Ralph Schoenbeck and Frederick D. TabbuW Reed College
Portland, Oregon
I
I
An hexpensive Spectrograph of Moderately High Resolution
A
number of spectrographic experiments exist which quantitatively demonstrate aspects of quantum chemistly. For most experiments, however, the cost of a spectrograph which has the necessary resolution is prohibitively high. This article describes a spectrograph with a resolving power greater than 6000 which can easily be built for a cost of parts less than 680. Experiments can be performed with this spectrograph which are applicable to courses ranging from high school science t,o college experimental physical chemistry.
Table 1identifies the parts in the first five figures and indicates their source and cost. The construction of the spectrograph is sufficiently described in these figures that a detailed explanation of the construction is
412' STEEL LEG
BOLTEO 1 0 BOTTOM
1 -
1
,s,, 1 -
Fig. 2. Fig. 1.
Entrance slits detoil.
Top view (cover removed).
Spectrograph
Construction. The spectrograph uses the monochromator of Ehert (I). Its construction is similar to that described previously for a spectrophotometer ( 2 ) . An over-all view of the spectrograph is shown in Figure 1. Figures 2-5 show details of the important parts. We would like to express our appreciation to the Course Content Improvement Section of the Special Projects in Science Edueation branch of the National Science Foundation. This paper is taken in part from the BA thesis of it. Schoenbeck, Reed College, 1962.
452 / Journal of Chemical Educafion
unnecessary. It should be noted that none of th? dimensions is particularly critical. Students can easily constrnct these housings. Alignment. To focus the spectrograph the reflecting surface of M1 is adjusted to 30 in. from the slit. Then, in a darkened room, a shielded light bulb is placed before the slit and moved laterally until its image falls squarely on mirror M I . A white card is placed in front of the grating, facing M I , and M1 is adjusted until the light through the slit falls squarely on the grating. The grating is rotated until it is nearly parallel with the side on which the slits are mounted. The white card is then placed in front of M2 and the
grating adjusted until the card is fully illuminated with white light. (It may be necessary to adjust the tilt of the grating.) This position of the grating corresponds to the zeroth order. M2 is adjusted until the image of the first slit is centered in the 1-in. X 5-in. slot in side A where the film holder is clamped.
Figure 3.
Grating mount detail.
plate factor in angstroms per millimeter of film determined. The wavelengths of unknown lines are then determined by interpolation. Actually, the plate factor is not exactly linear. Since the film is held flat and not curved along a radius from M 2 , the plate factor will decrease symmetrically around the center of the film. This deviation can be determined from a known spectrum. A reasonable plate factor (21 A/mm) is used to measure wavelengths from the edge of the spectrogram nearest the grating. The correction in angstroms, which must be added to the measured wavelengths to obtain the correct wavelength, is plotted in Figure 6. These corrections are obtained from an examination of the known liues in an iron arc spectrum and they vary as M2 is shifted. This correction graph is applicable to any rotational position of the grating. Measurements of other portiop of the iron spectrum have an accuracy of 0.25 A with the use of such a graph. Adequate accuracy is possible by using only a single experimentally determined plate factor and interpolating from the nearest mercury line. The results which are cited in the experimental section were determined usiug the latter method. Table 1.
Figure 4.
Optical Parts List far Spectrograph
Part
Amount
Supplier
3-in. spherical mirror Cat. No. 50082
2
3 in. mirror mount kits Cat. yo. 50169 Plane refleectmg grating2in. X Zin., 15,00OIines/in (Jarrell-Ash) Cat. KO.30320
Edmund Scientific Co., Barrineton. New J&):
2 1
Total cost($) 15.30
...
5.90
J ~ Y ~ L Co. A s ~ 50.00 26 Farwell Street, Newtonville 60. Mxss.
Crotr rectionof spheric01 reflecting mirror assembly.
The final focusing of the spectrograph is performed visually, then photographically. The light bulb is replaced with a GE 275 watt sun lamp. A translucent sheet of cellophane or glass is taped to the outside of the slot a t the same distance from M2 that the film will he. The grating is rotated until the first order spectrum comes into view. Mirror iM2 is adjusted until the lines appear sharpest. A vely fine opening in the slit is advisable for this adjustment. Finally the spectrum of the iron arc is photographed for minor changes in the setting of M2. The setting which shows the maximum separation of lines is chosen from an examination of the exposures. The spectrograph is now focused for any rotation of the grating. Because of the long focal length of the mirrors, an error of 1-2 mm in the adjustment of M2 does not have a significant effect on the resolution. Calibration. The calibration of a spectrum in waveleugth is accomplished by a multiple exposure (3). Half of the length of the slit is covered with tape and an exposure taken. Then the tape is moved to the other half and anexposure of a known source, usually mercury (sun lamp), is taken. The lines in the known spectrum are identified. A linear dispersion is assumed and a
Figure 5.
Film holder detail.
Performance. Czerny and Turner (4) demonstrated that a symmetrical optical system like the Ebert monochromator is theoretically free of aberrations. The lack of distortion in addition to the long focal length of the mirrors results in a spectrograph which can produce remarkably sharp spectra very easily. An examination of the iron spectrum with the traveling Volume 40, Number 9, September 1963
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453
micrpope has revealed that two lines which are about 0.7 A apart (4408.424407.72, 4250.74250.13) can be resolved whereas a 0.3 A separation (4233.614233.95) is unresolved. A separation of 0.7 k at 4100 A corresponds to a resolving power of 6300.
Figure 6.
A colibrationcvrve for the spectrograph.
The resoh~tioncan be enhanced a t the expens of intensity by using higher orders of the grating. In doing this one must use caution since overlapphg orders produce a very confusing spectrum. If a filter is inserted between the source and the slit, the unwanted orders can be eliminated, however, at an additional cxpense in intensity. Although we have not exploited this in our measurements, the resolution to be gained is demonstrated in Figures 7a, b, c, and d. These are the spectra caused by the intense emission of CN in a carbon arc in air. A blue filt,er (blue cellophane which transmits between 3600 A and 4700 A) was used and
Figvre7. CNvioletfrom a carbon arc in air: (01 6.5, order, ponotomic X, ~mollertslit opening poarible, 2 second exposure (bl ~econdorder, Panatomic X, ~ m d l e r trlit opening porrible, 1 minute exposure ( c ) third order, Ponatomic X, smollert rlit opening possible, 4 minuter exporure [dl fourth order. Royal Pan, smdest slit opening porrible, 4-8 minuter exporvre Throqhovt this work all f i h r were developed with DK-70 developer.
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Journal of Chemical Education
exposures made in the first, second, third, and fourth orders, Note thatin the first order the region between 4216 A and 4198 A appears to be a continuum but by the fourth order it has developed into definite rotational fine structure. It should be noted that the sp&mgraph has all reflecting optics. Consequently it is usable in any spectral region. Our photographic measurements have been confined by the use of commgrcial sheet film to the region between 2980 A and 6234 4. Measurement of Spectral Lines. Three methods were compared for measuring distances between lines. All three involved a magnification of the spectrum. A traveling microscope was first used; however, measnrements were tedious, which, coupled with the expense of the microscope, detracted from its general use. Yext a densitometer was assembled and used. This had the advantage of a quantitative comparison of intensity but offered no advantage in wavelength accuracy. Finally, and most simply, white paper was taped to a blackboard and the spect,rum projected onto it with a lantern slide projector. The lines of interest were marked on the paper and subsequently measured witaha ruler. A comparison in accuracy of the three methods is described in the iodine experiment. It is sufficient to say here that the t,hird met,hod was the most accurate. Experiments
Fraunhofer Lines (5). One of the easiest spectra to obtain is that of the sun. Satisfactory photographs can be made on Panatomic X film using the smallest possible slit opening and less than 1 sec exposure. The Fraunhofer lines are spread over too large a wavelength range to obtain them on the film with a single exposure. The grating must be rotated. I t should be noted that for equivalent resolution a more narrow slit is required in an absorpt,ion spectn~msuch as this than in an emission spectrum. Ralmer Lines ( 6 ) . The Balmer lines, like the Fraunhofer lines, require two exposures as shown in Figure 8. The spectra were obtained from a Geissler tube using for power a neon sign transformer whose primary vokage was controlled by a variable transformer. A 100 ohm resist,or was placed in series with the t,uhe and
Figure 8. Bolmer lines, Ponotomic X, slit 0.5 mm (wide), exposure time 10 minuter. The prime ('1 I n d i c d e ~the eiperimentol value bored on interpolotion from mercury liner.
Table 4.
Results of Swan Band Spectrum.
.."(em-') C~.lculrtted Herzberg (8e)
w*'(~m-~)
1607 1641
w."z.'(cm-')
w.'z.'(cm-')
8. 11.7
23. 16.4
1760 1788
Measurements hased on traveling microscope method. Table 5.
~~.
Snmrre ......
-
0.I
Densitometer Projection Traveling microscope Herzberg (8d)
215.9 214.6
Summary of Iodine Resultsa
..
DP
mm
wr.(E*i -, .
12,315 12,317 12,371 12,440
15,532 15,591 15,543 15,598.3
19,913 19,915 19,969 20,037
nb 4,381 4,324 4,426 4,439
w.'
w,'~,' .
Teb
133 127.7 129 128
1.045 0.970 0.921 0.834
15,635
~
15,641.6
~
All values are in cm-'. D." is the heat of dissooiation of the lower state and b Te is the energy separation between the potential minima. of the two states. Doof the upper state. a
the current through the secondary adjusted to 10-20 ma as measured by a vacuum tube voltmeter across the resistor. H, in Figure 8 is due to the transition n = 3 to n = 2. He is due to n = 4 to n = 2, etc. By plotting the frequency in wave number versus l/n2, where n is the quantum number of the initial state, a straight line is obtained whose slope is the Rydberg constant. The value in wave numbers for n = corresponds to the ionization energy from the n = 2 level. Table 2 is a tabulation of the results obtained. It should be noted that the isotopic shift in the spectmm for Hz predicted in the derivation of the Rydberg constant should be easily resolved with this spectrograph. A mixture of H1and H2would yield a spectrum of doublets. A wide slit (ca. 0.5 mm) was used to detect the less intense lines in the series.
-
Table 2.
Results of Balmer SpectrumE
Rvdberg constant Graphical Least squares Accepted value
11.1 X lO"~m-~ 11.01 X IO' em-' 10.9678 X 10' cm-'
progressions and considerable fine structure due to rotational transitions. An analysis of this spectrum to obtain vibrational constants for the upper electronic state of C2 has been described in detail elsewhere (7, 8a). To explain briefly, equations (1) and (2) are each substituted with the data from three lines yielding six equations with six unknowns. K - (a'w.' - v'hx.) for constant v' K' - ( v " ~ . " - uW2w."z,")for constant v"
mow =
wund=
(1)
(2)
I n these equations w , is~the energy in wave numbers of the line produced by a transition from the upper level of vibrational quantum number u' to the lower level, u". w,' and w," are the vibrational frequencies in wave numbers for the upper and lower states respectively, and w.'x,' and w,"xan, the first order anharmonicity corrections. K and K t are constants for a constant u' and v" respectively. w,.,. for the observed transitions between v" and u' levels are conveniently tabulated as shown in Table 3 (a DesLandres Table). Using this data, Table 4 gives a comparison of the experimental results.
p~
" Measurementshased on projection method Table 3.
C2Swan Bands. The radical, C2, which is found in carbon arcs and hydrocarbon flames has a characteristic emission in the region from 4380 to 6190 A. An oxyacetylene flame is a convenient source. Exposures were made with the smallest slit possible for about one hour on Panatomic X film. The spectrograph has sufficient resolution to show clearly the vibrational
Figure 9.
4
DesLandres Table of Swan Band Measurements
...
...
.. .
2.134
.. .
" All values X 10' em-'.
Absorption spectrum of iodine; Panatomic X, smdlert slit
slightly le.3 than one minute exposure.
Volume 40, Number 9,'September 1 9 6 3
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455
Table 6. Exciting line wavelength (A)
Results of Roman Spectrum of Liquid Benzene
Wavelength of ",(A)
A~(cm-)
Wavelength of v2(A)
Au(cm-')
975 991 981 949 914
5021 4611 4127 4107 4097
3031 3025 3085 3014 2989
QQZ
Figure 10. Graphical determination of the heot of disraciation of iodine: experimental slope lwe'xe'l, 0.970 sm-I; heat of disociation of upper electronic state 14'-area under line), 4324 cm-I; heot of ditraciationof difference in dissociation limits, 7598 lower electronic state ID,' = w~ cm-'l.12.317 rm -I.
-
Iz Absorplion Spectrum. Iodine like all diatomic halogens has an absorption spectrum whose lines merge into a continuum representing the dissociation limit (86, 9). Figure 9 is an absorption spectrum of gaseous iodine. The iodine spectrum was obtained by passing the light from a 100 watt projection bulb through a tube 20 em long and 25 mm wide which was close to the slit. The ends of the tube were sealed fairly flat and some iodine introduced through a small side arm. Sufficient iodine vapor was obtained by heating the tube with a low wattage light bulb placed beneath the tube. Most of the molecules exist in the lowest vibrational level of the ground electronic state (u" =O). The absorption lines correspond to a sequence of transitions from this level to u' =0, v' = 1, v" = 2 etc.. until finally the s,' level is reached which is the dissociation limit. Although the temperature of the
456 / Journd of Chemicol Education
2n~i
cell was only 30-40°C,the v' = 1 state is also significantly populated so that transitions from it are also evident. The manner in which the heat of dissociation of the ground state of iodine and the vibrational constants of both states can be calculated has been described in detail (7, 8c, 10). The method for iodine is inherently more accurate than C since iodine has more lines and they are nearly all used in the calculation. Figure 10 shows a typical curve. Table 5 is a tabulation of the experimental values measured by the three methods described above and the accepted values for comparison. R a m a n Spectrum. Although the spectrograph has the necessary dispersion for resolving Raman spectra the loss of intensity which accompanies thc use of a grating makes this measurement a marginal one. A spectrum was obtained by irradiating a 1 em diameter tube filled with liquid benzene with three GE sun lamps arranged radially about the tube. One end was sealed flat and set against the slit. The other end was shaped like a horn and taped on the outside with electrical tape to reduce the amount of scattered light. The results are tabulated in Table 6. Literature Cited (1) FASTIE,W.G.,J Opl.Soc.Arn.,42,6-11 (1952). (2) TABBUTT,F. D., J. CHEM.EDUC.,39,611 (1962). (3) See HARRISON,G. R., LORD, R. C., A N D LOOFBOUROW, J. R.. "Practical Speetroscopy," Prentice-Hall, Inc., New York, 1958, chap. 9. (4) CZERNY, M., A N D TURNER, A. F., Z. Physik, 61, 792 (1930). (5) BRODE,W. R., "Chemical Spectroscopy," John Wiley and Sons, Inc., New York, 1939, p. 441. C. W., "Experiments (6) SHOEMAKER, D. P., A N D GARLAND, in Physical Chemistry,'' MeGraw-Hill, New York, 1962, pp. 31621; Herzberg, G., "Atomic Spectra and Atomic Structure," 2nd ed., Dover, New York, 1944, pp. 11-38. (7) D ~ v r ~M. s , J., J. CHEM.EDUC.,28, 474 (1952). (8) Hereberg, G., "Spectra of Diatomic Molecules," D. Van Nostrand and Company, 2nd ed., New York, 1955, pp. (a) 151-5; ( b ) 388-94; (c) 90-101; ( d ) 54lLl; ( 6 ) 513. (9) BARROW, G. M., "Introduction to Molecular Spectroscopy," MeGraw-Hill, New Yurk, 1962, pp. 230-44. F. E., J. CHEM.EDUC.,39,626 (1962). (10) STAFPORD, (11) "Rnmnn Spectml Data." American Petroleum Institute Research Project 44, Csrnegie Institute of Technology, Pittsburgh, Pa., 1960.
