PHYSICS 116 SPECTROSCOPY: DETERMINATION OF THE WAVELENGTH OF LIGHT
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1 Name Date Lab Time Lab TA PHYSICS 116 SPECTROSCOPY: DETERMINATION OF THE WAVELENGTH OF LIGHT I. PURPOSE To use a diffraction grating to investigate the spectra produced by several unknown gas discharge tubes. Then compare the measured wavelengths to spectral charts of the elements to determine the composition of the gases. II. APPARATUS Three different gas discharge tubes with high-voltage power supplies, meter stick spectrometer (3 meter sticks, holders and diffraction grating), a length of string, and a white light source and chart of spectral lines in the front of the room. III. INTRODUCTION That small part of the total electromagnetic spectrum to which our eyes are sensitive is what we call "visible light." We know that the visible spectrum consists of various colors (red at one end, violet at the other), but color is a subjective quantity. The corresponding physical quantity is the light frequency. (This is similar to the way the frequency of sound waves corresponds to their observed pitch.) Frequency, wavelength and the speed of light are related by the familiar expression: where is the wavelength, f is the frequency, and c is the speed of light (= 3 x cm/sec in vacuum). c f (1) Since the frequency of visible light ranges from 7.5 x Hz (deep violet) to 4.3 x Hz (deep red), Eq. 1 tells us that the wavelength of visible light is extremely small: 3 x 10-5 cm (deep violet ) to 7 x 10-5 cm (deep red). Two questions come to mind: 1) Is it possible to measure something this small? and 2) Physics 116 Spectroscopy Summer 2002 Page 1.
2 If we can, why would we want to? First, it is possible, and we will do so in this experiment. Second, among other things, it is a useful tool for identifying minute amounts of different elements in a sample. Each element in the periodic table has its own characteristic atomic structure. An element in a gaseous form and excited by some means will, upon de-excitation, emit light of various discrete (i.e., separate) frequencies which are characteristic of that element only. We say that each element has its characteristic spectrum. The more complicated the atomic structure the more complicated is the spectrum. * If we can determine these frequencies, we have a means of identifying the element(s) present in the source. Astronomers, for example, use this technique to determine the chemical composition of stars. A forensic expert might use this technique to identify the origin of a chip of paint collected from the scene of a crime. Using the technique to study light from a source is called spectroscopy and the instrument a spectroscopist uses is called a spectroscope. High quality spectroscopes are expensive, but we can gain some understanding of how they work with some inexpensive equipment. A. DETERMINATION OF WAVELENGTH If we pass a beam of white light through a prism, each color (strictly speaking, each frequency) is deviated (bent) by a different amount (Fig. 1). As a result, a prism is capable of "breaking up" light into its constituent colors. We call this "broken up white light" a spectrum. Since an inexpensive prism does not "bend" or separate out the various colors very clearly, we shall use a different device called a "diffraction grating". Photography allows us to create high-quality, inexpensive diffraction gratings, so we will use them for our experiment. Figure 1. The Prism. * Hot solids emit a continuous, rather than discrete spectrum. Page 2 Physics 116 Spectroscopy Summer 2002.
3 Now if we replace the prism in Fig. 1 by a diffraction grating (which consists of many equallydistant narrow slits) we find that it also separates the incoming light into component colors (Fig. 2). The principle in terms of which we explain the action of the diffraction grating is that of interference. A diffraction grating can be thought of as many double slits side by side. There exists a very simple mathematical relationship between the angle of deviation of a given color and its wavelength: d sin( ) (2) where d is the (very small) distance between adjacent slits (usually stamped on each grating). Figure 2. The Diffraction Grating. So all that one has to do to determine the wavelength is to measure the corresponding angle of deviation. In our experiment sin( ) in Eq. 2 will be obtained from the ratio of two measured lengths (X and R; see Fig. 3). The grating equation, Eq. 2, will then take the final form: d X R [grating equation] (3) Physics 116 Spectroscopy Summer 2002 Page 3.
4 B. THE METER-STICK SPECTROMETER The equipment to be used is very simple: various light sources, three meter sticks, a piece of string and a diffraction grating in a holder. The experimental arrangement of the "meter-stick" spectrometer is sketched in Fig. 3. Several long and narrow (pencil shape) light sources are supplied that yield line spectra (e.g. mercury, helium, hydrogen, argon and neon). All of these sources are in a gaseous (or vapor) form and are continuously excited by electron bombardment. The purpose of the experiment is to determine the wavelengths of all prominent spectral lines emitted by sources labeled I, II and III and thereby identify each element. Figure 3. "Meter-Stick" Spectrometer. In spite of the apparent crudeness of the apparatus, the "meter-stick spectrometer" is capable of yielding values for wavelengths significant (i.e., meaningful) to 3 digits, provided the spectrometer is correctly set up. Meter sticks #1 and #2 should be accurately at right angles to each other (a special 90 template is available to check this) and the light source should be positioned directly in front of the 50 cm mark of meter stick #1. Make sure that both these requirements are satisfied for each setup before you start taking any data. Page 4 Physics 116 Spectroscopy Summer 2002.
5 IV. PROCEDURE A. Qualitative: Place a diffraction grating close to one of your eyes and look through it at each of the light sources in the lab. 1. The room needs to be dark in order to see the weaker spectral lines. You may need to use a flashlight to see the marking on the meter sticks. 2. Start with the white light source first and note that there are two continuous spectra, one on each side of the source. Also note that the red end of the spectrum is deviated through a greater angle than the blue. 3. Next, observe the line spectra from each of the discharge tubes. B. Quantitative: 1. Next, use the "meter-stick" spectrometer attached to one of the discharge tubes labeled I, II or III. You should see several distinct lines, each of a different color, superimposed on meter stick #1. 2. Concentrate on the spectral lines to one side of the source, say right (see Fig. 4). Note the reading on the meter stick (to the nearest 0.1 cm) which coincides with each spectral line. Write these down in the table provided on the last page of this write-up. If you subtract 50 cm from each meter stick reading, you have the required value of X. Figure 4. What you should see when you look through the grating (assuming the line source emits light of one frequency only). 3. To obtain R (see Fig. 3), use a third meter stick; R will need to be less than 100 cm. Record the positions of the spectral lines on meter stick #1 and the position of the diffraction grating on meter stick #2. Now remove the grating from meter stick #2, lay the third meter stick on edge across the other two at the two recorded points, and write down the measured value of R (to the nearest 0.1 cm) for each line in the table. Physics 116 Spectroscopy Summer 2002 Page 5.
6 4. Using Eq. 3, calculate the wavelength for each spectral line. The value of d for our gratings is 189 x 10-6 cm, or 189 millionths of cm. 5. Finally, compare your values of the wavelengths with those on the spectral chart in the lab. Hence, identify the element. 6. Repeat for the other two labeled sources. Summarize your findings on the data sheet provided on the next page. Page 6 Physics 116 Spectroscopy Summer 2002.
7 Light Source I DATA SHEET Spectral Line (color) Meter Stick Reading (cm) X (cm) R (cm) X/R Your Value d X/R (10-6 cm) Chart Value (10-6 cm) Element is: Light Source II Element is: Light Source III Element is: Physics 116 Spectroscopy Summer 2002 Page 7.
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