Simple Laser-Induced Fluorescence Setup to Explore Molecular Spectroscopy. Abstract

Transcription

1 Simple Laser-Induced Fluorescence Setup to Explore Molecular Spectroscopy S. B. Bayram and M.D. Freamat Miami University, Department of Physics, Oxford, OH (Dated: July 23, 2012) Abstract We will demonstrate a relatively simple, affordable and highly visual experiment to explore molecular spectroscopy by measuring the laser-induced fluorescence (LIF) spectrum of the iodine molecules at room temperature. Iodine is a uniquely suited molecule for LIF measurements since it conveniently absorbs about 20,000 lines in the 490- to 650-nm visible region of the spectrum and serves excellent example of displaying discrete vibrational bands at moderate resolution and rotational structure at high resolution. The apparatus consists of a diode laser 532 nm (or a laser pointer), an iodine cell, and a handheld spectrometer. We will scrutinize the LIF spectrum about the potentials associated with the vibrational states of the diatomic molecules and assign spectral lines based on the transition probability between vibrational levels, build vibrational energy level diagram and tabulate Deslandres table, evaluate the harmonic and anharmonic characteristics of two states and thereof the merits of the harmonic approximation for the molecular oscillator, and finally extract the molecular constants such as dissociation energies of the molecular potentials. Electronic address: bayramsb@muohio.edu Electronic address: freamamv@muohio.edu 1

2 I. INTRODUCTION Iodine is the heaviest common halogen (atomic number=53, atomic mass=127) and like the other halogens, iodine vapor consists of a weakly bound diatomic molecule. The vapor has the appearance of a violet gas, indicating a visible absorption. This absorption corresponds to a spinforbidden transition from the lowest vibrational levels of the singlet electronic ground state to high vibrational levels of a triplet excited state. In this experiment we are going to study the laser induced fluorescence of iodine in the gas phase at room temperature. The aim of the study is to determine the molecular parameters, that is the dissociation energy of the ground X and excited B states, vibrational frequency, anharmonicity constant and the force constant, of iodine in the ground state. This will be done by measuring the vibrational spectrum of the fluorescence from an iodine vapor, which is excited by a 532-nm laser beam. Laser induced emission can be analyzed to give a great deal of information about the molecular structure and potential energy curves for ground and excited electronic states. The visible absorption spectrum of iodine vapor in the 490- to 650-nm region serves as excellent example, displaying discrete vibrational bands at moderate resolution and extensive rotational structure at high resolution. The rotational structure is not seen at a resolution of 0.2 nm, a common limit for commercial ultraviolet-visible spectrometers, but the vibrational features can be easily discerned in both absorption and emission measurements. A green 532 nm laser is used to excite the iodine in its B state from the lowest v =0 vibrational level of the ground electronic state to higher level vibrational level of the excited state. The excited molecule will relax to different vibrational levels in the ground state. The spectrum of the X 1 Σ + g B 3 Π + g transitions has more than 20,000 absorption lines in the visible and some of them near 532 nm, and it complements the absorption spectrum. Observation of emission spectrum from the Laser Induced Fluorescence (LIF) using a green laser pointer at 532 nm exhibits Stokes and anti-stokes emissions, and offers not only vibrational structure but also rotational structure with adequate resolution. In this experiment, we concentrate on the LIF spectrum of I 2 in order to obtain vibrational frequencies, anharmonicities, and other molecular parameters for the ground X 1 Σ + g and excited B 3 Π + g states involved in this electronic transition. 2

3 A. Background theory The relevant potential energy curves for I 2 are shown in Fig. 1, which also shows some of the parameters to be determined from the spectra. The spacing between levels in the two electronic states can be measured by laser induced fluorescence spectrum. The total energy of a diatomic molecule has E = E e + E vib + E rot. (1) where electronic E e, vibrational E vib and rotational E rot energies are individually quantized. FIG. 1: A partial potential energy diagram for I 2 : the curves X and B are associated with the respective ground and excited electronic states. The horizontal lines within the curves indicate the vibrational energy levels of the electronic state. There is no strict selection rule for the change in vibrational quantum number during an electronic transition; thus sequences of transitions are observed. The selection rules for electronic transitions are based on conservation of angular momentum (which govern which electronic states 3

4 can be accessed), and on the Franck-Condon Principle (which governs which vibrational states can be accessed). The X B transition is allowed according to the electronic selection rules. Thus, we must turn to the Franck-Condon principle to understand which vibronic transitions we can expect to see. This principle, also based on the fact that electrons are much lighter than nuclei, says the electron redistribution which results from an electronic transition occurs instantaneously with respect to nuclear motion. That is, the nuclei do not move during a transition, they only adjust after the absorption event is complete. Since the internuclear distance does not change during the absorption of a photon, the transition is drawn with a vertical line on the potential energy diagram: we say that electronic transitions must be vertical as seen in Fig. 1. Furthermore, transitions of the highest intensities occur when the overlap between the ground and excited state wavefunctions is largest. This means that the most intense transitions originate from the center of the v =0 level (i.e. the equilibrium internuclear distance). There are two main consequences of the Franck-Condon principle for the absorption spectrum of I 2 : Because the potential wells for iodine are substantially offset along the x-axis, transitions to low-lying vibrational states, (X, 0) (B, small v ), are not observed (that is, vertical transitions are not possible to small v ). For iodine, observable vertical transitions terminate at vibrational levels in the region of v = Transitions to very large v are not observed because the overlap between ground and excited state wavefunctions is too poor. Thus, Franck-Condon selection rules predict that the absorption spectrum for iodine at room temperature will primarily consists of transitions such as (X, v ) (B, v = 20,..., 50). In order to define the energies in terms of wavenumbers, it is convenient to divide Eq. (1) by the quantity hc, where c is expressed in units of cm 1, to get the so-called term value T, which has units of cm 1. Thus T = E/hc = T e + G(v) + F (J), (2) where T e is the electronic term value (E e /hc), G(v) is the vibrational term value (E v /hc), and F (J) is the rotational term value (E rot /hc). The advantage of this change is that the frequency (expressed in cm 1 ) for a transition between two electronic states can be simply expressed by T T = (T e T e ) + (G(v ) G(v )) + (F (J ) F (J )), (3) 4

5 where primed ( ) parameters are properties of the upper state, while the double-primed ( ) parameters are lower state properties. Here, T e is zero since it refers to the ground electronic energy state and T e is the frequency of the transition between X and B. Since the rotational energies will not be resolved in the experiment, we will ignore the rotational contribution. The vibrational term value is G(v) = E v /hc = ω o (v + 1/2) ω o x o (v + 1/2) 2, (4) where ω o (calculated in cm 1 ) is the fundamental frequency of the vibration. Because the product ω o x o quantifies the first order energy deviation from that of a harmonic oscillator, it is termed anharmonicity. II. EXTRACTING MOLECULAR CONSTANTS To take into account of the anharmonicity of the vibrations, we use the Morse potential to describe the potential curve V (r) = D e (1 e β(r r 0) ) 2, (5) where D e is the dissociation energy given by the depth of the potential well, and β relates to the force constant k as β = (k/2d e ) 1/2. (6) The fundamental frequency of the vibration, ω 0, is naturally related with the other parameters of the oscillator: ω 0 = 1 k 2πc µ = β D e c 2π 2 µ, (7) where µ is the reduced mass of the iodine. By subtracting the energies of successive levels v within a state characterized by (ω 0, ω 0 x 0 ), one obtains the vibrational energy spacing: G(v) = E v /hc = ω 0 2ω 0 x 0 (v + 1) (8) which suggests that the energy steps are fairly constant at low v, as confirmed experimentally by the regularity of the spectrum peaks within each progression and the inter-level energies, but reduce 5

6 gradually at high v, up to a maximum level v max = 1/2x 1 corresponding to the dissociation energy D e. This argument stays behind the so called Birge-Sponer treatment [1] that uses the linear plot of G against (v + 1). Based on this linear plot, fundamental frequency ω o can be found by extrapolating the linear fit to the G axis. The anharmonic term ω o x o is the slope of the line. The dissociation energy D 0 with respect to the zero-point level is simply given by the area under the linear plot in the interval (0, v max ). Since E 0 /hc ω 0 whereas E vmax 0, the zero-point dissociation energy is D 0 /hc = ω0 2/4ω 0x 0. Combining with equation 4, the students can furthermore calculate the dissociation energy D e relative to the equilibrium point (that is, the bottom of the potential well) as shown in Fig. 1.: D e /hc = E 0 /hc + D 0 /hc = 1 2 ω ω 0x 0 + ω2 0 4ω 0 x 0. (9) Insofar as D e and ω 0 can be substituted in Eq. (7) to find β. Theoretical constants are given in references [2, 3]. Franck Condon table for the 532 nm excitation was given in reference [4]. In our earlier paper [5], we showed how to extract upper level molecular potential well using a simple nitrogen capillary discharge tube. III. CALIBRATION After obtaining the spectrum, one can calibrate the spectrum using various light sources. A reference spectrum can be obtained from Hg source which exhibits a bright green at nm and two yellow lines at 579 nm and nm as seen in the figure below. Neon lines can be used to further calibrate the spectrum at nm, 534. Helium light source gives many lines in between 400 nm and 600 nm, and can be used to calibrate the spectrum as well. The most important information about the atoms and their strong emission lines, transition probabilities and etc. can be found at When you enter the site, click on Periodic Table to select the atom of interest. FIG. 2: Typical Hg strong lines. 6

7 IV. TASKS Next 4 pages (4 TASKS) will guide you through the basics of how to extract molecular constants quickly and easily without using sophisticated programs or computer. The figures 3 below show a typical spectrum you will obtain from the experiment and our simple experimental apparatus Vibrational spectrum of I 2 excited by 532 nm laser Intensity (arb.) Wavelength (nm) FIG. 3: Typical LIF spectrum and experimental apparatus consists of an iodine cell, a 532 nm laser, and a handheld spectrometer with fiber. 7

8 T a s k 1 : S p e c tr a l lin e a s s ig n m e n t U s e th e F ra n c k -C o n d o n fa c to rs in th e in s e rt to a s s ig n e a c h p e a k o n th e s p e c tru m a p o s s ib le B (v ) to X (v ) tra n s itio n s. A s s ig n a t le a s t 2 0 o f th e m T ra n s itio n fro m B (v = 3 2 ) In te n s ity (a rb.) W a v e le n g th (n m )

9 Task 2: Data tabulation in a Deslandres table for iodine Use once again the I2 emission spectrum to fill out the table below with the following parameters for each spectral line: The emitted wavelength, λ (nm). Employ the program provided to verify the values. The transition energy, G v v (cm 1 ). The energy separation between successive levels, ΔG = Gv v Gv v +1 (cm 1 ) Then, to get a sense of the vibrational fine structure, use any pair of successive lines to estimate the energy separation within the X-state. v λ (nm) Gv v (cm 1 ) ΔG (cm 1 ) Transition energy in cm 1 from wavelength: G v v nm 1 cm cm nm Transition energy in ev from wavelength: E v v hc 1240 nm ev ev nm Apply this expression to two arbitrary consecutive vibrational levels and subtract to estimate the separation between energy levels in ev: E Evv Evv 1 ev

10 Task 3: Data analysis using Birge-Sponer treatment As explained in the manual, the energy separation between vibrational levels varies linearly with the ground level quantum numbers v, as given by ΔG = ω0 2ω0x0 (v + 1). Collect a sufficient number of (ΔG, v + 1)-values from the table and build a graph on the frame provided below. Then ΔG (cm 1 ) Approximate a linear fit and sketch a smooth straight line through the distribution. Notice that the ΔG-axis intercept is ω0, that is, the fundamental frequency of the diatomic molecule if it were a perfect simple harmonic oscillator. Extrapolate the linear fit, estimate ω0 and feed the value in the provided box. On the other hand, the slope is 2ω0x0, that is, the anharmonic term describing how much the molecular quantum oscillator deviates from the simple harmonic model. Estimate it and feed the value in the provided box ω0 = intercept = ω0x0 = ½ slope = v + 1

11 Task 4: Summarizing the results As explained in the manual, the fundamental frequency and the anharmonic term can be used to determine other parameters of the molecular vibrational state under scrutiny: the force constant k0 of the bond, the dissociation energies D0 and De with respect to the lowest level and the equilibrium position (bottom of the potential well), and the factor β in the Morse potential. Use the provided formulas to estimate these parameters for the ground level X of the iodine molecule, and list them in the table below. Parameter Experiment Literature SHO force constant: ω0 (cm 1 ) k c 0 0 Dissociation energy from v = 0 level: ω0x0 (cm 1 ) k0 (N/m) D0 (ev) 1.55 D x 0 0 Dissociation energy from equilibrium position: D D e o o o x o De (ev) β (cm 1 ) Factor β in the Morse potential k 0 D 2 e r r 0 V() r De 1e : Conversions: E ev E cm cm ev E J E cm cmj amu kg from cm 1 to ev: 1 4 from cm 1 to J: 1 23 reduced mass of iodine molecule: 1 cm 1 = x10 4 ev

12 Acknowledgments The financial support from the Research Corporation and the Dean of the College of Arts and Science at Miami University are greatly acknowledged. [1] R. T. Birge and H. Sponer. Phys. Rev., 28:259, [2] Ian J. McNaught. The electronic spectrum of iodine revisited. J. Chem. Educ., 57:101, [3] L. Mathieson and A.L.G. Rees. Electronic states and potential diagram of the iodine molecule. J. Chem. Phys., 25:753, [4] J. Tellinghuisen. Laser-induced fluorescence in gaseous I 2 excited with a green laser pointer. J. Chem. Educ., 84:336, [5] S. B. Bayram and M.V. Freamat. Vibrational spectra of N 2 : An advanced undergraduate laboratory in atomic and molecular spectroscopy. Am. J. Phys., 80:664,