Instructional Goals: PHSY133 Lab 5 Goal: Investigate the wavelengths of light produced b atoms. Background Reading: Background reading for this lab can be found in our class notes and Chapter 5 of our text (The Essential Cosmic Perspective, 7e) Equipment provided b the lab: High voltage power supplies for discharge tubes Vertical markers on transverse meter stick Meter Sticks mounted at right angles in a T shape Diffraction grating mounted in a slide Background: As an object gets hotter, it glows brighter, which is another wa of saing that it emits light. In the case of solids and even some liquids, the emitted light tends to be a continuous spectrum. However, a gas with a powerful electric current running through it emits onl certain wavelengths in the electromagnetic spectrum. For a gas, the atoms or molecules are far enough apart to be independent of each other, so the light emitted is light from individual atoms or molecules. An atom consists of a nucleus, which contains most of the mass of the atom and is comprised of protons and neutrons, and electrons, which have ver little mass but occup most of the Figure 1 - Spectra lines for several elemental gases. Note that even though some elements ma share some lines, the set of lines for each element is unique. UDel Phsics 1 of 9 Fall 2018
space of the atom. Electrons which are given more energ (b the electric current) jump "up" to higher energ levels. The soon fall back down to the lower energ level, giving up the energ b emitting light. These energ levels are particular to the atom or molecule. Thus, each element has a particular set of energ levels between which the electrons can move (see Figure 1). As such, the atom must receive and emit onl particular amounts of energ that correspond with moving from one energ level to another (see Figure 2). Solids, b contrast, have some electrons which can exist in man, man energ levels, which means almost an jump in energ is possible, and so almost an wavelength of light can be emitted, meaning a continuous spectrum of light. An instrument called a spectroscope is used to separate the various colors (which have different wavelengths or frequencies) of light. Light is let through a slit at one end of the instrument. Near the center of the instrument, at the end of the first tube in this particular stle spectroscope is a diffraction grating. A diffraction grating is a clear plastic film with man, man lines ruled onto it. These man grooves diffract some of the light. Diffraction means the bending of the light into a new direction from the straight line in which it had been traveling. In fact, most of the light still continues straight through the diffraction grating and causes the bright line of light seen at zero degree deflection, called the principle image. The various diffracted light ras interfere with each other, to produce bright, single color spots (lines in our case) at a particular angle that depends on the wavelength (color) of the light according to the formula n dsin Figure 2 Wavelengths of s for neutral hdrogen. The energ of the photon emitted/absorbed is equal to the energ change of the electron going from one level to another. Figure 3 Dispersion of light through a diffraction grating. Where λ is the wavelength of light, d is the distance between the slits on the grating and θ is the angle b which the path of that wavelenth has changed. The lower case n indicates the order, which sas the colors can repeat multiple times. There is, of course a maximum order as sin cannot exceed one. The second tube of the spectroscope contains two lenses. This tube is a telescope like instrument can be swung in an arc. At exactl zero degrees the straight through bright line called the principle image occurs. Your spectrascope can give a slightl different value due to it s aligent, but since the lines appear smmetricall on either side, it won t matter in the calculations. The first set of colors will be for n 1, which is the first order. These first order spectra are what ou want to look at in each case. If ou have trouble seeing the colors, go back to the single colored line that is the principle image and check that the telescope part is focused OK on a vertical line. If so, and ou still cannot find the colored spectra to each side when the scope is swung out to large angles, make sure the grating and slit are vertical. You can ask our instructor for help. Some people can also have trouble seeing some lines near the edge of the visible spectrum in either red or violet. Each person in the group should get a chance to examine the spectra of lines. UDel Phsics 2 of 9 Fall 2018
Procedure and Analsis: The appartus should be setup when ou arrive. The directions below will help ou understand wh things are arranged in this fashion. 1. The setup should appear as to the right. 2. When ou look through the diffraction grating at the discharge tube, the s will appear to the left and right. 3. While one partner looks through the diffraction grating, the other will move the pointers until the line up with the same line on both sides. Diffraction Grating Pointer Discharge Tube Using these positions of the diffraction grating and pointers ou will find the angle the lines appear to have shifted and hence their wavelengths. A. General Information 1. Write down the distance of the diffraction grating from where the meter sticks meet. 2. From a mark on the diffraction grating itself (or from our TA), record how man lines per mm are etched onto our diffraction grating. 3. Convert this to a distance between the lines in (nanometers). Pointer B. The Visible Spectrum of Hdrogen (Balmer Series) 1. Looking through our diffraction grating, ou should see two sets of lines (one on each side of the discharge tube). For Hdrogen, ou should see three to four lines. 2. Note the colors ou see, in order, from closest to the center outwards. Check the spectrum to each side of the center (i.e., the first order spectrum to each side). Are the colors long wavelength to short wavelength or vice versa? Can ou continue to higher angles and see the second order spectrum? If so, state at approximatel what angles the second order spectrum range. 3. Your goal is to determine the line on the meter stick running across the face of the power suppl. While looking through the grating, direct one of our lab partners to move a pointer mounted on the meter stick to rest underneath the red line. Record the pointer, which is the same as "the line left of center," 1. UDel Phsics 3 of 9 Fall 2018
Repeat this measurement for the red line to the right of center to obtain "the line right of center," 2. Repeat this procedure again for the blue green line of light and the violet line of light. All of the students should look through the grating to see the spectrum, but it is critical that onl one student make the observations for this experiment. When making the observations, it is critical that ou look first directl at the light source through the grating, then move our ee, not our head. If ou move our head, ou will introduce parallax into the experiment and get inaccurate results. Move onl our ee! If the meter sticks move during the experiment, ou must start over! 4. For each line of light, calculate the distance between the two lines that ou observed (left and right). We will refer to this distance as 2 = 2 1. 5. Divide 2 b 2 to get. We know the left line and the right line are equidistant from the source of light the "center" but we have not measured the location of the center. Instead, we divide the distance between the two lines in half to arrive at the distance of each line from the center, wherever it is. It's a shortcut (one less measurement to make), and it helps to reduce sstematic error. 6. Using the diagram below and a little trigonometr we can find the relationship between θ,, and L. For each, solve for the angle between the line from the diffraction grating to the source of light (the centerline) and the line from the diffraction grating to the, θ. Pointer L Pointer tan L L 1 tan Diffraction Grating 7. In theor, the wavelength of the light observed (the color of the light) is related to the angle at which the light is observed and the slit spacing of the diffraction grating: n dsin, where n is the order of the s being observed. (Here, n=1.) Use this relationship to solve for the wavelength of each line of light. 8. The expected values for the wavelengths of light from quantum theor are given in the table on the worksheet in nanometers (10 9 m). Again, pa attention to the units. UDel Phsics 4 of 9 Fall 2018
C. Other Elements. Look at the spectra of each of the gas tubes and pick three to four lines for each. 1. Find the wavelengths of the brightest lines of at least three other elements (e.g., Hdrogen, Neon, Oxgen, etc.) Repeat steps B3 through B8 for each lamp. 2. Using the wavelengths ou found, determine which elements ware in the tubes using Table 1 below. Conclusion: Be sure to include a statement that restates the objective and the main results. For this lab, ou need to complete the attached worksheet(s) and an other tasks indicated b our lab instructor. UDel Phsics 5 of 9 Fall 2018
Table 1 Line Wavelengths Uncertaint of line center is taken to be 0.01. Source: NIST Source λ () Source λ () Source λ () Na 371.11 O 441.49 Na 568.26 O 391.20 Ar 442.60 Na 568.82 O 397.33 Ne 443.09 N 575.25 He 402.62 Ne 443.09 Hg 576.96 Hg 404.66 N 444.70 Hg 579.07 O 407.59 Kr 446.37 Ne 585.25 H 410.17 He 447.15 Kr 587.09 Na 411.37 Kr 447.50 He 587.56 Na 412.31 Ar 454.51 He 587.60 Ar 415.86 Kr 457.72 Na 589.00 O 418.98 Ar 457.94 Na 589.59 Ar 420.07 Ar 458.99 N 594.17 Ne 421.97 Ar 460.96 Hg 614.95 Na 423.33 Kr 461.92 O 615.60 Na 424.09 N 463.05 O 615.68 Kr 427.40 Kr 463.39 O 615.82 Ar 427.75 O 464.91 Ne 618.22 Na 429.25 Ar 465.79 Ne 621.73 Na 429.29 Kr 465.89 Ne 626.65 Na 430.88 He 468.57 Ne 640.23 Na 430.90 He 471.32 O 645.60 Kr 431.96 Ar 472.69 N 648.21 Na 432.09 Kr 473.90 Ne 650.65 Na 433.73 Ar 476.49 H 656.27 H 434.05 Kr 476.57 H 656.29 Na 434.41 Ar 480.60 Ne 659.90 Hg 434.75 Kr 483.21 N 661.06 Ar 434.81 H 486.13 He 667.82 Kr 435.55 Ar 487.99 Hg 690.75 Hg 435.83 Na 498.28 Ar 696.54 Kr 437.61 N 500.15 O 700.22 Ne 437.96 N 500.52 He 706.52 Ne 439.20 He 501.57 He 706.57 Na 439.28 Kr 557.03 Hg 708.19 Ne 439.80 N 566.66 Hg 709.19 Ne 440.93 N 567.96 Ar 714.70 UDel Phsics 6 of 9 Fall 2018
Worksheet Lab Section Names Apparatus setup values Distance between the meter stick used to measure the spectral lines and the diffraction grating. What is the slit spacing on the diffraction grating? L = mm 1/d = lines/mm d = mm/line d = /line Hdrogen Lamp spectral line line (left of center) 1 line (right of center), 2 2 red blue-green violet (degrees) d sin () experimental theoretical red 656 blue-green 486 violet 434 UDel Phsics 7 of 9 Fall 2018
Additional Bulb 1: color line (left of center) 1 line (right of center), 2 2 d sin experimental theoretical color (degrees) () What is in this discharge tube and how did ou determine this? UDel Phsics 8 of 9 Fall 2018
Additional Bulb 2: color line (left of center) 1 line (right of center), 2 2 d sin experimental theoretical color (degrees) () What is in this discharge tube and how did ou determine this? If a continuum of light passed through a cool gas, what would ou see? UDel Phsics 9 of 9 Fall 2018