NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT Physics 211 E&M and Quantum Physics Spring 2018 Lab #9: Diffraction Spectroscopy Lab Writeup Due: Mon/Wed/Thu/Fri, April 30/ May 2/3/4, 2018 Background All wave phenomena exhibit common properties including energy transfer, interference and diffraction. The proponents of the wave theory of light were given a big boost when Young s Double-slit experiment first showed that light produces interference patterns. Interference patterns will be produced when multiple light waves that have the same phase interact, producing "bright" and "dark" fringe patterns. The bright fringes are due to the peaks in the light waves adding together to produce a larger amplitude and the dark fringes are due to a peak adding to a trough so the resulting amplitude is zero. A diffraction grating consists of 1000 s of vertical slits and act as "super" prisms splitting white light with larger angular separations then a prism. Read the section of your physics textbook on diffraction gratings for more background on this subject. Electrons orbit an atom's nucleus at defined distances for each atomic element. Electrons can jump to higher orbitals if the atom absorbs the appropriate amount of energy. The atom will always return to the lowest energy level as soon as possible via the electron falling back from the higher orbital to a lower orbital. Conservation of energy requires that a photon be released with an energy E hf that equals the difference in energy levels of the atom. Each atomic element has unique electron orbitals and energy levels that can be identified by measuring the energy of photons released when electrons fall from higher to lower orbitals. The released photons produce an emission spectrum with visible light at various wavelengths (colors) corresponding to the energy of the photons. This is explained in the section of your physics textbook covering the Bohr Model of the atom. The purpose of this lab is to use a spectrometer s diffraction grating to study the emission line spectra of several element sources to understand how the energy released by atomic electrons produce light waves with corresponding wavelengths that can be measured using light wave interference. 1. Overview A. Light Waves
A Young's double slit experiment is shown below. Light is incident on a single slit, which produces a new set of light waves ( S 0) that are all in phase (the original light source may contain light waves of varying phases). The in-phase light waves are then incident on 2 slits each producing a light wave source ( S 1 and S 2 ). The 2 light wave sources then interfere with each other and produce a fringe pattern on a screen as shown below: Figure 1 A diffraction grating is a glass or plastic transparent screen that has 1000's of scored lines that are only nano-meters apart. Each scored line acts as a tiny slit for any incident light, so interference patterns are produced as shown below: Figure 2 2
Note that the interference patterns have narrower bright peaks and wider dark fringes when compared to the 2- slit interference pattern. The "geometry" that results in bright and dark fringes is due to the fact that each light wave travels a different distance to the screen except. Looking at the inset drawing above, we for the central or zeroth-order maximum ( m 0) see light waves coming from 2 of the slits that travel a different distance is called the path length difference. The diffraction equation is m dsin d sin, which Where m is the order number of the bright fringe ( m 0, 1, 2, ) ; d is the distance between the diffraction slits; is the wavelength of the light. Note that sin is proportional to the wavelength of the light, which means that the longer the wavelength of the light, the farther the bright fringe will be offset from the center. Hence, white light will be separated by wavelength (color). B. Spectral Emission Lines White light produces a "continuous" emission spectra representing all wavelengths of visible light as shown below. Emission "line" spectra can be produced by passing a large voltage through a gas of a certain element. The voltage will provide the required energy that causes electrons to jump to higher orbitals and emission spectra will be produced as the electrons fall back to lower orbitals. However, each atomic element has a unique set of electron orbital levels (and only certain electron transitions are allowed within the orbitals) and hence will produce a unique emission line spectrum. Looking at hydrogen below there are 4 dominant visible wavelength transitions that produce an emission line spectra. Hydrogen is the simplest element with only 1 electron, hence the analysis is simple. Elements with many electrons have so many orbitals that the analysis of electron transitions is very complex. 3
Figure 3 Hydrogen Atom A spectrometer is a device that allows us to determine the exact wavelength of the incident light based on how far it is diffracted by a diffraction grating. A spectrometer is shown below. The source light is collimated (passes through a small aperture that results in all waves having the same phase) and then passes through a diffraction grating that produces an interference pattern, based on wavelength where the longer wavelengths are diffracted to a wider angle then the shorter wavelengths. Depending on the quality and spacing of the diffracting grating, multiple orders ( m 0, 1, 2, ) of the emission line may be seen as constructive interference occurs at many angles on either side of the central maximum (Figure 2). The spectrometers telescope is movable and contains a circular table that indicates the angle in degrees as the telescope moves. Figure 4 Spectrometer 4
2. Procedure Apparatus includes:. Spectrometer. Diffraction grating. Gas discharge tubes (2). Flashlight Make sure your TA has checked that your spectrometer is set up properly. READING THE SPECTROMETER VERNIER SCALE The spectrometer vernier scale is graduated in degrees, arc minutes, and arc seconds. The conversion factors are: 1 60 (in words: 1 degree = 60 arc minutes) 1 60 (in words: 1 arc minute = 60 arc seconds) On the bottom scale shown above, the region between 10 to 20 is divided into 60 divisions. 20 10 60 Thus, the smallest division is: 10. 1 ( ) 60 C B A Thus, minor division A is 30 (the dial reading at A would be 10 30 ), and the major division B is 150 (the dial reading at B would be 10 150 ). The actual reading for this measurement is at C and would then be 10 150 30 find the number of arc seconds, we must examine the graduations on the upper scale (see below). Each division of the upper scale is 10 (thus the 20 on the upper scale is 200 ). Carefully look for where a line in the upper scale lines up with a line at the bottom scale. a little more in arc seconds. To 5
D The bottom and the top graduations appear to line up at D. This point is at 45 10 450. The final reading for the spectrometer vernier scale would then be: 10 150 30 450 10180 450 To convert this all into degrees, use the conversion factors above: 1 1 10 180 450 10 3 0.125 13.125 60 3600 A. Activity #1: Diffraction Spectroscopy 1. Familiarize yourself with the spectrometer. Move the telescope and note the degrees/minutes reading on the Vernier scale. Do NOT touch any of the knobs on the spectrometer. 2. Your assignment is as a CSI lab technician who must determine the type of gas that was found in the lungs of two deceased scientists that were analyzing a meteorite in their lab. The gas from the scientist's lungs has been sealed and placed in 2 different gas discharge lamps. Take the first lamp and fit the collimator into the hole of the lamp housing. Turn on the lamp (which applies a high voltage to the gas) and move the telescope to the straight through position (aligned with the collimator). You should see a vertical bright band of light in the center of the eyepiece when you have the telescope aligned with the collimator. Center the cross hair on the center of the vertical central maxima 6
slit image and write down the vernier scale reading in degrees, arc minutes, and arc seconds. The central maximum is found when the moving telescope is in line with the fixed lens of the spectrometer (perpendicular to the diffraction grating) the value may not be constant for each lamp, so redo this step when you change lamps. After you have found & recorded the central maximum position, you can open increase the size of the collimator by SLOWLY turning the end piece (next to the lamp) of the collimator to get a brighter beam, which should help in finding the fainter emission lines. DON'T open the slit too wide while looking at the central maximum! Focus the eye piece at the end of the telescope by turning it so the slit is sharply defined and you can see the cross hair as it overlays the slit image. Make sure the diffraction grating is inserted in the metal "fingers" so the lines of the grating are perpendicular to the vertical slit in the collimator see your TA if you're not sure how to do this. 3. Find the first bright color emission line by slowly moving the telescope to the left of the center position. Center the cross hair in the middle of the emission line and record the degrees to the nearest degree and minute (find the number of degrees by subtracting the degrees from the central maxima found in step 2 above when the telescope was in the center). Move the telescope back to the center, then slowly to the right and find the same emission line again, center the cross hairs and record the degrees and minutes. Note: the difference between the "left" and "right" reading should be less than 1 degree if it isn't repeat your measurement or check with you TA. Average the 2 readings (one on either side of the center point) and record the result in your lab notebook and in the following table using Excel: 4. Repeat Step 3 for four more different colored emission lines that represent electron transitions for this element. Note that some elements have a "doublet" that is 2 emission lines that are very close together record data for each of these if you see them. 7
5. Remember that as you move the telescope to higher angles you will start to encounter the 2 nd order constructive interference line for each color. In your lab notebook, make a diagram of the emission line colors you see on either side of the central maximum and notate which ones are 2 nd order vs. 1 st order (use colored pencils or do on your computer). Record the data for the second order emission line for only ONE dominant color from the first order emission lines you recorded. 6. Repeat steps 2, 3 & 4 for the other gas lamp. You will be starting with the dominant emission line, then find 4 more emission lines. 7. Use the diffraction equation to calculate the wavelength of each emission line for each gas. Note that you must calculate d, the diffraction grating spacing take it out to 6 decimal places for calculating the wavelengths, also use 6 decimal places for the "sin" function. Your data section should contain: o A data table for each gas containing the degree/minute/arc second reading of the central maxima and the average (of the left and right angles) degree/minute/arc second reading for each emission line along with your notes as to the color of the emission line. Your Results section should contain: o The calculated wavelengths for each of the emission lines you found for each of the 2 gases. o Comparison of your calculated wavelengths to the theoretical wavelengths of the element you are "proving" is Gas #1 and Gas #2. o A diagram (hand drawn or computer generated) of the emission line colors you found for each gas. Include an actual emission line spectra (from a text book or online) for the gas you have "proven" is in each lamp. 8
4. Questions Note: You should use the textbook references cited in the lab as well as your own independent research. 1. For each of the emission lines you measured for the 2 gases, describe which electronic transitions produced the emission line. 2. Use the wavelengths you calculated for each element to identify composition of the gas inside the discharge tube. Research which elements have prominent wavelengths (or colors) that match what you calculated. You need to "prove" how you determined what the 2 gases are. Remember that every atomic element has a unique emission spectra. 3. Document the differences in your experimental calculation of the wavelengths for each element vs. the theoretical values you found. 4. Calculate the minimum voltage required to generate the shortest wavelength emission line you measured for each element, i.e. equate the energy of the photon emitted to the voltage required to first raise the electron to the higher orbital shell. 5. Why do you find the same wavelengths (or colors) on each side of the central maxima? 9