons in 11 conjugated
double bonds (n A = 11, n B = 12) and a length L
= 1.771 · 10 -9 m of the conjugated p-system, as estimated from
atomic radii, from which ∆E = 4.418 · 10 -19 J can be calculated
as being the excitation energy required for the lowest energy
electron transition. According to equation (1), the longest wavelength
absorption band in the UV-visible spectrum belonging to
this is expected to be at a wavelength of l = 449.6 nm. These
results correspond to the experimental findings shown in Fig. 3.
The absorption spectra of the pure isomers are characterized by
the following data:
a-Carotene: l = 420 nm (shoulder); l = 443 nm (maximum 1);
l = 472 nm (maximum 2)
b-Carotene: l = 425 nm (shoulder); l = 450 nm (maximum 1);
l = 479 nm (maximum 2)
g-Carotene: l = 430 nm (shoulder); l = 446 nm (maximum 1);
l = 490 nm (maximum 2)
Note
The graphical evaluation of the measured values can be very
easily carried out by means of ‘Measure’ software. A downloadfile
of this software is available as freeware for use in evaluating
and graphically representing measured values under URL
„www.phywe.com“. Fig. 3 was created by this software.
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen P3070301 3

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Excitation of molecules
PHYWE series of publications • Laboratory Experiments • Chemistry • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen