Kent R. Logan Foirfox County Public Schools Marshall High School Foirfox, Virginia
I Some Experiments in Atomic Structure
One of the more exciting areas of investigation and, traditionally, one in which the opportunities to explore on a secondary level are few is that of atomic structure. Not uncommon are demonstrations of flame tests and gas discharge tubes in familiarizing students with concepts related to line spectra and quantized energy. This approach is often adequate. Yet, it is possible to pursue this difficult hut interesting area further and offer students a chance of better understanding based upon first-hand experience. Uncertainties are certain in quantum phenomena, and confusion is natural without sufficient guidance or experience. Laboratory experimentation offers one way to red a c e inexoerience with meanink'. For the'past two years now, I have been investigating the roll of spectral color slides in laboratory situations. The slides, developed and used in conjunction with Purdue University's (NSF supported) master of science degree program, consist of various individual bright line spectra. Several advantages have encouraged my continued use of these slides; the chief of these are (1) The various spectra are beautiful to observe. (2) A fairly realistic color representation of the spectrum can be simply presented. (3) The necessary materials far the performance of such an experiment are easily obtainable. (4) Detailed observation can be easily made on a given spectrum. (5) For demonstration purposes, difficult to see and often obscured colors of flame spectra can be presented in diffracted form, leaving little argument as to the presence of certain colors. (6) Although less sensitive beyond 6703 A than the human eye, chrome film is more responsive to the violet and beginning uv regions. (7) Once a set of spectrograms is acquired, it lasts a great many years, considerably longer than the lifetime of many spectral gas dischargetubes. Three laboratory experiments designed to enhance the use of spectral slides are: (1) Color and Wavelength (2) Evidence of Quantization (a determination of Planck's
100 cm
Di:harge
camera Figure 1. Sef-up for photographing spectra.
constant) and (3) The Ionization Energy of the Hydrogen Atom. In each experiment, measurement of the relative spacings between lines is made with a meter ruler and taken off a nonmoveable projection screen (such as a wall). A brief descriotion of each experiment follows. Color and Wavelength
Use A = d sin 8 to calculate the wavelengths of assigned bright lines. A is the wavelength, d the given (predetermined) grating constant, and sin 8 the ratio of the distance (x) off the screen to the distance between projector and screen-defined as the square root of (1W2 x2) (see Fig. 1). Notice that (from Fig. 1) 1W cm was used at the time of photographic exposure. Depending on its design, the projector used may be placed a t a distance other than 100 em, but the important distance for experimental purposes is whatever distance was used a t the time the spectrograms were made. Given are a sample calculation as well as typical data for the helium spectrum.
+
X = d sin 8
d = 1.72 x 10-4 em, found by the instructor and x = 42.1 ern for He red line and measured off projection screen by the student. (42.1) (421 cm) A = 1.72 X lo-' cm ilW + 42,12 cm = 1.72 X lo-' cm A = 6.67 x
cm
Also. see Table 1.
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Table 1. Helium
Color
ii Trials
Actual Wavelength (X cm)
Red Yellow Green I Green I1 Blue-Green Violet I Violet I1 Violet 111
10 8 8 9 6 9 9 9
6.68 5.88 5 .05 5.02 4.92 4.71 4.47 3.89
Distance Range (cm)
Ideal Distance (cm)
Wavelength Range (X em)
Class Average (X cm)
6.64-6.74 5.85-5.90 5.02-5.06 5 .OO-5.04 4.91-4.95 4.68-4.73 4.45-4.49 3 99-3.92
6.68 5.87 5 .04 5.02 4.92 4.70 4.47 3 .90
h-Range (erg sec)
Class Average (erg sec) ( X lo-? 6.60 6.62 6.60 6.62 6.63
Table 2. Mercurv Range Distance Color
-- ---- -
Green I1 Violet I Violet I1 Violet I11
(4
#Trials
Energy (ergs) ( X lo-")
. .
9 11 12 10
33.2-33.7 26.1-26.3 24.1-24.3 21.6-21.8
-
Range Wavelength ( X lo-$ c m ) 5.71-5.80 5.42-5.50 4.35-4.37 4.034.06 3.62-3.66
Table4. Calculated Wave Numbers in A i r of Measured Spectral Lines for Hydrogen (X10km-') Line I1 (Blue-Greed
2.02 2.03 2.04 2.05
IV (Violet)
2.40 2 . 4 1 2.42 2.43 2.44 2.45 5 7 1 5 8 4 5
Line
A = d sin lJ d = 1.72 X 106 em
6.56-6.60 6.58-6.68 6.57-6.62 6.60-6.64 6.59-6.65
Table 3. Typical Student Data
Evidence of Quantization Presented to each student are the energy values of assigned lines along with the speed of light constant. For each line, the value of h, Planck's constant is determined. From E = h u and "A = c one obtains E = h c/A. E represents the energy of the photon; v , the frequency of the photon; A, the wavelength associated with the photon; c, the speed of light which is 3.00 x 1O1O cmfsec; and h, Planck's constant which can he represented from the equation as h = E A/c. Given E and c, the student measures and determines A off the projected image and uses this value to compute h. Provided are a sample calculation and data. Given: E = 54.5 x 10-l3 ergs, c = 3.00 x 1010 cm/sec, and measured: x =21.7 cm.
( X 10-9
Number reported
2 . 0 6 2.07
2.46 2.47 0
1
Table 5. Rydberg Constants from Student Graphs (X 105cm-1) -
X = 365 X 10- cm for third intense violet line of Hg
Rydberg values Number reported Clam average
Actual value
1.09 x 10r em-' 1.10 X 10rem-1
Also see data Table 2. The Ionization Energy of the Hydrogen Atom The Rydherg equation is used to determine the ionization energy of the hydrogen atom. The equation
or so t h a t
R is significant in that it stands for the ionization energy of the hydrogen atom in units of cm-I. The value of R can he easily related to the treatment of the hydrogen atom by Bohr. i. stands for wave number (cm-I) which is proportional to energy. R is the Rydherg constant expressed in em-l. n, represents any lower energy state (stationary state) while n, represents any higher (excited) stationary state. nx and n, are always integers but ny must always be greater than n, for a given series (Lyman, Balmer, etc.). The relevancy of R can be shown by defining the conditions necessary for ionization in terms of the Rydherg equation. For this condition, we associate an electron transition from n, = 1 as the ground state to n, = infinity as the final state. Therefore 412
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converted to kcalfmole is 314 kcal/mole. Student Procedure After measuring the first four lines of the Balmer series (more than four lines show up on tungsten film), A is calculated and converted to F (s = 1/A). A table is made of lfn,? and i values. I t may be necessary to advise the student that work in the visible range demands the Balmer series be used in which nz = 2 and n, is greater than 2. An "ideal" table would look like Table 3. Other typical data are presented along with a sample calculation. Refer to Tables 4 and 5 and Figure 2.
lowing material will curtail the waste of time and film one is otherwise subject to. The equipment consists of a 35mm camera with a wide angle lens (f12.8, 35 mm) attachment. An inexpensive ($10) diffraction grating was used, hut a more expensive one would not significantly improve accuracy since the ultimate measuring device is the meter ruler. Various gas discharge tubes (H, He, Hg, Ne, Kr, Xe) and, no less important, a heavy cardboard sheet mounted with black construction paper allowing a very narrow slit for the emission of light conclude the necessi. ties. The specific directions in filming involve placing the camera with the grating over the lens set a t a specific distance from the light source, a convenient number being 100.0 cm. Viewing the spectra through the camera before photographing to ensure proper alignment and darkening the room completely to avoid stray light are essential. Diagrammed in Figures 1and 3 are the particulars. Photographic Specifications
Film type: Kodachrome, ASA 64 (Din 191, except for hydrogen, where tungsten film was used. exposure time
element
H He Hg Ne
f-stop
2.8 2.8 2.8 2.8
(set)
2.0 20 90 10
slit width
0.5mm or less 0.5mm or less 0.5mm or less 0.5mm or less
Figure 2. Image as viewed through camera.
For demonstration purposes, the following flame spectra of metal ions can be prepared. Film type: Kodachrome ASA 64; slit width: wide (6mm approx.).
Black .Covered Cardboard
E l Liht Emitted
Figure 3. Graph of class results.
Sample Caiculation For hydrogen blue-green line, a student measured x = 29.5 cm from the screen. X = d sin 0
A
= 4.865 X 10" crn 1 -" = -1= = 2.06 X 4.865 X lo-' cm
x 10'
cm?
Since the blue-green line is the second line of the spectrum, the corresponding n, value must he 4. All this can he discussed with the students in relation to the Bohr theory and Balmer series. A plot of l/ny2 on the x axis and i. on t h e y axis is made by each student. The slope of the graph represents the negative of the Rydherg constant. The negative is because the value of l/nY2 is actually negative in the equation, hut, usually, its positive value is plotted.
element K Cu
Li
f-stop
2.8 2.8 2.8
exposure time (sec) 5 1
5
Limitations Standardizing a spectrogram for use can he tedious. One way is to use one line on the spectrum as a reference, set to the same distance used in filming the spectra. Other lines can then he used for experimental measurement. Film warping under the intense heat of the projector lamp may introduce significant error to the extent that only two significant figures can he obtained. A wellventilated projector is recommended. In deciding what is to he the correct distance, a standard wavelength must be used to known accuracy. A complete description of intensities and wavelengths may he referred to as a means of identifying each line of the spectrum. An excellent table of descriptions is the "American Institute of Physics Handbook," For standardizing one wavelength a t a known distance on the screen, w = d sin 0 is used. Transformed, the equation becomes
in which w is the standard wavelength ohtained from the literature; d, the grating spacing constant, is previously determined in the laboratory; and x represents the to-hemeasured distance from the center of the spectrum to the standard wavelength. Students use the same equation except measure x and solve for w ; d must he given. The foregoing laboratory experiments have not proven to he without difficulty. Certain colors are not well repre-
Teaching Guidelines
Creating a satisfactory set of spectrograms is a function of trial and error. Hopefully, the data presented in the folVolume 51, Number 6, June 1974
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413
sented on film. Deep reds, orange, hlue, shades of yellowgreen are cast in untrue form. The krypton spectrum exhibits a strong yellow line in the midst of other green lines, a physically misleading "fact" about the true spectrum made possible by the different emulsion layers on color film. Spectra should he checked during every class period to correct for any possible movement as the projections are extremelv sensitive to the slightest iar. Accuracy is enhanced by working exclusively with t h e right half df the ~roiectedimage and positioning the meter ruler with its Eh.0cm mark on the center of the spectrum. As could happen when using a low cost grating, the right and left halves of the spectra may not agree perfectly in measurement although they should. This trouble can he offset by standardizine onlv- one side of the image. In the final analysis, three significant figures of data-limit results to at best +3 on the third significant digit.
-
Extensions Two recentlv exolored ideas which have Droven acceotable for spect;ogrs'm demonstrations are tl;e Zeeman ~ f fect and detection of infared radiation usine ir film. The splitting of spectral lines in the presence of a strong magnetic field (Zeeman Effect) has little application to chemistry on a secondary level, hut the use of ir film has offered a way to detect and verify the emission of radiation other than visible light emanating from atoms. The use of ir in spectrograms increases the sensitivity range to a limit slightly beyond 80M) A. While infrareds emerge as reds on ir film, other colors are shifted toward the blue end of the spectrum. Visible red appears yellow and some-
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/ Journal of Chemical Education
times even green, yellow as hlue, violet as violet, and ultraviolet appears magenta. IR film discriminates hetween uv, visible, and ir radiation all on the same spectrogram. Although spectroscopy is a relatively untested area in secondary schools and in terms of deeper theory should remain as such, the means and opportunity are great for those with the desire to explore quantitatively the elementary concepts. A good example of combining quantitative work with elementary theory is the Bohr theory of the atom and its application to the hydrogen atom. Although inadequate in many respects for the beginner, this theory is often relied upon in explaining spectra to students in secondary chemistry. Even for those that go heyond this, the Bohr postulates still offer the gentlest way of introducing the difficult ideas of quantum mechanics. Those who merely survey chemistry, however, will find that a t the very least, many of the spectrograms are heautiful to observe and serve to illustrate qualitatively the same fundamentals studied by others mathematically.
General References Eestman K d a k Ca.. "Color as Seen and Photographed," Rochester. New Yolk. 1966, pp 248. ~ ~cmgeR., ~ hrd. i~ i ~ ~c.. h and ~ Lmmoumw, ~ d , h h n R., spdms: copy." h n t i e - H a l l hc., Englewod Cliffs. New J e ~ y 1959, , pp 1M117 and 141221. -~
Sernat. Honrv. "lntmduction b, Atomic and Nuclear Physics." Holf. Rinihart, end win^ ston. NeuYork, 1 9 6 6 . p ~390-307. Shoemaker, Dand P.. and Garland. Carl W.. "Experiments in Physical Chemidry: McCraw-HillBm*CompanyInc.,NewYork, 1962.pp316-321.
