Diffraction Gratings and Spectral Lines 1. Introduction Chemists long knew that when certain elements were burned they emitted characteristic colors. Sodium, for example, in a flame emits a particular yellow line. Now, it s not necessary for the element in question to react, just to be heated. For example, an electrical discharge through sodium vapor gives the same yellow line, and is the basis for the yellowcolored street lamps in use in many places. Now, Sodium is not the lowest element in the periodic table: that s Hydrogen. Hydrogen, let us remind you, is one electron circulating about one proton. Thus, it seemed to physicists in the early 1900 s that such a simple entity should be explicable by simple physics. Yet this simple atom posed an immense challenge to the physicists who observed them in that day. Atoms were known to contain charged particles (electrons) which, thanks to Rutherford s experiments, were clearly spread out and zipping around a tiny nucleus, in the planetary model of the atom that is the common cartoon of an atom today (just watch the opening of the Big Bang Theory on TV!) What troubled the physicists is that they knew (as you know too) that orbital motion involved centripetal acceleration, and they also knew that accelerated electrons emitted radiation. (This was how radio got invented after all.) So why didn t these accelerating electrons, inside the atom, constantly emit light till, losing their energy by radiation, they crashed into the nuclei? And why not emit all wavelengths of light, as the electron spiraled in? Why only particular lines, that never changed? The short version of a long and fascinating story is that electrons (and all matter) is actually part wave! The electrons that surround an atom make standing waves. (Remember them?) Just like on a guitar string, the standing waves only exist for certain lengths, which, wrapped around an atom, gives discrete orbits. Moving to the overtones and returning is what accounts for the discrete lines. The distinct colors that you will record today are the result of the electrons moving between these unique stable energy levels levels that provide the fingerprint of the various elements. For a quantitative analysis, we must go beyond the output decoded by the 3 color-sensitive visual receptors that are found in our eyes. (Put another way, not all yellow-orange light is equivalent!) If the light emitted by a single element is put through a prism, the result is quite remarkable, because the color breaks down into very discrete wavelengths. Sodium s yellow-orange, for example, turns out to be two exceedingly close yellow-orange wavelengths, and nothing else around at all. When you use a prism, you note that you can represent the light it disperses in a drawing in two dimensions. You draw it viewed from the top, and you can draw how light disperses. What about the third dimension (sticking out of the page)? Well, that is irrelevant to resolving color, so you may as well use as much of that space as you can in the process of observation. In the horizontal plane, you break the light down, but in the vertical plane you want to get lots of light for observation. In addition, the light sources are often long and skinny. The result is
that what you see are lines of color, and it becomes physics jargon to speak of spectral lines. We could have equally well called them spectral spots, for the height of a line only reveals something about the spectrometer and light source input used by the observer. In this experiment we will observe the emission spectrum of hydrogen, the simplest of the elements, and that of mercury as well. Prism dispersion is not the best way to separate colors. What works best is a diffraction grating. These devices were perfected in the late 1800 s by the careful machines built by William Rowland of Baltimore. They use interference of light waves travelling through many slit-shaped apertures to separate colors very efficiently. There are gratings that work by reflection, and these are the best (and what we will use). There are also transmission gratings where the light waves go through the grating and out, pretty much the way light would go through a prism. When a diffraction grating separates the different wavelengths in a beam of light, longer wavelengths are diffracted at a larger angle than the shorter wavelengths, by reflection of light off a grooved surface. Although we can t open up the spectrometers you will use in this lab to show you the diffraction gratings, you can see the same effect by playing with an everyday DVD. They have 625 grooves or lines per mm. If you hold one nearly horizontally at arms length in a well lit room (see picture below) and tilt it back and forth you can see dramatic color that depend on the exact tilt angle: different colors emerge at different angles. The spectrometer uses that fact to disperse the colors in a systematic way. https://oceanoptics.com/product-details/usb4000-optical-bench-options/ The grating we use reflects light. We included in each setup a small grating that works with transmitted light. We have no systematic experiment planned for it, but you may want to use it with each light source as we go on to see what it looks like to the unaided eye. Once the light from the source has been diffracted, it falls on a closely spaced collection of detectors, called a photodiode or CCD array. This is a one-dimensional version of what occurs in two-dimensions in your cell-phone camera (and all digital cameras). 2
2.1 Apparatus One hydrogen discharge tube and one mercury tube with a discharge tube power supply. An Ocean Optics spectrometer (Model USB4000-UV-VIS) with associated fiber cable(s). One transmission grating 2.2 General Precautions. The gas atoms (hydrogen or mercury vapor) are excited by creating an electrical discharge between two electrodes surrounded by gas in a glass tube. Once operating, the discharge tubes can get very hot and should not be touched. Once the power supply has been shut off, wait at least 10 minutes to remove the tube from the power supply sockets. Use a paper towel to hold the tube. The optical fiber cable should not be bent sharply as this can cause cracks in the fiber. Never touch the free end of the fiber cable with your fingers as this can leave residue on the fiber tip or scratch the fiber tip surface and degrade the performance of the fiber cable. When not in use, cover the cable tip with the protective cap. 2.3 Experimental Setup and Data Collection Plug in the power supply but leave the power supply switch in the off position. Insert the hydrogen tube between the spring loaded sockets. Turn the power supply switch to on position. Plug in the spectrometer to one of the USB ports of your computer. Insert one end of the fiber cable into the input port of the spectrometer. Click on the SpectraSuite icon to launch the spectrum analysis program. Remove the protective cap from the other end of the fiber cable, and position it about two inches away from the light source (e.g. discharge tube) using the clamp provided. On the top left hand side of the screen adjust the acquisition time to 50msec. (Note: increasing the acquisition time increases the spectral intensity while decreasing it lowers the intensity). By adjusting the position of the input fiber end with respect to the source you should be able to obtain a spectrum such that its highest peak intensity is between 50,000 to 60,000 counts. DO NOT EXCEED 60,000 COUNTS. 3. Data Analysis 3.1 How to record the spectrum. After you have the desired spectrum, simply click on the floppy disk icon above the graph. A window will pop up to continue the saving procedure. in the toolbar 3
Figure 2. Snapshot of software for the experiment. Click on Browse and specify where you would like to save the data and give the graph a file name. You will not see the save button yet. Click on the device that recorded the data to finally save the file. (In this case, there is only one device in the window, as shown below) Figure 2b. 3.2 Reading the spectral wavelengths. In SpectraSuite, go to [File > Open > Load Processed Spectrum] to open the graph (intensity vs. wavelength plot) (Look for the file you have saved in the specified directory and double-click to open. On the left, you will see a new item in Data Sources with the name of your graph. Figure 2c. Right-click on the new item (your graph) and click on Show as overlay. When a window pops up, click on load. Another window will pop up asking where to save the file. 4
Figure 2d. Check Show data in new graph and click on Accept. (If you want to view multiple spectra on a single graph to compare, then check Show data in active graph and click on a graph to overlay different plots. At this point TURN THE POWER SUPPLY OFF if you are looking at the spectral lines. To read the data, you can click anywhere on the graph and a vertical cursor line should appear. To read the data accurately, read the window at the bottom of the plot. To adjust the position of the cursor line, simply click on the UP arrow or DOWN arrow to move to a different spectral peak. Enter the wavelengths of the various peaks in a data table. 4 Data to Collect and Analyze Before using the spectrometer to do the careful scientific work, we want you to take advantage of this instrument to learn some things about the world around you. 4.1. Collect the light from a conventional flashlight. This spectrum is actually famous! It s known as the blackbody spectrum from the physical principle that an object that was a perfect absorber (black object) would also be a perfect emitter. Note the fact that it is a broad, continuous spectrum. Watch your count level! 4.2. Collect the light from an LED flashlight. That extreme whiteness is due to the injection of strong blue light. In fact, the blue light is absorbed by a phosphor which then re-emits over a range of wavelengths, so you see a sharp peak of the blue LED, and a broad peak of the phosphor. Where is the blue LED peak? 4.3. Collect the light from your cell phone (set to flashlight if you have the option). What do you see? Note that since we humans have only 3 different colored light sensors, it only takes 3 colors to generate anything we can see. 5
4.4 Collect the spectrum of the Hydrogen source. Interestingly, the predictions of the first foray into what would become known as quantum mechanics made a prediction for the wavelengths of these lines. It was that where R is the Rydberg constant, and is 1.097 x 10 7 m -1. For the visible lines, n 1 = 2. (For ultraviolet, which we can t see, it s =1). n 2 is a number in sequence, so when n 1 = 2 then n 2 starts at 3, and goes on up by integers. At 3 is the lowest wavelength you can see in the visible. We want you to record the positions of the lines you observe for H, and then record the predictions from the old quantum theory. So record the spectrum, turn off the lamp, and while it cools do your analysis. 4.5. Collect the spectrum of Mercury. 1 λ = R 1 2 n 1 2 1 n 2 Note the difference. While we can today figure out where the spectral lines ought to be, the theory that described Hydrogen which we quoted above (due to Neils Bohr) doesn t have good prediction for mercury spectra. Note how we can have white source that is continuous like the flashlight, semicontinuous like the LED, or discrete like mercury. Blame Biology! 6