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HOMEWORK #13 My star name is _______________ (Due at the start of class Tuesday, March 1) GOALS for the student: 1. To deepen your understanding of the word “spectrum;” 2. To understand the characteristics of light emitted by ALL opaque objects in the Universe, i.e., a “blackbody spectrum.” BASIC INSTRUCTIONS: See previous homework. Required Reading In class we introduced the word “spectrum” to describe the wide range of “wavelengths” or “frequencies” that represent light. In order of increasing wavelength (decreasing frequency) the “electromagnetic spectrum” of light consists of -rays, X-rays, ultraviolet, visible, infrared, and radio waves. In reality these labels are arbitrary boundaries in a continuous, infinite range of wavelengths. From this perspective, a spectrum of light is only one-dimensional. However, to astronomers an object’s spectrum has two dimensions. The two dimensions of a spectrum are the amount of each wavelength. Like your favorite dessert, the spectrum of an object’s light is a recipe specifying the amount of different ingredients (i.e., wavelengths). The spectrum shows the measured amount (“intensity” or “flux”) of any wavelengths present in the object’s light. A “blackbody spectrum” exhibits a smooth variation of intensity vs. wavelength with a peak intensity at a specific wavelength that depends only on the object’s temperature. The study of blackbody spectra led to the discoveries that energy exists only in discrete amounts called “quanta” and light consists of particles called “photons.” Amazingly, all opaque objects emit light with a blackbody spectrum that includes every wavelength. The spectrum’s characteristic shape is determined only by the object’s temperature, not composition, and is expressed by a single, simple equation. Read the following items about blackbody spectra. Make sure you understand “Wien’s Law” and the “Stefan-Boltzmann Law” before answering any questions. Please read and view: Textbooks: Hawking (pp. 53-54; 87-89); Bennett (pp. 159-160) Web site: http://astro.unl.edu/naap/blackbody/spectra.html YouTube video: http://www.youtube.com/watch?v=AjnBGWLAoZY Questions: (In each case explain your reasoning carefully.) #1. The blackbody spectrum of an object at temperature 3000 K is shown below. If the temperature increased to 3500 K, the total amount of light emitted by the object would A. increase and the peak intensity would shift to the left. B. increase and the peak intensity would shift to the right. C. decrease and the peak intensity would shift to the left. D. decrease and the peak intensity would shift to the right. #2. Based on the blackbody spectra above, which object(s) would appear red to the human eye? [Remember that our eyes see all the light combined. The blue and red ends of the visible portion of light are labeled.] A. A and B B. D and E C. C and D D. E E. C #3. Based on the blackbody spectra above, which object would appear white to the human eye? Circle one: A, B, C, D, E. #4. Answer all the following questions using proportional thinking together with Wien’s Law and the Stefan-Boltzmann Law. Remember to show all your numerical work. A. If the temperature of an object increases from 3000 K to 6000 K, how many times more is its total emitted energy in the form of light? B. By what factor does the wavelength of maximum brightness decrease? C. How would the perceived color of the object change? #5. Use the following “Blackbody Simulator” tool to check your predictions for #4. List your measurements and the resulting ratios. Explain why your measurements either agree or disagree with your answers in #4. http://astro.unl.edu/naap/blackbody/animations/blackbody.html #6. Among the three spectra below, circle the one that emits the most total energy when considering all wavelengths together. #7. Which of the three objects below would appear the bluest and which object the reddest?
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