Experiment 5 Vibronic Spectrum of Iodine by UVVis Absorption
I. Introduction
UVvisible light spectroscopy is a method commonly used to investigate the
quantum mechanics and atomic structure of elements. In this experiment, one of our
goals was to determine the vibrational energy of atomic iodine as internuclear spacing
varies. In doing so we were able to identify the equilibrium interatomic radius of iodine,
the state the molecule is most commonly found in. In other words, this is the spacing
which maximizes entropy, minimizes energy, and thus occurs most frequently in nature.
From the raw spectroscopy data, our first task was to generate a BirgeSponer
plot. By graphing the difference between successive vibrational energy states, ΔG
v
,
against (v +1), a line of the form
=

( + )
∆Gv ωe 2ωexe v 1
was produced where ω
e
indicates the harmonic frequency and ω
e
x
e
is the first
anharmonicity parameter which can be found from the intercept and slope of the line
respectively.
Next, in calculation of the Morse potential, the group had to complete several
intermediate calculations such as the dissociation energy, D
e
, and Morse parameter, β.
The Morse parameter equals,
=
β 8π2cμωexeh
where in addition to the variables mentioned above are the constants the speed of light, c,
Planck’s constant, h, and the reduced mass, μ.
The group used spectroscopy to create calculations for the Vibronic energy levels
at a range of interatomic spacing of each iodine molecule.
=
[   ( 
)]
VR De 1 e β R Re 2
From the Morse Potential graph, the equilibrium radius may be observed. Because
molecules are most likely to populate their lowest energy states, we expect the most
likely energy levels for Iodine to be the interatomic radius, r, where the Morse Potential
V(R) is minimized. In actuality chemical bonds are not perfect harmonic oscillators. As
chemical bonds stretch, they weaken and upon compression, interatomic repulsions raise