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ASTR101 Astronomy Laboratory Grist Spectroscopy 1 NAME Laboratory Exercise: Spectroscopy (online version) In this exercise you will learn the basic techniques that are utilized by astronomers to find the composition and temperature of stars and distant atmospheres. You will learn about spectra and their uses as well as about atomic structure and how it effects atomic spectra. I. Introduction All matter is made of atoms. All atoms are composed of combinations of three subatomic particles. These are protons, neutrons and electrons. The protons and neutrons have almost all of the mass of the atom and make up the core or nucleus of the atom. The number of protons an atom has defines what it is, so we call the number of protons the atomic number of the atom. For example whether an atom is carbon, with six (6) protons, or nitrogen, with seven (7) protons, it’s defined simply by the number of protons. What about electrons? Atoms also tend to have the same number of electrons as they have protons, so a simple carbon atom has six (6) electrons. An individual atom that loses an electron is called an ion. The electrons exist in a space outside of the nucleus of the atom. In order to have a basic understanding of the mechanics of atoms, and the functions of an atom’s electrons, we use a simple model of an atom called the ‘planetary model’ of atomic structure or the Bohr Model after physicist Niels Bohr who suggested this model. The Bohr Model shows the nucleus at the center of the atom, much like a sun, and the electrons orbiting around the nucleus, much like planets. Figure 1 Figure 1 is a typical planetary model of a carbon atom. An atom’s electrons are involved in making bonds with other atoms to form compounds and structures. In addition to the physical motion of an atom, the position of its electrons (their energy state) is the way for an atom to store energy. Atoms can take on or give off energy, called transferring energy. Much of the energy that an atom transfers is through the change of energy state of electrons. Due to the fundamental laws of thermodynamics, energy will tend to spread out as much as possible, rather than pile up (called entropy). You can see this if you drop a handful of coins on a table top. The coins will tend to spread out into a disorderly low pile, not stack into neat orderly columns! This may seem ridiculous – of course coins don’t sort and stack themselves – but this phenomenon is the same one that dictates that water runs downhill and that hot things cool down, or that electrons go to lower energy states if they can. When an atom has energy, one or more of its electrons is in a higher energy state. When that electron can, it will give up that energy to move to a lower state by emitting a small particle of light called a photon. Light is Electromagnetic (EM) radiation. The color of the light is a function of its frequency or wavelength; this is due to the energy that that photon has (Equation 1). E = h f Equation 1
ASTR101 Astronomy Laboratory Grist Spectroscopy 2 For instance, much of our Sun’s emitted energy is in the visible range of light. If the photon has a very low amount of energy, then the ‘color’ can be in the infrared (IR) – like your TV remote control. If the photon has a high amount of energy then the ‘color’ can be in the ultra-violet (UV), or even higher like the X-ray or Gamma ray. See Figure 2 for a look at how this spectrum fits together. Figure 2 II. Task 1: Continuous Spectrum and Temperature Plasmas like the interior of a star and hot metals emit a continuous spectrum that looks like a rainbow of colors. An example is the hot metal filament in a standard light bulb. This is due to the fact that the electrons on the surface of the metal are only loosely associated with any one atom. We call them ‘free electrons’; these means that they do not have specific energy states, so they will emit a wide variety of different photons as they have a wide variety of energy states. The plasma of a star is hot and under tremendous pressure; it is almost all ions. This means that there are lots of free electrons which can emit a wide variety of different photons too. Figure 3 V I B G Y O R Rainbow of Color
ASTR101 Astronomy Laboratory Grist Spectroscopy 3 Observation of Continuous Spectra. Figure 4 Figure 5 Looking at Figures 3-5, answer the following questions: Based on this observation, is a bright bulb Hotter or Cooler than a dim one? (circle answer) How does the temperature affect the lamp’s intensity? How does the temperature affect the colors that are seen? When the lamp is dim, which colors are missing?
ASTR101 Astronomy Laboratory Grist Spectroscopy 4 Intensity Curve Peaks and Temperature Graphical Analysis In continuous spectrums the color with the greatest intensity indicates the temperature of the object. We can make an intensity curve of the spectrum of various objects with a known temperature, and then use these intensity curves to find the temperature of other objects such as stars. Figure 5 showed these curves for two light bulbs; Figure 6 shows a set of these curves know as Planck Curves or Blackbody Curves. The peak for each curve has a dot, and a dashed trend line connects the dots so that we can estimate where the peak would be for other temperatures. Label the visible portion of the graph ROYGB (no IV) along the x-axis; recall that red is on the right. Figure 6 Note that 1µm = 1,000 nm and K stands for Kelvin. After labeling the axis, look at the curve peaks and trend line on the graph to answer the following: What temperature is the surface of a star that appears red? What temperature is the surface of a star that appears yellow? What temperature is the surface of a star that appears orange? (estimate) What temperature is the surface of a star that appears blue? Intensity Curve Peaks and Temperature by Calculation Well the blue one is off the charts! All we can say about it is that it’s more than the temperature of the hottest curve (>6,000 K). But since we have a set of data that represents how the wavelength of the intensity peak changes with temperature, we can model this with an equation that will
ASTR101 Astronomy Laboratory Grist Spectroscopy 5 allow us to find what wavelength (and therefore color) any temperature will give us. This model is known as Wien’s Law and looks like this: T(K) = 2.898 x 10-3 m K ÷ λpeak Equation 2 Where λpeak is the wavelength that the curve peaks at and T(K) is the temperature in Kelvin. Now instead of doing a graphical estimate like we did before, we can actually calculate the temperature once we observe and measure what wavelength the star peaks at. First step would be to observe our star (or other object) of interest and then pass its light through something like a prism that will spread out its light to separate it into wavelengths. Once we have the light spread, or spectrum, we can measure which wavelength has the greatest intensity (brightness); this is our peak wavelength or λpeak. Using Equation 2 and Figures 7 and 8 answer the following questions: Note that nm is a “nanometer”, which is 10-9 m, or a billionth of a meter. For help you can visit Appendix C in the online textbook and google instructions for how to do scientific notation on your calculator… Example: how to [your calculator make/model] scientific notation Example: Object #0 has a measured λpeak of 700nm, so its spectral band and color would be __VIS, red__ and its temperature is____4,140 K____ (2.898 x 10-3 m K ÷ 700 x 10-9 m = 4,140 K) Object #1 has a measured λpeak of 455nm, so its spectral band and color would be____________ and its temperature is_______________ Object #2 has a measured λpeak of 800nm, so its spectral band and color would be____________ and its temperature is_______________ Object #3 has a measured λpeak of 175nm, so its spectral band and color would be____________ and its temperature is_______________ Object #4 has a measured λpeak of 550nm, so its spectral band and color would be____________ and its temperature is_______________ Figure 7 Figure 8 Spectral Band Wavelength λ Radio Frequency (RF) >1m microwave, mm 1-0.0003m Infrared (IR) 0.0003m-750nm Visible (VIS) 750-380nm Ultraviolet (UV) 380-10nm X-ray <10nm ASTR101 Astronomy Laboratory Grist Spectroscopy 6 III. Task 2: Emission Spectra This looks like a pattern of colored lines on a black background. Atoms and compounds (molecules) have very specific energy steps based on their structures. No two different atoms or compounds have the exact same structures, but every one of the same atom (or compound) has the same structure; so for example all Carbon Dioxide (CO2) are the same and unlike anything else. This means that the photons emitted by each type of atom or molecule are specific to that one atom or molecule! So if we look at the pattern of colored lines emitted by a sample, we can tell what atoms or compounds emitted the light – just like fingerprints! Observation of Emission Spectra Now we’re going to see and sketch some of these spectral lines. Watch the “Spectral Lines Demo” video posted in this lab module in Canvas (or at https://youtu.be/2ZlhRChr_Bw). Note that this video doesn’t have any audio. In the video the person doing the demo (demonstrator) will hold up a little square white frame; this has something called a diffraction grating in it, which produces an image something like a prism would. Write in the name of each element, then pause the video when the demonstrator holds the diffraction grating to the right of the screen. You should be able to see the various emission lines then within the white frame; sketch the lines in the rectangles provided. Don’t worry about being super precise here, just record how many lines you see and how they are distributed between Violet and Red. Recall that Red is always on the right. Name of element Violet Red #1 #2 #3 #4 What did you notice about the lines and the line patterns? Were any of the patterns the same? ASTR101 Astronomy Laboratory Grist Spectroscopy 7 IV. Task 3: Absorption Spectrum (Dark Line Spectra) Figure 9 So far we have been considering hot to very hot objects, but what if the object is cooler? The gases surrounding stars for instance are relatively cooler than the plasma region of the star; for these cooler gasses most of the atoms are in their respective ground states. Recall that the atoms have specific energy levels and they can give up their energy by emitting a photon; well they can also take on specific amounts of energy by absorbing a photon. When an atom absorbs a photon of a specific energy, one or more of its electrons will change to a higher energy state. When there is a continuous spectrum being emitted behind relatively cooler gas (like at the surface of a star) the atoms of the cooler gas will absorb the specific colors (energies) from the continuous spectrum; the result is called an absorption spectrum. This is a continuous spectrum with specific colors removed, which makes it look like a rainbow with dark lines on it; this type of spectra is also called dark line spectra. In Figure 9 you can see an intensity curve on the lower half with its corresponding absorption spectra above it. A simple way to show the absorption lines pattern is by drawing a rectangle with dark lines as in Figure 10. Figure 10 Pictured below are the spectral curves for three stars (A, B, and C). In the rectangles provided below each star’s spectral curve, draw the appropriate dark line spectra. Circle the name of the star that has similar spectral lines to Figure 10. Wavelength Wavelength Wavelength Which of these stars would be the hottest? Which would be the brightest (highest luminosity)? Star B Star A Star C Energy Output per second Energy Output per second Energy Output per second ASTR101 Astronomy Laboratory Grist Spectroscopy 8 V. Task 4: Doppler Shift Doppler Shift and Direction When an object like a star or galaxy is moving relative to us, we can observe that the spectral lines are shifted relative to the direction that the object is moving with respect to us. If the object and observer are getting closer, the lines will be shifted a bit towards the blue end of the spectrum (blueshifted); moving apart will shift them towards the red end of the spectrum (redshifted). The interesting thing is that all of the lines will be shifted the same amount and the line pattern will be preserved so we can still identify what atoms or compounds are responsible. As the Earth orbits the Sun, a star is observed to have the dark line spectra below. Label when the earth is moving towards, away from and parallel to the star. Doppler Shift and Direction Not only will the spectral lines be redshifted or blueshifted depending on relative direction, the amount they are shifted will depend on how fast we are moving towards or away from each other. In other words, spectral lines are shifted proportional to the speed (velocity). Astronomers typically use the Hydrogen Alpha line (Hα – no joke, Ha!) to figure this out. We use the difference (Δλ) between what wavelength it’s observed to be compared to what it would be if nothing was moving (λ = 656.3 nm); then we can calculate the velocity. The relationship looks like this: V = C x (Δλ ÷ λ) Equation 3 Where V is the velocity and C is the speed of light (3 x 108 m/s). Now we can find the how fast something is moving even if it’s incredibly far away! Example: The Hα line for the absorption spectra of an object is observed to be λ = 656.1 nm (shorter λ so blue shifted). How fast is it going? (3 x 108 m/s)(0.2 nm ÷ 656.3 nm) = 91.4 x 103 m/s = 91.4 km/s The Hα line for the absorption spectra of an object is observed to be λ = 656.5 nm. Is it redshifted or blueshifted? (circle the correct one) Calculate: How fast is it going?
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