Hydrogen and Helium Spectra 1 Object To determine the line spacing of a diffraction grating using known wavelengths of the hydrogen spectrum and to determine the visible wavelengths of the helium spectrum. 2 Apparatus Diffraction grating, hydrogen and helium spectral tubes, light source, spectrometer. 3 Theory When sufficient energy is added to an atom, the electrons in one energy state will shift to a higher energy state. Later (a very short time later), they will shift back to their original state and in so doing, emit the energy they absorbed as photons, some of which will be in the visible range. Because each atom has its own unique electron states, each will have its own unique emission lines. These lines can be analyzed by use of a diffraction grating, which in this experiment is a glass plate with many parallel lines etched into it. Plane monochromatic rays (that is, rays of the same color and wavelength) passing through the grating will be broken up into many rays, seven of which are shown in figure 1. If the rays interfere constructively (adding up waves that are in phase ), there will be a bright area. If the rays interfere constructively (adding up waves that are out of phase ) there will be a dark area. Two adjacent rays will be in phase (and interfere constructively) if their path length differences ( L) are exactly an integer number of wavelengths, that is L = 0, ±λ, ±2λ, ±3λ,.... Since all the rays are approximately parallel, they are all at an angle of θ with respect to a line perpendicular to the grating (the dotted line in figure 1). If the slit-to-slit spacing is d, then the path length difference between two adjacent slits is L = d sin(θ) (see figure 2)). Therefore, the condition for constructive interference of monochromatic light from the diffraction grating is mλ = d sin(θ), where m = 0, ±1, ±2, ±3,... The purpose of the spectrometer (figure 3) is to serve as a visual recording aid. The collimator adjusts the light from the source so that it the waves are parallel. To make sure this is the case, the collimator is adjusted until the image of the slit is clearly visible with the naked eye. The parallel rays are passed through the diffraction grating and is refocused by the viewing telescope. The telescope should be focused so that something very far away as well as the crosshairs are clearly visible. The net effect when viewing through the slit through the telescope should be a clear image of the slit and the crosshairs. You will be using the known wavelengths of the hydrogen spectrum to determine the line spacing of your diffraction grating d. The accepted wavelengths of the (visible) hydrogen spectrum are: Color λ Red 656.3 Green 486.1 Blue 434.0 Violet 410.2
Figure 1: Interference using a diffraction grating (from College Physics: Reasoning and Relationships by Nicholas J. Giordano). ray 1 d θ L ray 2 Figure 2: Path length difference between approximately parallel rays is L = d sin θ.
Figure 3: Spectrometer (from Understanding Physics by Karen Cummings and others).
4 Procedure 1. Note the number of lines per unit length in your diffraction grating. The basic adjustments to the spectrometer are described briefly in the theory section. Follow these procedures to set up the spectrometer if either the image of your slit or the image of the crosshairs is out of focus. 2. Make sure the hydrogen tube is in the lamp. 3. Set the viewing telescope such that the image of the slit is in the crosshairs. Record the angle. This will be θ 0. 4. Set up the diffraction grating on the central table (between the collimator and the viewing telescope) such that the plane of the grating is centered on the table approximately perpendicular to the axis of the collimator and the grated side of the glass is towards the viewing telescope. Be sure that the grated side of the glass is in the center of the table. 5. To better align the diffraction grating: (a) move your telescope to the left until you can see the first red spectral line in the crosshairs. Record this angle as θ l. (b) Now swing it past θ 0 to the right until you can see the first red spectral line in the crosshairs on this side. Record this angle as θ r. (c) Compute θ left = θ l θ 0 and θ right = θ r θ 0. For your telescope to be properly aligned, you should find that θ left = θ right to within about 30 minutes of arc (1 = 60 ). If they are, you re good to go. If not, you ll need to make some minor adjustments. i. Compute your correction using = θ right θ left 2. Recall, the point is to have θ left = θ right to within about 30. ii. Set your telescope to the new angle (if θ right > θ left, you want to make θ right smaller by and θ left bigger by and vise versa), then carefully rotate the table your diffraction grating is on (not the grating itself!) until the red line is in your crosshairs again. Check your alignment according to (a) - (c) above to make sure you didn t rotate your grating the wrong direction. 6. Once your alignment is good, record the angular position of the central maximum (this is the zero-th order, m = 0). 7. Moving the telescope to the left, record the angular positions θ of the four brightly colored lines (given in the table above), the wavelength of the line (refer to the colors in the table), and the order of the line (those to the left should be negative). The order is the number of appearance of a particular line. For example, the green line may appear several times, but the first time it appears to either side of the central maximum is order one (m = ±1, where m = 1 is the first line to the left and m = +1 is the first line to the right). Continue making measurements until the lines become too dim to see. Repeat for the lines to the right, recording the orders as positive values. 8. Ask your instructor or the TA to replace the hydrogen lamp with a helium lamp. Repeat step 7 using the helium lamp. Measure the angular positions of two orders of only the bright yellow line, two bright green lines, and the bright blue line (four lines in all and a total of sixteen measurements four measurements of each line).
5 Calculations 1. For each hydrogen measurement, calculate and tabulate (it s best to do this in a spreadsheet) θ θ 0, sin (θ θ 0 ), and mλ. Caution: What units should your angle θ θ 0 be in? 2. Plot mλ versus sin (θ θ 0 ). This means sin (θ θ 0 ) should be on the horizontal axis. You should see a straight line. 3. Fit a straight line to your data. What are the units of the slope? What is the physical interpretation of your slope? What should your intercept be? Remember, you are looking for the line spacing d and its associated uncertainty. How does this value relate to the number of lines per unit length in your diffraction grating? What is the theoretical value of d? Does your measured value agree with that? 4. For each helium measurement, compute and tabulate the wavelength for each spectral line using λ = d sin(θ θ0) m. Find an average and associated uncertainty for each color line (using all orders, positive and negative, of a given color) and compare to the accepted values (given in the table below). Bright Lines Dim Lines Color λ Color λ Red 667.8 Red 706.5 Yellow 587.6 Green 504.7 Green 501.6 Blue 438.7 Green 492.2 Violet 402.6 Blue 471.3 Blue-Violet 447.1 6 Questions Why do atoms emit line spectra and not continuous spectra? Why is the spectrum of hydrogen different from that of helium? What are some reasons why some lines are brighter than others? Why can two similarly colored lines have different brightnesses? Is the positioning of your diffraction grating important for the accuracy of your results? Suppose there had been an impurity in the light source. How do you think that would affect the results?