PhysicsOpenLab Modern DIY Physics Laboratory for Science Enthusiasts
Abstract: in this post we describe the spectroscopic analysis of the absorption of iodine vapors. The maxima of the absorption are related to the transitions between the vibrational levels of the diatomic iodine molecule.
Introduction
Iodine is a substance which, at standard pressure and temperatures easily obtainable in the laboratory, can give rise to changes in state such as sublimation and frost. At room temperature, iodine appears as a dark, bluish-violet solid with an almost metallic luster (as shown in the figure opposite). At slightly higher temperatures than ambient, iodine sublimates into a violet vapor with a characteristic and irritating odor. Iodine vapors are formed by the diatomic molecule I2. When excited by intense green light, for example from a 532 nm laser beam, the iodine vapors exhibit a characteristic yellow-orange fluorescence (which we discussed in the previous post Iodine Vapor Fluorescence). In this project we will instead deal with the spectroscopic analysis of the absorption of light by iodine vapors. Also this analysis, similar to that on fluorescence, will provide us with information on the vibrational energy levels of the iodine molecule.
Theory
As we have already seen in the post on the fluorescence of iodine vapors, the bonds of molecules can vibrate with characteristic energies, each energy is associated with a particular quantum state of the molecule. Atoms and molecules can also take on several different electronic energies, each of which is associated with a particular electronic quantum state. Each electronic state corresponds to a particular distribution of electrons (certain orbitals). The electronic configuration with the lowest energy is called the ground state, all the higher energy states are called the excited states. The potential energy experienced by electrons in a given state is described by a potential energy curve. The potential energy diagram showing the first three electronic states of molecular iodine is shown in Figure 1.
Fig. 1 – potential energy diagram for the I2 molecule. Curve X describes the ground electronic state and curves A and B describe excited electronic states. The horizontal lines within the curves indicate the vibrational energy levels within the particular electronic state
molecular iodine is purple in color because it absorbs light in the visible (yellow) region of the electromagnetic spectrum. This absorption of light causes an electronic transition, that is, a transition between potential curves resulting in a change in the distribution of electrons in the molecule (electrons are distributed between the orbitals in a different way). In general, transitions between potential curves are also accompanied by changes in vibrational energy. Such transitions are called vibronic (vibrational and electronic) transitions.
The objective of this experimental activity is to obtain the values of the molecular parameters from the experimental vibronic spectrum of I2 which we measure through the spectroscopic analysis of the absorption by iodine vapors.
As we explained in the post on the fluorescence of iodine vapors, the trend of the potential in a diatomic molecule is well described by Morse’s law:
V(r) = De( 1 – e-α(r – re))
Where De is the dissociation potential, and re is the equilibrium distance between the two nuclei.
We also need the potential curve to represent and analyze the radiative transitions between molecular energy levels. Compared to the modifications that during the transition involve the electrons, the nuclei, since they are much heavier than the electrons, are practically stationary, so the internuclear distance remains constant and the electronic transitions are represented by vertical lines. This is called the Born-Oppenheimer approximation. Electronic transitions obey selection rules based on angular momentum conservation and the Franck-Condon principle. This principle states that an electronic transition from one vibrational level to another is more likely the more the wave functions corresponding to the two states are superimposed. Figure 1 shows the absorption transitions in the iodine molecule.
From the spectroscopic study of electronic transitions it is possible to obtain quantitative information on the trend of the molecule’s potential. The energy, in the spectroscopic field, is commonly expressed in units equal to cm-1 and is indicated with the letter: G = E [cm-1] = 1/λ = ν’, the energy differences between a level and the adjacent level will be given by:
ΔG = G(ν+1) – G(ν)
For a Morse potential it can be shown that:
G = ωo(ν + ½) + ωoXo(ν + ½)2
Where ωo is the fundamental frequency and the anharmonicity product ωoXo models the first order deviation from a harmonic oscillator. By calculating ΔG we get:
ΔG = G(ν+1) – G(ν) = ωo – 2ωoXo(ν+1)
The trend of ΔG with respect to (ν+1) is linear with a slope of 2ωoXo and intercept equal to ωo (this relationship is known as Birge Sponer’s law). From the spectroscopic analysis of the absorption we can measure ΔG as a function of (ν + 1), determine the regression line that best approximates the data and then derive the parameters of the Morse potential.
The data we obtain derive from the spectroscopic analysis of the absorption transitions, from the fundamental level (potential X of Fig.1) to the first excited level (potential B of Fig.1). These data will then provide us with information on the development of the Morse potential of the first excited level.
Experimental Setup
To examine the absorption of light by iodine vapors, a classic spectrometry cuvette is used in which solid iodine fragments are introduced, as shown in Figure 2. The cuvette is then subjected to heating, for example with a flow of hot air, so that iodine vapors are developed in sufficient quantities.
Fig. 2 – The cuvette with the Iodine sample
The cuvette saturated with iodine vapors is placed in the sample holder cell and the absorption spectrum is acquired (as described in the post Absorption Spectroscopy ). The light source is an incandescent lamp from Thunder Optics, while the spectrometer is the B&W Tek model already used in the Raman DIY system. The setup scheme is shown in Figure 3.
Fig. 3 – Setup for the measurement of the absorption spectrum
Results
In the following images we report the absorption spectra of iodine vapors acquired with our instrumentation. In figure 4 we report, without any elaboration, the spectrum we have obtained.
Fig. 4 – Absorption spectrum of iodine vapors
In figure 5 we report the spectrum, corrected by the baseline, which allows to highlight the maxima that correspond to the vibronic transitions of absorption. It is immediately noticed that the separation of the maxima tends to increase as the wavelength increases, this is in agreement with the Morse anharmonic potential model which foresees a thickening of the energy levels, and therefore a reduction of the ΔE, as the number increases. vibrational quantum ν.
Fig. 5 – Detail of the absorption spectrum of iodine vapors
With the wavelength data relating to the maximum absorption we can draw the Birge_Sponer graph and determine the regression line with the parameters ωo and ωoXo. The graph is shown in figure 6 and the parameters of the linear regression line are the following:
ωo = 148,45 cm-1
ωoXo = 1,31 cm-1
From these data, and knowing the reduced mass of the iodine molecule μ = 1,05×10-25 Kg, we can also calculate the other parameters of the Morse potential of the molecule for the first excited state:
De = 4279 cm-1 = 0,53 eV
K = 82 N/m
Fig. 6 – Energy transition ΔE as a function of the vibrational quantum number ν
It is also interesting to compare the absorption spectrum with the fluorescence spectrum (Figure 7). The fact that, in general, the maxima do not match is a demonstration that the vibronic transitions of fluorescence are different from the vibronic transitions of absorption: they occur between different pairs of energy levels.
Fig. 7 – Comparison between the absorption spectrum and the fluorescence spectrum
Conclusions
The spectroscopic analysis of the absorption of iodine vapors, carried out with our DIY instrumentation, allowed us to investigate the vibrational energy levels of the diatomic iodine molecule
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