Principles of Spectroscopy

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Introduction

A stellar spectrum is one of the most fundamental and important astronomical tools available. By examining the lines in the spectrum of a star or galaxy, we can determine such important properties as temperature, chemical composition, velocity of approach or recession, pressure, and rate of rotation. A spectrum is observed when light from an emitting source, such as a star, passes through a dispersing element such as a prism or diffraction grating and is broken up into its component colors, or wavelengths. An instrument consisting of a dispersing element and the other necessary components needed to produce a useful spectrum is called a spectroscope.

Spectroscopy involves fundamental atomic physics and is based upon three laws formulated in 1859 by Gustav Kirchhoff:

  • An incandescent solid, liquid, or opaque gas emits a continuous spectrum.

  • A rarefied incandescent gas emits an emission-line, or bright-line, spectrum. Each chemical element and molecule produces a series of emission lines with unique wavelengths and relative intensities.

  • If the light from a hot, luminous source emitting a continuous spectrum passes through a gas or transparent liquid or solid that is at a lower temperature than the source of the continuous spectrum, an absorption-line, or dark-line, spectrum results. In this case, a continuous spectrum crossed by dark absorption lines is seen and the wavelengths of the dark lines are exactly the same as those emission lines which would be seen if the cooler material were radiating alone.
  • In this Exercise we will investigate these three laws of spectroscopy and learn about their relevance to astronomy. Although we will be working in the visible part of the spectrum, it is important to remember that the electromagnetic spectrum consists of a range of energies well beyond that of visible light, and much insight into the nature of the stars and galaxies can be obtained from analyses of gamma rays, X-rays, ultraviolet, infrared, and radio radiation. Kirchhoff's laws hold for all wavelengths of the electromagnetic spectrum.

    The inner layers of a star's photosphere produce a continuous spectrum, and as the radiation passes through the outer, relatively cool layers, an absorption spectrum is produced. The overall appearance of the spectrum and the intensity of the absorption lines produced by various elements and molecules depends largely on the temperature of the stellar atmosphere. From the background continuum of a stellar spectrum, the so-called blackbody temperature of the star can be deduced making use of the observation that the color (wavelength) of maximum intensity in the continuum shifts toward the blue, or shorter wavelengths, as the temperature of the source increases. The physical law governing this effect is named after its discoverer, and is known as Wien's law. As a mathematical formula, Wien's law can be expressed:

    lmax = 2.89x107   K /T,

    where lmax is the wavelength of the peak intensity in angstroms, , and T is the temperature of the blackbody source in degrees Kelvin. The angstrom is the most commonly used unit for measuring the wavelength of visible light in astronomy, and it is equal to 10-10 meters. Another common unit of wavelength is known as a nanometer (nm), where 1 nm = 10-9 m.

    Wien's law informs us that hot stars display a peak intensity in the ultraviolet or blue region of the spectrum, while cooler stars have spectra which peak in the red. The total energy radiated per second by each square centimeter of a radiation source is known as the "flux" in the terminology of physics. The flux produced by a blackbody source depends on the temperature of the source according to the Stefan-Boltzmann radiation law:

    E = sT4  W m-2,

    where s, the Stefan-Boltzmann constant, is equal to 5.56x10-8  W m-2 K-4. In words, this law simply states that, as the temperature of a blackbody increases, the total flux (energy emitted per unit surface area per second) increases with the forth power of the temperature.

    Diffraction Gratings and Spectroscopes

    In this Exercise we will use a light dispersing element known as a diffraction grating which is produced by carefully etching thousands of parallel grooves per inch onto a transparent medium like a glass plate. Like a prism, a diffraction grating breaks light up into its component colors, but, unlike a prism which does this because of the wavelength dependence of the refraction index, the grating produces a spectrum by a process involving constructive and destructive interference of light. The grating replica you will receive in this lab was formed by rolling a stiff plastic over an original metal etching, thus imprinting it with grooves, much in the way that vinyl records are mass produced from the original expensive cuttings. There are various technical and practical advantages to the use of gratings over glass prisms, and in fact many modern astronomical spectrographs use a combination of the two elements known as a "grism". In looking through a transmission grating at a light source, the source itself is seen in the center, and symmetrically on either side of it are seen the spectra of the source. Further still from the center of the field of view are higher order spectra with higher dispersion. That is, in these high order spectra, the wavelengths are more widely separated, but generally fainter.

    A spectrum with more detail than seen in the simple hand-held gratings is produced by a spectroscope which contains a slit to select a thin section of the light source, a collimating lens or mirror to make the light rays from the source parallel, a higher quality dispersing element (prism or grating), and an eyepiece to view the resulting spectrum against a calibrated wavelength scale. See Figure 1.

    Schematic Diagram of a Spectrograph
    Figure 1 -- Schematic Diagram of a Spectrograph

    With this introduction and the assigned readings in your textbook, you should now be able to investigate the properties of different types of spectra following the format of the following work sheets. Your instructor may choose to "walk" the whole class through each section of the lab, or to let you work your way around each station individually. When you are finished, staple your work sheets together and hand them in to your instructor.

    Principles of Spectroscopy -- Preview Questions

    1. Why are objects that radiate with a Planck distribution called "blackbodies"?








    2. What is the characteristic, or peak, wavelength of the blackbody radiation emitted by a human being? In what part of the electromagnetic spectrum is it found? What real-life applications does this have?








    3. Look up the terms resolution (in your textbook) and dispersion (in a dictionary).
      Which has better resolution?

      Which has better dispersion?

    Principles of Spectroscopy -- Work Sheets

    Continuous Spectra

    A continuous spectrum is emitted by an incandescent solid, liquid, or opaque gas. All colors of the spectrum from red to violet are represented in a continuous band of light. Such a spectrum tells us nothing about the chemical composition of the source; however, the relative intensities of the colors indicate the temperature of the emitter. From Wien's law, you should know how the color of a spectrum changes as the source gets hotter.

    1. Obtain from your instructor some diffraction grating material and find an incandescent lamp to examine the spectra described earlier. You should notice the presence of more than one spectrum as you look through the grating. We refer to the first spectrum on each side of the light source as the first order spectrum, and the spectra located at greater angles from the line of sight are known as higher order spectra.
      1. How many higher order spectra can you see?

      2. Compare the overall appearance of these higher order spectra to the first order spectrum. What do you notice? You should be able to find two major differences between these and the first order spectrum.




    2. Look through the grating at the spectrum of the bulb.
      1. With the voltage set very low (about 30 volts or less). At this low voltage, which is brighter, the blue end of the spectrum or the red?

      2. How does the overall brightness of the spectrum change when the voltage is increased from the low voltage to over 110 volts?

      3. At the highest voltage, which has gotten significantly brighter, the blue end of the spectrum or the red?

      4. Is the spectrum continuous, or is it discrete (are there breaks in it)?

      5. At what voltage is the bulb hottest?

      6. How is this type of radiation actually produced in the light bulb? Be specific. What type of physical processes are going on?


    3. Would you expect a red star to be hotter or cooler than a blue star? Why? Do not use Wien's law and the Stefan-Boltzmann law to answer this question. Base your answer on your observations of the bulb.







    4. If two stars, one blue and the other red, have the same physical size, would you expect the red star or the blue star to be intrinsically brighter? This time explain your answer in terms of Wien's law and the Stefan-Boltzmann law.







      Emission Spectra

      An emission-line spectrum is emitted by a glowing, low-density gas. The gas may be excited to the state where it emits its characteristic wavelengths when collisions between atoms at very high temperatures occur, stimulating transitions between two specific energy levels in the atoms of the gas, with the corresponding release of photons of a particular wavelength (color). Since the energy levels are different in different atoms and molecules, each atom and molecule has its own unique set of emission lines.

      1. Use the black or gray laboratory spectroscopes to view one of the discharge tubes. Note that you can adjust the slit width with a screw on the front.
        1. Open the slit as wide as possible. How does the resolution (separation) of crowded emission lines change as you close the slit?





        2. Now open the slit again. How does the overall intensity of the spectrum change as you close the slit?





        3. Suppose you are observing a bright star and a faint star. How would you obtain high-resolution spectra of these stars? What happens to the intensity? So, would it be easier to obtain a high-resolution spectrum of a bright star or a faint star? Explain.








      2. Using any of the available spectroscopes, examine the spectra of various elements in the gas discharge tubes set up around the room. In the following set of grids, sketch the relative positions of the bright lines of hydrogen and at least three other elements as accurately as you can. Use dark marks for the bright lines and indicate the colors you perceive the lines to be for future reference. Also, examine the hydrogen spectrum carefully. From your textbook readings and lectures you should know the characteristic visible lines in the hydrogen spectrum. If you see many more lines in addition to those that you expect, indicate on your sketch that these are not hydrogen lines. Label the bright hydrogen lines clearly. What is the origin of these other spectral lines?




      3. Now that you have examined the spectra of various discharge tubes with a spectrograph, look at them again with the spectrophotometer, which is operated from one of the computers. In the second set of grids on page 7, sketch the digital spectrum of each of these elements, being sure to note relative intensities. Label the exact wavelength of the three strongest lines.

      Observations from spectrographs:


      Chart for drawing spectra
      Absorption Spectra

      A dark-line or absorption spectrum is observed when a relatively cool gas a liquid, or a solid is interposed between a source of continuous radiation and the spectroscope. The absorption lines correspond exactly to the emission-line pattern that would be observed if the same interposing medium were sufficiently excited. The medium is transparent to most colors, but opaque to those colors in which it can emit its own characteristic spectrum. If the medium is hot, but the background continuum source is hotter still, the line radiation emitted by the foreground medium will be dark by comparison with the nearby bright continuum radiation.

      Astronomers use the concept of absorption to their advantage, especially when using small telescopes near urban areas. Filters are pieces of glass or plastic that are created such that certain energy photons will, or will not, go through the filter. As an example of absorption, we will use a filter that can be easily attached to the end of a Celestron 8 or 11 inch telescope.

      1. Look at the spectrum of an incandescent lamp with a diffraction grating as in the Continuous Spectra part of this Exercise. Now hold the SkyGlow filter between the light source and the diffraction grating.
        1. Describe what you see.




        2. What elements have strong spectral lines in the region that the SkyGlow filter absorbs?


        3. What are these elements used for (i.e. why is this filter called a SkyGlow filter)?




      2. So far, we have applied our knowledge of spectra only to laboratory sources. In stellar spectra we find a continuous spectrum superimposed with many absorption lines.
        1. Keeping Kirchhoff's radiation laws in mind, what part of the star does the continuous radiation come from?


        2. Which part produces the absorption lines?



        3. What can you say about the relative temperatures of the outer layers of a stellar atmosphere with respect to the layers which lie further within the star?



      3. Using the hand-held spectrograph, examine the spectrum of a fluorescent light bulb.
        1. What type of spectrum do you observe?



        2. How might you explain this spectrum? You may need to get hints from your instructor to answer this!









      Principles of Spectroscopy -- Concluding Questions

      1. For part of this lab, we use our eye as the detector and for another part we use a spectrophotometer. Name three advantages the spectrophotometer has over the eye as a detector. (Hint: the detector in the spectrophotometer is like a CCD.)









      2. To which of the three types of spectra does Wien's law apply? Notice that the mercury discharge tube glows bluish-white while the neon tube is bright red. Can we use Wien's law to tell the relative temperatures of the gas within the tubes? Explain clearly.









      3. Calculate lmax for the following stars and estimate which color dominates the visual spectrum.

        Star Temperature     lmax         Color    
        Sirius, Vega 10,000 K    
        Sun 5,800 K    
        Betelgeuse, Antares 3,000 K