edited by
FRANK DeHAAN Occidental College LOSAngeles, California 90041
Pure Rotational Raman Spectroscopy: A Dry-Lab Experiment L. Claron Hoskins University of Alaska Fairbanks, 99701 Raman spectroscopy is becoming a common structural technique and is being used in used i n undergraduate lahoratories. However, because of financial problems t h a t exist in many schools, purchase of Raman equipment often cannot he justified. T o help remedy this problem DeHaan, Thiheault, and Ottesen' developed a "dry lab" which uses Ramau spectroscopy t o determine point groups of ZXY3 compounds. Recentlv t h e current author2 vointed out t h a t Raman spectroscopy can also he used t o determine accurate hond distances for homonuclear diatomic molecules. Based on this article a "dry lab" is now given t h a t will permit t h e student t o analyze the pure rotational Raman spectra of hydrogen and carbon dioxide and determine t h e hond distances.
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Figure 1. Rotational Raman spectrum of hydrogen. Pressure was 1 am and the instrumental conditions were: 5 X 103 cps, 2 cm-' spectral ditwidth. 10 cm-'/mi" scan rate, 2 s time constant. and 200 mW of 488 nm laser power.
Spectra Figures 1and 2 show t h e rotational R a m a n spectra of hydrogen and carhon dioxide gases. T h e instrumental conditions are eiven in t h e fieure cautions. T h e snectra were recorded using a ~arrell-~shYmodei25-400 laser k a m a n spectrometer equipped with a Spectra Physics model 164 argon-ion laser, photon-counting electronics, a n d standard gas optics. T h e scattered light was observed at 90" t o t h e incident laser beam. ~
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Experiment I n this experiment you will analyze t h e spectra given in Figures 1 and 2 and determine t h e hond distances of Hz a n d CO.,.Vt is necessarv t h a t vou carefullv read t h e article eiven inreference (2) which discusses t h e theory of rota&nal Raman snectrosconv. References t o eauations a n d t h e table are in this article. Proceed in your analysis a s follows
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1) Determine the line wavenumbers (Awl and assign rotational quantum numbers (J)to each. The data in the table may he helpful. Remember that A 4 J ) = 4RdJ + 312). Tosave time use only the first ten lines in the COz spectrum. 2) Make linear plots (or perform linear least-squaresfitsonacaleulator) of the line wavenumbers versus the quantum numbers. According to eqn. (19) the slope is 4Bo and the intercept is 6Bo. Determine Bo values for bath Hz and COnfrom the slopes. For Hz calculate ro using eqn. (21). Since eqn. (21) does not apply to Con, it will have to be modified. The moment of inertia of Conis I = 2moro2,where mo is the mass of the oxygen atom and ro = rdC-0). Using this result and eqn. (41, it canshow that eqn. (21) isvalid for Con if M is replaced by 2Mo = 31.98982. Make this substitution into eon. 121) , . and calculate m for COI. 3) Compare your values of ro with those given in the table or that you calculate using the data in the table and eqns. (7) and (21). 4) Repeat steps 2 and 3 for Hz but this time determine both Ro and Do using eqn. (22). Compare your values of Do and Bowith those calculated using the data in the table and eqns. (7) and (8).
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642 / Journal of Chemical Education
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Figure 2. Rotational Raman spectrum of carbon dioxide. Pressure was 300 torr and the instrumentalconditions were: 5 X l o 3 cps, 1 em-' spectral slitwidth, 5 cm-'/mi" scan rate, 2 s time constant, and 250 mW of 488 nm laser power.
5) Construct rotational energy-level diagrams far Hz and Con and draw arrows showing the observed transitions (refer to Figure 1 in reference (2)).For COz use the first ten rotational levels. Comment on the differences between these diagrams. 6) Calculate relative intensities of the lines in the rotational spectra of Hz and CO;?using eqns. (3) and (11).For CO;?consider lines assigned to J = 2, 14, and 40. Do you get agreement between calculated and observed intensities? 7) Using the results of 5 and 6 above, comment on the differences between the H2and CO;?rotational Raman spectra. Extra Credit Problem Do step 4for COz usingall of the lines in the spectrum. You will have to derive an equation similar to eqn. (22) that applies to the CO;?spectrum. 1DeHnnn. .- --- , -F. P.. Thibeault. J. C.. and Ottesen. D. K., J. CHEM. EDUC., 51,263 (1974). Hoskins, L. C., J. CHEM. EDUC., 52,568 (1975). 3 Large scale copies of these figures are available on request.
Analysis of Spectra
Carbon Dioxide
Hydrogen
The rotational Raman spectrum of carbon dioxide given in Figure 2 shows a large number of lines that do not exhibit an alternation in
The rotational Raman spectrum of hydrogen given in Figure 1 shows only four lines which do not have the usual line patterns that occur for heavier molecules like Oz m d NP.This is because of the large value of Ro which causes the Boltzmann factor to become small very rapidly. The nuclear spin of 112 also causes the line intensities to vary considerably (g, in eqn. (11)). Since all rotational lines occur far a nonzero spin, the first line is assigned to J = 0, the second to J = 1, etc.
intensities. This is due to the zero nuclear spin of oxygen. The statistical weights of either all even or all odd levels are zero. Far C02, which has a 'L: ground electronic state, all ofthe odd levels are missing. Furthermore, the J = 0 line isnot observed since i t is too close to the laser line. The first observed line is J = 2, the second J = 4, etc.
Volume 54, Number 10, October 1977 / 643
