General Physics Experiment 6 Spectrum of Hydrogen s Emission Lines Objectives: < To determine wave lengths of the bright emission lines of hydrogen. < To test the relationship between wavelength and energy as implied by the Bohr model. < To determine the value of the Rydberg constant. < To observe and describe the more complex spectra of other atoms including the doublet structure of 5 sodium lines and to identify the atomic species of three unknown sources. Equipment: < Spectroscope platform and lab jack < Grating post and diffraction grating < Hydrogen geissler tube light source < Other geissler tube light sources < Mercury light source < Sodium light source < Unknown sources < Instaspec spectrometer and computer < Winsco Spectrum Analysis chart < Graphical Analysis software Physical Principles: The relation between the velocity c of a wave, the wavelength 8, period T and frequency f is given by 8 c T c f where c 3 10 8 m s (1) When two waves (assume equal amplitudes) arrive at a point such that both waves have their maximum disturbances at the same time, the resulting disturbance has an amplitude which is the sum of the two amplitudes (twice the amplitude) and we say the waves are in phase. The energy of the disturbance increases as the square of the amplitude (4 times the energy in one wave). When the two waves arrive such that one wave has a maximum disturbance (crest) when the other has its disturbance in the opposite direction (trough), the resulting amplitude is the difference between the amplitudes of the first and second wave (zero, for example), and we say that the waves are 180E out of phase. The diffraction grating consists of a large number of very narrow slits (750 slits per mm for our gratings). Light from a source passes through a slit and after traveling a distance D arrives at the grating. The waves Experiment 6 Page 25
reaching different points of the grating are in phase. Light rays which leave the grating at an angle 2 will have phase differences which are the bases of the triangles illustrated in figure 1. If the base of the smallest triangle is equal to the wave length 8, the waves will be in phase and a bright line (image of the slit) will be seen at the angle 2 from the slit. If this base is much different than the wavelength light from many pairs of slits will be nearly out of phase and will cancel and no light will be seen in this direction. Thus the condition that the slit will be imaged by a color with a wavelength 8 at an angle 2 d sin2 n8 (2) d 8 28 38 48 58 68 2 First order maximum Figure 1 Phase differences of light leaving a diffraction grating. where the angle 2 (in radians) is given by 2 x D (3) with x the distance along the arc from the slit to the direction of the bright image of the slit in that color and D =.5 m is the radius of the scale. This follows from the definition of angle and the fact that the grating is placed at the center of curvature of the scale arc. The grating has 750,000 slits per meter so that d = 1/(750,000 m -1 ) = 1.333x10-6 m. Thus an observation of the distance, x, of the first order (n=1) virtual image of the slit in a particular color with equations (2) and (3) gives the value of the wavelength. 8 d sin x D (4) Light energy is absorbed by atoms in bundles called photons. The energy of a photon is related to the frequency and wavelength of the photon by the Einstein relation E h f h c 8 (5) where h = 6.624x10-34 Js, Planck's constant. Atoms exist in certain discrete energy levels and in the case of the simple atom of hydrogen the energies of these levels are given by E & E o n 2 (6) where n is some positive integer, 1, 2, 3,..., and E o = 13.6 ev = 2.18x10-18 J. m=7 m=6 m=5 m=4 m=3 m=2 red blue violet When atoms are in excited states (n values greater than 1) Figure 2 Hydrogen atomic transitions from level m to level n=2. Experiment 6 Page 26
they can emit a photon and enter a state with a lower (more negative) energy and smaller value of n (see figure 2). If m is the integer for the higher state and n is the integer for the lower state the energy difference between the states is equal to the energy of the emitted photon. Thus and from equation (5) E photon E o 1 n 2& 1 m 2 (7) 1 8 E o h c 1 1 n 2& (8) m 2 where R = E o /(h c) = 1.09678x10 7 m -1 is called the Rydberg constant. For the hydrogen lines in the visible spectrum (.4x10-6 m <8 <.7x10-6 m) and n = 2 and m = 3, 4, 5, 6,.... Procedure: Patterns caused by diffraction gratings Insert the hydrogen tube in the power supply shown in figure 3 and turn on the electric power. Set the spectroscope platform on the lab jack in front of the light source and adjust the height so that the slit is at the level of the center of the Geisler tube. Set the platform slit close to the source and align it so that the light source is in line with the grating and slit. Place the grating on the grating post and place the post in the hole on the platform. Rotate the grating about a horizontal axis while looking through the grating toward the slit until the colored lines are in a horizontal row on both sides of the slit. Measure and record the distance D between the grating and slit. Read and record the position x of the red hydrogen line (m = 3) on the right (or left) side of the scale, in a table. Compute and record the value of 2 in the table and from there calculate the wavelength (8). Compare this with the accepted value. Repeat the process for the blue (m = 4) and violet lines (m = 5). Figure 3 Hydrogen light source. Experiment 6 Page 27
Table 1: Hydrogen optical spectra color x m 2 (from equation 3) 8 (from equation 4) red blue violet Hydrogen spectrum Use the Oriel Multispec Spectrograph to record a hydrogen spectrum. The light source should be aligned along the line shown on the top of the spectrometer coming from the center of the entrance aperture. Turn on the computer and type cd insta and press RETURN to select the instaspec directory. Type instaspc and press RETURN to execute the program. Press RETURN and cover the entrance aperture. Type I and press ALT and D to take a dark spectrum. To select the proper printer type G for graph, then type Z for printer setup. To select the Epson FX series type 1. Press the space bar to take the spectrum. Use the left and right arrows the adjust the green box to include the red line at 656.5 nm (m=3 to n=2 transition) and the ultraviolet line at 389 nm (m=8 to n=2 transition. Press the RETURN key. Figure 4 Oriel Multispec Spectrograph. Check that the printer is 'ON LINE' and that the paper perforation is at the print head, then enter u (dump). After the lower menu bar reappears hold the Ctrl key down and use the left and right arrows to move the marker to the maximum (center) of each of the six lines visible. Use the left and right arrow keys to move the green box to just above the 410.3 nm line (m=6 to n=2 transition) and just below the 389 nm (m=8 to n=2 transition), then press the RETURN key to see this region of the spectrum enlarged. In the same way the down arrow may be used to increase the peak heights in the plot. Print a copy of this region of the spectrum. The shift left and right and shift up and down key combinations will return the display to view the full spectrum. Complete table 2 and compare your measured values with the accepted ones. Construct a plot of y = 1/8 versus x = 1/m 2 using your experimental values. From the graph determine the value of the Rydberg constant ( R = -slope) and determine the percentage of error from the accepted value of 1.09678x10 7 m -1. From the y intercept show that in equation (8) n = 2. Table 2: Hydrogen spectra Experiment 6 Page 28
Energy level Accepted Wavelength Measured Wavelength Percent Error m = 3 m = 4 m = 5 m = 6 m = 7 m = 8 656.5 nm 486.3 nm 434.2 nm 410.3 nm 397.1 nm 389.0 nm Spectrum of other light sources View two other Geisler tubes, fluorescent lights and tungsten filaments through the spectrograph and compare qualitatively your observations of the spectra with that of hydrogen. Do you think these spectra can be fit to equation (8). Explain your response to this question. Identify the elements in the two other Geisler tubes by reference to the Winsco Spectrum Analysis Chart. Sodium and Mercury light sources Use the Project Star Spectrometer shown in figure 5 to observe the sodium light source and the mercury light source and record the color and wave lengths of the bright lines. Note that when viewed with the Instaspec Spectrometer all the sodium lines are double. Can you suggest a reason why this might be so? Compare your observations with the values shown below. The wavelengths of the brightest lines of sodium and mercury are listed below in nanometers. Figure 5 Project Star Spectrometer. Sodium: 615.4, 616.1, 589.0, 598.6, 568.3, 568.8, 514.9, 515.4, 497.9, 498.3, 474.8, 475.2, 466.5, 466.9, 449.4, 449.8 Mercury: 579.1, 579.0, 546.1, 435.8 Fraunhofer absorption lines Direct the Project Star Spectrometer out of the window in HYH219 with the room darkened. Record in table 4 the wavelengths of four of the darkest of the Fraunhofer absorption lines. Can you identify any of these lines? Experiment 6 Page 29