AST1110_sai Kim

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Colorado Online @ Astronomy 1110 Lab 7 A STRONOMY 1110 S PECTROSCOPY Outcomes (Lab worth: 50 pts)  Connect frequency, wavelength, and energy for different types of light. (E, H)  Identify unknown elements based on their spectra (C, H) Instructions Answer all of the questions in the sections below. Questions requiring student responses have numbers, and sub-parts of questions are assigned lower-case letters. You should type your answers into the spaces below the questions. Be sure to read the directions carefully and to answer all parts of each question. Background The most important way that astronomers learn about distant objects is by examining the light they emit, absorb, or reflect. One of our most powerful tools to study this light is called spectroscopy . In spectroscopy, we break light into its constituent wavelengths, which we call a spectrum . From an object’s spectrum, we can infer the object’s temperature, what it’s made of, how it’s moving, and often more. Understanding how and why things emit as they do is critical to identifying the object and to understanding the rules that govern its behavior. Colors of Light Light demonstrates what we call additive color. When multiple light sources combine, our eyes perceive all the light emitted by every source. This is different from paint and other pigments, which demonstrate what is known as subtractive color. The most common example of additive color is covered in your reading for this week. White sunlight contains all the colors of the rainbow. Our eyes perceive this specific mixture of wavelengths as pure white. Blackbody Radiation A blackbody is a hot, opaque object that emits light at all frequencies . Kirchhoff’s first radiation law tells us that this is a continuous spectrum (an unbroken rainbow). The continuous spectrum has a characteristic shape with a peak, and Wien’s Law says that the wavelength of the peak emission ( λ peak ) is related to the object’s temperature (T): λ peak ∝ 1 T Page 1 Hot Blue Red

Colorado Online @ Astronomy 1110 Lab 7 Thus, increasing temperature leads to decreasing  peak and vice versa. Therefore, a hot object’s spectrum peaks at a shorter wavelength (bluer color) when compared to a cooler object. A hotter object also appears brighter following Stefan’s Law , which says that the energy per unit area emitted each second rises quickly with temperature . We can summarize this as: brightness  T 4 Thus, small changes in temperature lead to large changes in brightness. A hotter object is therefore much, much brighter than a cooler one. For example, if you double the temperature of an object, it emits 2 4 = 16 times as much light. Bright Line Spectra A hot, low-density gas will emit light only at specific frequencies . This is called a bright line spectrum (sometimes called an emission spectrum). The wavelengths of light that are present in bright line spectrum depend on the element(s) present in the gas. Different elements emit light at different frequencies that depend on the energy levels present within atoms of the element. By looking at the colors (wavelengths) of light present in a bright line spectrum, astronomers can determine which elements are producing the light. In this way, the emission spectrum might be considered a “fingerprint” that allows us to identify the element. Materials Required  Computer with internet connection Part I: Blackbody Radiation In this section, we’ll be using the Blackbody Spectrum simulator (http// https://phet.colorado.edu/sims/html/blackbody-spectrum/latest/blackbody- spectrum_en.html ) from PhET to examine how the brightness, color, and peak wavelength emitted by a blackbody depends on its temperature. Initially, we’re going to explore the relationship between the temperature of a blackbody and the wavelengths (colors) of light it emits. This relationship is summarized by Wien’s Law. (See the Background section at the beginning of this lab.) Page 2 Hot Bright Faint

Colorado Online @ Astronomy 1110 Lab 7 Figure 1: Simulated spectrum of a 2000 K blackbody. Labels on the graph refer to the wavelength and height of the spectrum at peak brightness. Wavelengths are reported in microns (μm), which are a millionth of a meter. The color of the emitted light is given by the star display at the top, center of the graphic. (Image credit: PhET , CC BY 4.0 ) 1. (Worth 6 pts) We’ll first consider a blackbody with a temperature of 2000 Kelvin. a. What is the peak wavelength of blackbody at this temperature? The peak wavelength of the blackbody at a temperature of 2000 Kelvin is approximately 1.449×10^−6meters. b. In which part of the electromagnetic spectrum (X-ray, UV, visible, etc.) does the blackbody peak at this temperature? The blackbody radiation peaks in the infrared part of the spectrum. c. What color light would our eyes perceive from a blackbody emitting at this temperature? the color of light our eyes would perceive from a blackbody emitting at this temperature would be a deep red color. Page 3

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Colorado Online @ Astronomy 1110 Lab 7 Figure 2: Simulated spectrum of a 3000 K blackbody. (Image credit: PhET , CC BY 4.0 ) 2. (Worth 6 pts) Next, we’ll increase the temperature to 3000 Kelvin, which is typical for the filament inside an old-style incandescent light bulb. a. What is the peak wavelength of a blackbody at this temperature? 9.66x10^-7 meters b. In which part of the electromagnetic spectrum does the blackbody peak? Infrared part of the spectrum. c. What color light does a blackbody at this temperature emit? Reddish orange. Page 4

Colorado Online @ Astronomy 1110 Lab 7 Figure 3: Simulated spectrum of a 6000 K blackbody. (Image credit: PhET , CC BY 4.0 ) 3. (Worth 6 pts) Now, we’ll increase the temperature again to 6000 Kelvin, which is approximately the temperature of the Sun. a. What is the peak wavelength of the blackbody at this temperature? 4.83x10^-7 b. In which color (red, green, blue, etc.) does the Sun’s peak wavelength occur? blue c. What color is the light emitted by the Sun? The sun is perceived as white. Page 5

Colorado Online @ Astronomy 1110 Lab 7 Figure 4: Simulated spectrum of a 10,000 K blackbody. (Image credit: PhET , CC BY 4.0 ) 4. (Worth 6 pts) Finally, we’ll raise the temperature to 10,000 Kelvin. This is the approximate temperature of Sirius, the brightest star in the night sky. a. What is the peak wavelength of the blackbody at this temperature? 2.898x10^-7 meters b. In which color (red, green, blue, etc.) does Sirius’s peak wavelength occur? blue c. What color is the light emitted by a blackbody at this temperature? white 5. (Worth 3 pts) What trend can you identify between the temperature of blackbody, the peak wavelength of its emission, and the observed color of the light? Is this consistent with your expectations? Why or why not? When something called a blackbody gets heated up, it starts to glow, but the color it glows depends on how hot it gets. At first, when it's not too hot, it gives off a reddish glow. But as it gets hotter and hotter, the color changes, going from red to orange, then yellow, white, and finally to a bluish color. This happens because as the blackbody gets hotter, it emits shorter wavelengths of light, which we see as different colors. It's like when you heat up metal it starts with a reddish glow, then turns orange, and finally gets bluish as it gets hotter. Next, we’ll explore how the temperature of a blackbody affects its luminosity. Watch the video as the narrator increases the temperature of the blackbody from 2000 Kelvin to 10,000 Kelvin. Page 6

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Colorado Online @ Astronomy 1110 Lab 7 Figure 5: Simulated blackbody emission using the Blackbody Spectrum simulator from PhET ( CC BY 4.0 ). Video by David Atlee (CC BY 4.0 via YouTube) 6. (Worth 2 pts) How does the brightness of the blackbody curve change with temperature? Consider both the height of the spectrum and the size of the star display. The brightness of the blackbody curve increases with temperature. As the temperature of the blackbody increases, the height of the spectrum curve also increases, indicating that more energy is being emitted across all wavelengths. Additionally, the size of the star display, which represents the total amount of energy emitted by the blackbody, also increases with temperature. This is because hotter objects emit more energy overall, resulting in a larger and brighter star display. 7. (Worth 2 pts) Is the observed change consistent with your expectations? Why or why not? Yes, the observed change is consistent with expectations. According to Wien's Law, as the temperature of a blackbody increases, the peak wavelength of its emission shifts to shorter wavelengths, resulting in a higher energy output. This increase in energy output leads to a brighter and larger star display, which aligns with our understanding that hotter objects emit more light. Therefore, the observed change in the brightness of the blackbody curve with temperature is consistent with our expectations based on fundamental principles of blackbody radiation. Part II: Bright Line Spectra In this section, we’ll examine the bright line spectra produced by several different elements. We’ll begin by directly examining the spectra of individual elements. Then we’ll try using the spectra of known elements to identify an unknown spectrum. This section employs the Neon Lights & Other Discharge Lamps simulator (https://phet.colorado.edu/en/simulations/discharge-lamps )from PhET. This simulator requires JavaScript to operate. If you have difficulty accessing the simulation, check your browser’s security settings. Remember that it is always possible to address the lab questions without operating the simulator yourself. Page 7

Colorado Online @ Astronomy 1110 Lab 7 Figure 6: The bright line spectrum of the chemical element helium. Bright lines appear wide, and faint lines appear narrow. (Modified from an original image by Thomas Wenzel/LibreTexts Analytical Chemistry, CC BY-NC 4.0 ) 8. (Worth 3 pts) Examine the bright line spectrum of helium in Figure 6. What color is the brightest line in helium’s spectrum? What color is its faintest line? The brightest line is red, and the faintest is blue. Watch the video below. It shows the production of a bright line spectrum for hydrogen gas, which can be accomplished inside an emission tube. Figure 7: Simulated hydrogen emission using the Neon Light & Other Discharge Tubes simulator from PhET ( CC BY 4.0 ). Video by David Atlee (CC BY 4.0 via YouTube) Page 8

Colorado Online @ Astronomy 1110 Lab 7 Figure 8: Bar graphs showing the relative brightness of the colored lines produced by hydrogen, neon, sodium, and mercury gases. Colored bars represent lines visible to the human eye. Grey lines are outside the human visual range. (Modified from original work by PhET, CC BY 4.0 ) The bar graphs in Figure 8 shows the relative brightness of the lines that appear in the bright line spectra of four different elements. Colors with tall bars will appear bright (wide in the spectrum), while colors with short bars will appear faint. 9. (Worth 8 pts) Examine the bright line spectra in Figure 8. a. What color is the brightest line of the hydrogen spectrum? Violet b. What color is the brightest line of the neon spectrum? Yellow c. What color is the brightest line of the sodium spectrum? Yellow d. What color is the brightest line of the mercury spectrum? Purple Page 9

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Colorado Online @ Astronomy 1110 Lab 7 10. (Worth 4 pts) Imagine combining all the colored lines produced by sodium gas in Figure 8. What do you think the combined light would have? What if you combined the lines from the neon gas? Explain your reasoning for both answers. I believe it would produce a yellow color with a hint of orange from all of sodium gas because yellow is the brightest on the spectrum. Neon would be an orange as yellow and red are its most dominant colors as well. Figure 9: The first mystery element. (Image credit: Public Domain from Wikimedia Commons/Adrignola) 11. (Worth 2 pts) Examine the spectrum of the mystery element shown in Figure 9. Compare the colors of these emission lines to the elements in Figure 8. Which element produced this spectrum? I believe this is hydrogen Figure 10: The second mystery element. (Modified from an original image by Wikimedia Commons/Deo Favente, CC BY 3.0 ) 12. (Worth 2 pts) Examine the spectrum of the mystery element shown in Figure 10. Compare the colors of these emission lines to the elements in Figure 8. Which element produced this spectrum? This looks like neon because it has the most range of colors and is predominantly red/orange References: 1. PhET. (n.d.) Blackbody Spectrum . University of Colorado, Boulder. https://phet.colorado.edu/en/simulations/blackbody-spectrum 2. PhET. (n.d.) Neon Lights & Other Discharge Lamps . University of Colorado, Boulder. https://phet.colorado.edu/en/simulations/discharge-lamps 3. Wenzel, T. (n.d.) Analytical Chemistry. LibreTexts. https://chem.libretexts.org/Bookshelves/Analytical_Chemistry Page 10

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