SPECTROSCOPY: Quantitative Analysis with Light

Transcription

1 SPECTROSCOPY: Quantitative Analysis with Light John R. Amend, PhD, Montana State University Dale A. Hammond, PhD, Brigham Young University-Hawaii Learning Objectives The objectives of this experiment are to: Identify band and line spectra, and relate the physical state of a light-emitting substance to the type of spectrum observed. Determine the relationship between the colors of the visible spectrum and wavelength and frequency. Determine the relationship between the energy, frequency, and wavelength of light waves. Examine the fingerprint nature of spectra. Construct a spectrograph calibration chart and identify an unknown element by measurement of its emission spectrum. Use an energy-state model to explain the atomic spectra of hydrogen gas. Introduction Atoms, as we have learned, are composed of tiny, massive, positively charged nuclei surrounded by a swarm of low mass, negative electrons. An atom by itself is not of great value to us, but when atoms connect together to form macroscopic aggregates of atoms, ions, or molecules, a host of new properties appear. Hydrogen and oxygen atoms combine to form water, one of the most prevalent molecules on Earth. Carbon, hydrogen, oxygen, and nitrogen combine in countless different ways to form the molecules that make our bodies and the food we eat. The joining of atoms to make molecules is of great importance to us. But how does this occur? An atomsized observer will tell us that what he sees is a swarm of electrons. When two or more atoms join together to form a molecule, what binds them together? It is the clouds of electrons that must somehow mesh to form a chemical bond. An understanding of bonding, then, must be prefaced by some understanding of the behavior of electrons in atoms. But how can we learn of this behavior? Electrons speak the language of light. When atoms are heated, electrons give back some of this energy as little bursts of light. The colors of light produced are both a fingerprint of the atom, and a clue to the way the atom's electrons are organized. This experiment is an experience into a foreign language - the language of electrons. To understand this language, we first have to learn a little about its words, which are the colors of light. This we will do in the first part of the experiment. We will see how the colors or spectra of light produced by hot atoms uniquely identify them, and finally, we will look at some of the experimental evidence that caused Niels Bohr to propose that electrons run in planetary orbits around their nuclei. This experiment is comprised of several small laboratory problems. Hot solid and gaseous sources of light are classified according to the type of spectrum they emit. 1

2 A simple diffraction grating and the concept of wave interference are used to develop a relationship between the color and wavelength of light. Light-emitting diodes are used to develop a relationship between the energy and color, frequency, and wavelength of light. An element in gaseous form is "finger printed" by its emission spectrum. An unknown element is identified by measurements made on a colored slide of its emission spectrum. Some evidence is collected to support Bohr's planetary orbit model for electrons. BACKGROUND: LIGHT IS A FORM OF WAVE MOTION. One of the more convincing bits of evidence supporting the wave model for light is the star pattern observed when a light is viewed through a close-mesh screen (Figure 1). The pattern of alternating light and dark bands radiating from each light source is called an "interference pattern," and the spacing of the bands is related to the wavelength of the light. Wavelength is defined as the distance between any two corresponding points on a wave, and thus has the units of length/wave. This commonly observed phenomenon may be explained by assuming that light has some properties normally attributed to waves, be they water waves, sound waves, or just waves on a jump rope. An important characteristic of waves is that of "interference." All forms of wave motion interfere. As waves cross, the individual disturbances add algebraically. If two wave crests (positive displacements) cross, a larger crest will result. If two wave troughs (negative displacements) cross, a larger trough will result. If a crest and a trough of comparable size cross, the positive and negative displacements will cancel, resulting in no displacement at all. Figure 2 presents a series of sketches that illustrate the crossing of small waves on a jump rope. Notice that when both waves have the same sign (positive or negative), they add when they cross, but when the displacements are of opposite sign, they cancel. A wave striking a barrier with two small slits will start two adjacent waves on the other side of the barrier. These two waves interfere in a very predictable pattern, resulting in the occurrence of constructive interference, or wave reinforcement, along a "centerline" drawn between the two slits and perpendicular to the barrier. In this region, wave crests cross and reinforce wave crests from the other source, and wave troughs cross and reinforce wave troughs. At a small angle from the centerline a region of destructive interference or cancellation exists (Figure 3). Along this line wave crests cross wave troughs, and wave troughs cross wave crests. This line of minimum disturbance is called a "nodal line." Farther out from the center is another region of constructive interference or wave reinforcement. 2

3 A difference in the interference pattern will be observed if the wavelength is changed. Figure 4 presents another sketch of this experiment, this time with shorter wavelength waves striking the slits. Waves with shorter wavelength form interference patterns closer to the centerline than do longer wavelength waves. At this point it seems that interference patterns may be used to determine the wavelength of light, provided that one could obtain a satisfactory slit assembly. Such an assembly is available in the form of a diffraction grating. This is a plastic material with approximately 14,400 slits ruled on its surface per inch. A simple diffraction grating spectroscope can be constructed utilizing about one cent worth of this material and an empty toothpaste tube box. A commercial version of such an instrument is sketched in Figure 5. Your laboratory instructor will have a supply of these simple spectroscopes on hand for your use in the laboratory, which may be the tube shown above, or a simple 35 mm slide mount with the diffraction grating plastic in it. Figure 5. A simple diffraction grating spectroscope. SAFETY PRECAUTIONS Observe all normal laboratory precautions. This experiment uses open flames and involves the use of several solutions. Normal laboratory precautions should be observed. Reagents: MATERIALS 1.0 M Solutions of NaNO 3, NaCl, Na2CO 3, and Na2SO4, LiNO 3, Ba(NO 3) 2, Sr(NO 3) 2, and 6.0 M HCl solution. Equipment: Spectroscopes, nichrome wire, incandescent lamps, fluorescent lamps, gas discharge tubes containing mercury, hydrogen, helium and neon, MicroLAB Model 210 Energy of Light module. Unknowns: Found in the program Atomic Spectrum on the computers. Operational instructions for this program, and how to obtain your unknowns will be discussed later. 3

4 Using the Spectroscope Look toward an incandescent light bulb through your spectroscope. You should see a spectrum by looking to either side. This, of course, is formed by the bright lines of the interference patterns of the various wavelengths making up the spectrum. You may be able to see a second-order spectrum at still a greater angle from the centerline. If the spectrum is a vertical band instead of a horizontal band, rotate the grating 90 degrees so that the spectrum appears horizontal. Problem I: Solid vs. Gaseous Spectra Examine the spectrum of an incandescent light bulb, and compare it to the spectrum of one of the discharge tubes that were examined, and with that of a fluorescent lamp. (Q1) Describe the spectrum observed in each. Look at a clean glowing nichrome wire held in a Bunsen flame. (It may be very difficult to eliminate the yellow color, due to sodium.) (Q2) Describe the spectrum observed there (Q3) Can you identify a basic difference between the spectrum observed from a heated solid and a highly heated gas such as the discharge tubes? Continuous spectra comprised of all colors are called band spectra. Line spectra are comprised of only certain colored lines. Obtain a yellow flame with your Bunsen burner by closing off the air supply. Look at the flame with your spectroscope (The region above the top of the burner itself). (Q4) Do you think it is composed of small bits of heated solid or matter in the true gaseous state? Record your observations in your lab notes and your lab report. Problem II: Color and Wavelength Look carefully at the arrangement of colors in the band spectrum of the incandescent light bulb. List them, beginning on the outside and moving toward the center. Now refer to Figures 3 and 4 and their associated discussion. (C1) Make a chart in your lab notes and for your report, listing the colors in order of decreasing wavelength. (Q5) From the previous discussion, which color has the longest wavelength? Which color has the shortest wavelength? Problem III: The Energy of Light Considerable experimental evidence indicates that electrons exist in definite states of energy within the atom. When electrons are excited to a higher energy state by application of heat or electrical energy, they absorb a specific amount of energy. When they then fall back to a lower energy state, they lose an amount of energy equal to the difference between the two energy states. See Figure 6. This energy, we believe, is radiated as electromagnetic radiation or light. The wavelength (and hence the color) of the radiation depends on the energy lost in producing it and, therefore, on the difference between the two states of energy between which the electron falls. Figure 6. Light is produced when electrons jump from higher energy to lower energy orbits. To explore the relationship between the energy and color of light, we will set up a simple experiment to produce colored light with light-emittingdiodes (LEDs). LEDs are commonly used for instrument displays, and are sometimes used in 4 Figure 7. Schematic of the Energy of Light board with current vs voltage graph.

5 digital clocks and cash register displays. LED's produce light when a voltage is applied across two electrodes, between which is a sample of semiconductor. When the voltage becomes great enough to promote an electron across the energy gap in the LED material, the electron will move up and then will fall back to a lower level, giving off light. The wavelength of light produced by some sample LEDs, in nanometers (nm) is listed in Table 1 and schematically illustrated in Figure 7. We will use the Energy of Light board to explore this relationship. It is designed with a series of LEDs that can be switched in, one at a time, a variable voltage source to increment the voltage to the LEDs, and a microampere bar indicator to indicate the number of microamperes of current passing through the LED. Each bar indicates twice the current as the previous one. Table 1 LED Wavelengths Red 635 Orange 600 Yellow 585 Green 550 Connect the Energy of Light board to the MicroLAB interface, and open the program called Energy of Light from the MicroLAB opening window. Set the voltage scale at 0.70 volts, the Auto Analysis Set Point at mv, select the red LED at 644 nm and then click on the Start/Stop button to begin the first scan. The Energy of Light program will now begin to increment the voltage by 20 mv every 250 milliseconds, each time measuring the current passing through the LED. As the current passes through mv, it will change the marker to a triangle to mark that current/voltage combination, and will plot a point on the Voltage/Wavelength lower graph. Click the Stop button when the current reading seen in the lower right window of the top graph has reached a value of 2500 milliamps. Take turns Watching carefully as the voltage is increasing to see at what current you can detect the first visible sign of light. It will help to do this in a darkened room, or to have a dark circular tube that you can place over the LED and hold your eye close to in order to block out any room light. Repeat this process for the orange, yellow/green and blue/green LEDs to give you relationship between the voltage required to obtain a current of milliamps and the color, or wavelength of each of the visible light LEDs. Now that you can see a pattern with the visible wavelength LEDs, complete the exercise by doing the same process for the 880 and 940 nm infrared LEDs, where you will not be able to see the LEDs turn on, but you can track them on the graph as for the other LEDs Print the Energy of Light screen image as follows: Simultaneously press CTRL + Print Scrn buttons. Open WordPad by clicking the sequence Start > Programs > Accessories > WordPad. Press Ctrl+V to save the screen image in WordPad, the Ctrl + P to print the WordPad page. Voltage versus Wavelength and Energy versus Frequency Frequency is defined as the number of waves passing a point per unit of time, which would then have the units of waves/time. Open a new MicroLAB experiment in the Hand Enter mode and enter voltage values into Column A and wavelength values into Column B, then using the Formula tool, calculate 1 /wavelength, and then click-drag this to Column C and to the Y1 axis, with Voltage plotted on the X axis. Turn this in with your report (G1). (Q6) What is the relationship between Voltage and? Make a table (T1)in your lab notes as instructed in Figure 8, showing the colors in order of increasing energy. Duplicate this in your lab report with discussion on the lower Energy of Light graph, click on the Joules and Frequency buttons and record in your lab notes the value of the coefficient of X (The slope of the line) in the upper graph. We will refer to this a little later. Color of Light & Energy Make a table or box showing colors in order of increasing energy, left to right. Fig. 8: The relationship between color and energy of light 5

6 (Q7) If wavelength has the units length/wave, and frequency has the units waves/time, what units will you get if you multiply these two? (Q8) What physical measurement has these units? (Q9) This quantity has a fixed value for electromagnetic radiation, and is called c. What is this value? When Max Planck explored this relationship of energy, frequency and wavelength, he discovered that the energy of light was quantized, i.e., that it came in fundamental units that could not be broken down into smaller portions. He symbolized this fundamental quantity with h, and it has become known as Planck s constant. Planck gave the equation for this relationship as E = h where is the frequency of the light. (Eq. 1) -34 This constant has been shown to have the value h = X 10 J s The accompanying data in Figure 9 was obtained with an interface which determined the voltage applied to the LED when the current was 0.5 ma. The MicroLAB spreadsheet currently cannot handle exponents as small as 10-34, so you will need to do the following either in EXCEL or QUATRO. Set this data up in the selected spreadsheet, then convert the millivolts to -22 Energy in Joules (J) by multiplying by 1.59 X 10. Convert wavelength to 8-9 frequency by dividing the speed of light, X 10 m/s by 1 X 10 m/nm, then dividing by the wavelength in nm, i.e., 8 = X 10 m 1.00 nm X 10 m nm s Wavelength millivolts Figure 9. Data from an experiment at 0.5 ma. Then graph energy in Joules vs. frequency and do a linear regression on the data. The slope of this data will -34 be a close approximation to Planck s constant of X 10 Js. Adjust the X and Y axes scale minimum values to just fit the limits of the data and be sure to include the regression equation and correlation value on the graph. Adjust the number of significant digits by selecting the equation, click on Format, then Number and chose 3. Make the graph large enough to be easily read, and print out both the data table and graph on a single page. (Q10) What is the value of the slope of this line? (Q11) How does it compare with Planck s constant? (Q12) Why does the Energy of Light program, with the current measured at 0.1 milliamperes give a better value of Planck s constant than the data taken at 0.5 milliamperes. By some simple unit conversions of the experimental measurements you made, you were able to derive Planck s constant. This shows the utility of graphing and massaging the data in the appropriate manner. Equation 1 has energy directly proportional to frequency. But we have already seen that energy is inversely proportional to the wavelength. (Q13) Therefore, what must then be the relationship between wavelength and frequency, and what would be the constant of proportionality between the two? (See question 9 above.) In your lab book and in your report, set up a table similar to Figure 10, showing the colors in order of increasing energy. Problem IV: The Fingerprint Nature of Spectra Light your burner and obtain a blue flame with no yellow tip. Examine the burner flame through the spectroscope. Notice that you see a band spectrum in the form of a series of burner tips in different colors, side by side. Now insert the nichrome wire into the hottest portion of the flame. When the wire is red hot, you will see a horizontal rainbow above the colored burner heads. When you have a salt solution on the nichrome wire, you will observe its color slightly higher above this colored band. Your laboratory will be equipped with several sets of test tubes containing lithium strontium, barium and several sodium compounds -- (sodium chloride, bicarbonate, or other sodium salts). These test tubes have stoppers with flame test wires mounted in them. Test the HCl test wire first by placing its loop at the hottest 6

7 part of the flame. In your lab notes, set up a 9 row by 3 column table as illustrated in Table 2 to answer the following questions concerning each of the solutions to be tested. (Duplicate this table in your lab report, T2.) (Q14) What color do you observe in the flame for each of the solutions? (Q15) Look at the flame through the spectroscope. What is the position of the color above the band spectrum of the wire? (You may have to replenish your supply of material on the flame test wire.) It works well to have one person hold the test wire in the flame and the other observe through a spectroscope, then trade off. The person holding the wire can then also watch to make sure the spectroscope does not approach so closely to the flame that it will catch fire! Solution Flame Color Spectrum Table 2: Ionic solution Flame colors Your laboratory instructor will set up discharge tubes containing elements in a gaseous state. Observe the emission spectra of these elements with your spectroscope and record your observations on the ATOMIC SPECTRA (C2) chart in your experiment packet similar to that sketched in Figure 11 and turn in a copy with your lab report. Note that this chart correlates color with the wavelength of light. Wavelength is indicated in nanometer (nm) units. A nanometer is an extremely small unit of distance commonly used to indicate the -9 wavelength of light waves. One nanometer (nm) is equal to 1 x 10 meter. Look carefully at the spectrum of the mercury discharge tube, then at the spectrum of the overhead fluorescent lamp. (Q16) Can you make any correlation between the complexity of the visible spectral lines with the element s position in the periodic table? (Q17) Can you identify an element present in the fluorescent lamp? Problem V: Identification of an unknown element from its discharge spectrum. Figure 10 shows a sketch of an instrument called a spectrophotometer. Figure 10 also shows a sketch of the spectrum of a sample of mercury that had been heated to vaporization and then excited with an electrical discharge. The color slides to be used in this section of the experiment were taken with similar equipment and color film. Note that the mercury spectrum contains several predominant colors or spectral lines. These colors range from yellow for the two closely-spaced lines on the right to violet for the left line. In some spectra you may see lines farther in the ultraviolet. Film is more sensitive to ultraviolet than the human eye, and can see spectral lines that are not visible when a person observes the spectrum. Violet Violet Blue Green 546 Yellow Yellow Table 3: The visible emission spectrum of mercury Figure 10. Spectra can be recorded on film using simple equipment. This figure shows the visible spectrum of mercury. When a different element is substituted for mercury and the spectrum observed, a different set of spectral lines are present. 7

8 Each element has a different set of spectral lines, and this set is always unique enough that it will be characteristic of only one or two particular elements and no others. The predominant spectral lines emitted by mercury are listed in Table 3. It is possible to identify elements and even mixtures of elements by observation of their spectra. In this part of this experiment you will be asked to identify one or two unknowns. Your laboratory instructor will provide you with a color slide of the emission spectrum of your unknown element. Unfortunately, it is difficult to determine the wavelength of the various spectral lines directly from the photograph or slide, since the camera has no calibration scale. However, if a known spectrum is included with the unknown, it is possible to project the slide onto a wavelength scale and construct a calibration graph similar to Figure 13, which relates position on the scale to wavelength. You will use a program in this experiment called Atomic Spectra which contains two spectra, both photographed through the same slit so that they will be in wavelength alignment along with a calibration scale. The top spectrum is that of mercury, and the bottom spectrum is either hydrogen, or an unknown, as selected from Image in the top control bar. You will first need to calibrate the system using the mercury spectrum, then we will run the hydrogen spectrum through as an example. 1. Click on the Atomic Spectra icon, click on the Calibration tab, select Image from the top menu, click on Hydrogen, then click on the button for nm for the mercury spectrum. Now click in the middle of the farthest left blue line of the mercury spectrum and a value will appear in the table at the lower left, and an x will appear on the graph. (You may need to have a darkened room to see this line.) 2. Repeat this for each of the remaining five wavelengths of the mercury spectrum. The second spectral line is the very faint line just to the right of the first blue line. Then there are two orange-yellow lines at the far right. 3. Now click on the Curve Fitting button, then on the Generate LS Curve button to get the regression line and equation. (See Figure 11.) The graph is now calibrated to the values of the mercury spectrum lines. 4. Click on the Unknown tab and then click on each of the lines in the hydrogen spectrum and the corresponding wavelength and pixel values will appear in the table. 5. Click on the Bring up Interactive Chart button to obtain a chart of line wavelengths for a number of elements. Figure 11. A sample calibration graph for your Atomic Spectrum unknown. Wavelength is on the Y axis, and the pixel value is on the X axis. 6. Change the value of the wavelength range at the bottom of the table to 5, then click Highlight to see where in that table that wavelength is found. 7. Repeat this for each of the points in the unknown to determine your unknown element. Of course, in this instance, we know that the unknown was hydrogen. You will notice that the 397 and 410 wavelengths don t show up in the hydrogen spectrum, as 410 is too faint, and 397 is in the UV region, below which most people can see, as well as faint. 8. When you do your unknown, print out the screen by pressing Alt-Prnt Scrn simultaneously, copy into WordPad using Ctrl-V, then print using Ctrl-P. Be sure to indicate the letter value of your unknown, and the identification of your unknown element in the space above the calibration table. 8

9 Problem VI: Some Support for Bohr's Planetary Electron Model. Niels Bohr was a young Danish postdoctoral student working for Earnest Rutherford when Rutherford s research group discovered the nucleus of the atom. Bohr returned to Denmark, intent on figuring out how electrons were arranged around the atom s nucleus. Because only certain colors of light were emitted by hot atoms, and because it was known at that time that light or electromagnetic radiation was produced by accelerating or decelerating electrons, Bohr proposed that electrons run in planetary orbits around atomic nuclei. See Figure 12. Each atom has a number of possible electron orbits. Electrons can be pushed to outer orbits by heating the atom, and Figure 12. A sketch of Bohr s planetary give off light when they fall back to inner orbits. Bohr used electron model. Bohr predicted that known laws of physics that governed circular motion, electrical electron jumps ending on level two would attraction, gravitational attraction, and the relationship between produce spectral lines ion the visible region energy and frequency or wavelength of electromagnetic of the spectrum. radiation to develop an equation that was able to predict the wavelength of light produced as an electron falls from an outer, higher energy orbit to an inner, lower energy orbit. Bohr figured this only for the element hydrogen, the simplest element in the periodic table. Bohr s equation is illustrated in Figure 13. In this equation, N 1 is the orbit on which the electron stops, and N is the orbit on which it starts its jump. 2 To produce wavelength numbers in nanometers, the constants that make up the left half of the equation work out to be Thus to figure out an electron jump from orbit 3 to orbit 2 would involve substituting 2 for N and 3 for N in the equation, giving: 1 2 Figure 13: Bohr s equation predicted that electron jumps beginning on different orbits would produce different colors of light. Bohr predicted that electron jumps ending on the second orbit would produce spectral lines in the visible region of the spectrum. (Table 6) Calculate these wavelengths for jumps of 4 to 2, and 6 to 2 to fill in the gaps in Table 6. Reproduce the completed Table 4 in your lab notes and include it in your report. (T3) Be sure to include your calculations in your lab report. Obtain the spectral lines of hydrogen gas from Table 4 to include in the Observed lab column and consider the following two questions. (Q18) Does Bohr s model appear to accurately predict the visible region spectral lines of hydrogen? Show this by setting up a table in your lab notes and in your report comparing the calculated wavelengths (4-2, and 6-2) and the observed wavelengths, as in Table 4. Table 4 : Hydrogen Spectral lines Jump Observed Calculated nm 4--2 nm nm 6--2 nm (Q19) Why are some of the lines brighter than others? Can you develop an explanation that involves the probability of each orbit having an electron heated enough to reside in it? 9

10 LABORATORY REPORT Your report should be computer generated and include your data and conclusions derived for each of the six experimental problems presented in this experiment. Be sure to include your, two charts, one graph, three tables, Atomic Spectra screen shot, the name of the unknown element identified from Atomic Spectra and the answers to the questions asked within the experiment writeup in the format listed below. Be sure you address all 19 of the questions throughout your report. 10