Experiment with the Hydrogen Spectrum (Effectively and Inexpensively) Eugene Reiss Independence High School, 61 11 Archwood Road, Independence, OH 44131 The teaching unit covering the electronic structure of the atom in high school classes must be done without supporting laboratory work. Only a few laboratory manuals have an exercise involvina spectral observations. One1 calls for the use of a s p e c t r o s ~ o ~hut e fails to relate the observations to atomic structure. The equipment is expensive and can be used by only one student a t a time. The other manuals2"call for a diffraction grating, hydrogen bulb, and high-voltage source. While reducing the cost considerably by substituting a grating for a spectroscope, these methods are limited toone student at a time unless one has anumber of hydrogen bulbs and high-voltage sources. At Independence Hiah School we have one hvdroaen - - bulb and spark coil. However, we do have a number of cheap diffraction eratines in cardboard. hand soectroscopes, and a method to put thkm all in use at the same time. T h e published m e t h ~ d requires ~-~ a right triangle, as the Pythagorean theorem is used to determine sine A in the equation X = d -ink A . The gratings can he lined up side by side for simultaneous \,iewing, and the need frrr the right triangle avoided by measuring three iides of the triangle and using the law of cosines to determine the desired angle A. A 6-V power source is used along with a spark coil to fire the hydrogen bulb. A reflector for the bulb can he made by cutting a paper towel tube in half lengthwise and lining it with aluminum foil. (It is possible to purchase an integrated unit to eliminate daneline wires and the iurv-riaeed appearance of this equipmek) kternatively, the tbwei'tuhecan he oainted with a flat white of hieh albedo. A piece of paper about 3 o r 4 m long and 6 in. wide is also needed. A broad magic marker is used to delineate 5-cm spacings numbered by tens. As the laboratory will he darkened, these marks must be bold enough to be seen. The paper strip is mounted horizontally 011-a wall with Scotch tape. It is mounted about a fuut above bench height *o it will be level wirh the diffmrtion rmtined. The lieht is oositioned vertically just in front of the zero mark on the paper. Students farthest from the liaht mav have trouble seeine" the " purple line, so it is best to center the light for observation. Hence, the paper strip should begin with zero in the center
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Wagner, M. Laboratory Manual for Chemistry; Cebco: Fairfieid, NJ. 1983; p 63. De Bruyne, K. I.; Kirk. L. R.; Beers. L. D. Semimicro Chemistry; Holt. Rinehart & Winston: New York, 1966: p 35. Toon. E. R.; Ellis. G. L. LaboratoryExperiments forFoundationsof Chemistry; Holt, Rinehart & Winston: New York. 1968; p 80. 'Ferguson, H. W.; Schmuckier. J. S.; Caro, A. N.: Johnson, A. Laboratory investigations in Chemist~y;Silver Burden: Morristown. NJ. 1978; p 67.
Difhanion gratings mounted on ringslands.
and be numbered by tens in both a right- and left-hand direction. The students will observe either the left or the right spectrum depending on their location with respect to the liaht. The order of the colors in the left spectrum will he the reverse of the right spectrum. Cardboard hand spectroscopes can be purchased cheaply from a number of science supdly houses. These have a replica grating in a cardboard end piece that can he removed and mounted in a test tube clamp on a ring stand. No slitted shield is needed for the long, narrow hydrogen bulb. The grating should be rotated so that one sees vertical images of the lamp on the paper measuring strip. The onlv other thines " needed are 4-m leneths of strine and some meter sticks. 'l'ht jtu~lent;a,ill measure the distances from the rratine to the hulband to t h e s ~ e c t r aline l uositii~ns with the itringand then measure thesestring lengt'hs with a meter stick. Three lines of the hydrogen spectrum are observed using a simple diffraction grating. By measuring the three sides of the triangle formed between the light, the grating, and the apparent position of a given spectral line, the frequency of that line can he determined. Three lines-red, aqua, and purple-are observed. Hence three triangles are formed, one for each color. The students are instructed to observe the spectral lines and record the apparent positions of the lines on the measuring strip. After the observations are recorded, the room Volume 65 Number 6 June 1988
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lights are turned on, and the students use the string to measure the distance from the grating they used to the hydrogen bulb and to each of the spectral line positions. T o avoid any possibility of electric shock, disconnect the apparatus before allowing the students to make these measurements. Themeasurements thestudents have are thesides of three overlapping triangles. (See the figure.) Side b, which is common to all three triangles, connects the bulb and the diffraction grating. Side a is the measuring strip and is shared by the three triangles; only the lengths are different. Side c is the span between the grating and the spectral line. Side c is the only line that is different in each triangle. Angle A is the angle of interest. The lengths of the sides of the triangles are used in conjunction with the law of cosines to determine angle A. The law of cosines is cos A = (b2 c2 -
+
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Journal of Chemical Education
a2)/2bc,where b, c, and a are the afore-described sides of the triangle. Once angle A is determined, the wavelength, X, can he found using X = d sine A. The spacing, d, is the reciprocal of the number of lines per centimeter in the grating. Our gratings are typical, with 5270 lines per centimeter. This number should be ascertained when purchasing the cardboard spectroscopes. Prior to the experiment, the students are exposed to the relation between frequency and wavelength ( X u = c) and how the frequency of the emitted light is related to energy changes in the hydrogen electron ( 6 = nu). After doing the experiment, the students determine the wavelength, frequency, and the electron's orbital energy changes. They then compare this last value with the published value to find the percentage error of their work. Careful work yields results with 1%error or less.
