Fig. 1. Excitation leading only to Stokes fluorescence. The energy levels are shown on the left, and the resulting vibrational spectrum is shown on the right.
This experiment is, in many ways, the inverse of the I2 absorption experiment. In that experiment, transitions which originated in a particular vibrational level of the ground electronic state and ended in several vibrational levels of the excited electronic state were observed. In the present experiment, you will prepare a molecule in a particular vibrational level of the excited electronic state, and observe its emission to several different vibrational levels of the ground electronic state.
Laser Excitation
Preparing a molecule in only one excited state requires a rather special method of excitation, and this is the purpose of the laser used in this experiment. The laser provides a source of light which that should ideally be so nearly monochromatic that it excites a single line in the I2 absorption spectrum. This exciting line will, then, populate a single state (a single value of v' and J'), which will then fluoresce to any of the ground state vibrational levels allowed by the Franck-Condon principle. In the present case, the 514.527 nm line of an argon-ion laser is used as an excitation source. Light of this wavelength causes the v'=43 <-- v"=0 transition to the B state from the X state1 (this laser line also promotes two rotational transitions - we will deal with this shortly.) We then observe an emission progression to the various vibrational levels of the ground state.
In general, the molecule will be excited from the v"=0 state to some excited state level at the laser wavenumber νL. Subsequent fluorescence will take the molecule back to some ground state level with vibrational term value G(v"), and the fluorescence will have the wavenumber νL-G(v"). Depending on the details of the geometries of the two electronic states involved, there might be a sequence of several lines, each separated from the exciting line by a vibrational interval: νL-[G"(1)-G"(0)], νL-[G"(2)-G"(0)], νL-[G"(3)-G"(0)].... Each of these lines will occur at lower wavenumber than the exciting line; the amount that each is displaced from the exciting line is called the Stokes shift. The resulting spectrum is shown in Fig. 1.
Fig. 1. Excitation leading only to Stokes fluorescence. The energy levels are shown on the left, and the resulting vibrational spectrum is shown on the right.
Although the vibrational ground state is the most populated level, there is no assurance that it will lead to absorption of the laser light. There may be no intensity in any transition from the ground state at that wavelength, or there may be no upper state with the proper energy separation from the ground state to be excited by the laser. In such a case, absorption of the laser light by a vibrationally excited state in the lower electronic state may occur (think of the origin of the vibrational hot bands in the earlier experiment.) Although such an absoprtion may be weak, it may be the only possibility for for absorption to occur. If we refer to the initially excited state as v"*, then the Stokes-shifted fluorescence lines will appear at wavenumbers equal to νL-[G"(v"*+1)-G"(v"*)], νL-[G"(v"*+2)-G"(v"*)], νL-[G"(v"*+3)-G"(v"*)],... In addition, one or more anti-Stokes shifted fluorescence lines will appear to the short wavelength (high wavenumber) side of the exciting line at νL-[G"(v"*-1)-G"(v"*)],...., νL-[G"(0)-G"(v"*)]. This is shown in Fig. 2 below.
Fig. 2. Excitation leading to both Stokes and anti-Stokes fluorescence. The spectrum represents vibrational structure.
Rotational Structure
Associated with each vibrational transition will be observable rotational fine structure. In this experiment, as opposed to our earlier work with iodine, we will attempt to resolve and interpret the rotational fine structure which accompanies the vibrational transitions. This rotational structure is particularly simple if only one excited state is populated by the laser light. In this case, the rotational structure will cause a doubling of the lines for each lower state: instead of observing single lines spaced by a single vibrational level (cf. Figs.1 and 2), sequences of doublets will be observed. If, as in the present case, the selection rule on the rotational quantum number J is ΔJ=+/-1, there will be two distinct lines for each vibrational feature (a P line for J" = J'-1 and an R line for J" = J'+1 as shown on Fig. 3.)
Fig. 3. The spectrum of Fig. 2 at higher resolution, showing the rotational fine structure of the fluorescence bands.
There is, however, no guarantee that the laser will excite only one line of the iodine spectrum. If the laser wavelength overlaps two (or more) absorption lines, then two or more P and R features may be present for each vibrational band. This situation is shown in Fig. 4.
Fig. 4. A vibrational band at high resolution, showing transitions from two distinct upper states with the same v' but different J' values.
The 514.527 nm line of an argon-ion laser promotes two transitions to the B state from the X state of iodine: v'=43, J'=12 <-- v"=0, J"=13 and v'=43, J'=16 <--- v"=0, J"=171. Under high resolution, we will osbserve triplet rotational structure due to overlap of the P and R doublets for the two originating J' levels. If we cannot completely resolve and assign this rotational structure, we will at least have an excellent opportunity to observe and discuss it.
The laser, spectrometer and detector must be allowed approximately one hour to warm up and stabilize prior to a run. The cell is mounted in such a way that the laser beam enters and leaves along one axis of a T-shaped quartz cell containing iodine at about 10-2 torr. The fluorescence in the cell will be quite visible (it is a yellowish color while the laser beam is rather green); the fluorescence image is detected through the other axis of the T-shaped cell. A focusing lens is used to focus the radiation onto the entrance slit of a 0.5 m spectrometer. Once the optics (the cell and lens) are aligned, be very careful not to misalign anything - alignment is very time-consuming. Also, be careful not to lean on the optical table where the experiment is set up.
The experimental setup on the optics bench is shown below. Look closely at the cell - the yellowish stripe in the center of the cell (along the beam axis) is the fluorescence radiation we are analyzing.
We will be using a CCD (charge-coupled device) camera for a detector in this experiment. Use the lab writeup for the Balmer series of Hydrogen as a guide for using the CCD camera effectively. Remember to save your active curves as you obtain them for later analysis.
We wish to collect data from 515-800 nm, and then to try to assign the individual vibrational bands and resolve them into their rotational fine structure. Start with the grating at 530 nm (this way you will avoid the 514 nm laser line, which easily saturates the CCD camera.) Good starting points are 60 sec exposure and 50 micron slit width.
When you are satisfied with the spectrum with the grating at this value, save the curve, and move the grating by ca. 22 nm. Repeat this procedure until you are near 800 nm.
Vibrational Analysis
The laser line (which you should not see!) represents the (0,43) band, the band near 520 nm the (1,43) band, the band near 526 nm the (2,43) band, etc. Assign as many bands in the progression as you can, and calculate and record their wavelengths accurately. Convert the wavelengths into vacuum wavenumbers and make up a Deslandres table.
The vibrational term value for the ground electronic state may be written as
G(v") = ωe(v" + 1/2) - ωeχe(v" + 1/2)2 (1)
where ωe is the frequency for infinitesimal amplitudes of vibration for the ground electronic state, and ωeχe is the anharmonicity constant for the ground state. The intervals between the vibrational lines in the fluorescence spectrum will correspond to the energy differences between vibrational levels in the ground electronic state; therefore, for the wavenumber between these states, we have
Substituting eq. (1) for the vibrational term values, you should be able to show that
A plot of Δν vs v"+1 is known as a Birge-Sponer plot. You should be able to extract values of ωe and ωeχe from your plot.
At some value of v" (the dissociation limit), the difference between adjacent vibrational levels becomes zero. Since this point is difficult to observe directly, it is most accuately obtained by extrapolating your Birge-Sponer plot to the point where it crosses the v" axis. Once you have obtained v" at the dissociation limit, compare it to that calculated from eq. 7 of ref 2. In tabular form, compare your results to literature values and the values you calculated in the earlier iodine lab. Please include quality estimates for your spectroscopic parameters. Turn in a plot of the spectrum and a copy of the Deslandres table with your report. Include one high-resolution spectrum which shows the rotational structure.