NatSci102 Professors G. and M. Rieke Homework Due Feb. 8 Homework on spectroscopy, colors, and light. Lecture notes for Jan 29 and Feb 1 will be very helpful. This homework will be due on Feb 8 but working through it will be helpful in preparing for the first exam. Answers shown in boldface italics. 1. Is the spectrum below a. an absorption line one b. a continuum c. an emission line one d. Doppler shifted e. unresolved 2. If a photon of energy E has a wavelength of 0.6 microns, what energy photon will have a wavelength of 0.3 microns? a. 2 times E b. Half of E c. 4 times E d. ¼ of E e. the energy cannot be determined accurately Go to the Wikipedia article on spectroscopy (http://en.wikipedia.org/wiki/spectroscopy) and scroll down to the section on Fluorescence and examine the spectrum shown there from a fluorescent light (the long tube type of lights or the new compact ones that are tubes in a spiral shape). Answer questions 3 6 using this image and the electromagnetic spectrum shown in the Jan 29 lecture on light. Note that an emission line appears as spike in this type of plot. 3. Which of the numbered spectral lines is located in the bluest portion of the spectrum? 4. Which of the numbered spectral lines is located in the reddest portion of the spectrum? 5. Which of the numbered spectral lines is located near the reddest wavelength you can see with your eye? 6. Which of the numbered spectral lines is located in the yellow portion of the spectrum? 7. The figure on the left illustrates electronic transitions from 3 higher levels to a lower one An energy level diagram showing the 3 hydrogen transitions which give the strongest lines in the visible spectrum. (5 2, 4 2, or 3 2) in the hydrogen atom. Which transition produces a photon with the highest energy? a. 5 > 2 b. 4 > 2 c.3 > 2 1
8. Which transition produces a photon in the reddest portion of the spectrum? a. 5 > 2 b. 4 > 2 c. 3 > 2 9. What type of spectrum does the observer see in the figure on the right? a. absorption b. emission c. continuous 10. How are the electrons in the atoms in the hydrogen cloud in this figure behaving? a. They are jumping from a lower to a higher level b. they are jumping from higher to lower c. They are leaving the cloud d. we cannot know how they are moving 11. The young, hot star in picture to the left heats up the gas in the cloud. Assume that the observer can only see radiation emitted by the hydrogen cloud and cannot see the star. What type of spectrum does the observer see? a. absorption b. emission c. continuous 12. How are the electrons in the atoms in the hydrogen cloud in this figure behaving? a. They are jumping from a lower to a higher level b. they are jumping from higher to lower c. They are leaving the cloud d. we cannot know how they are moving 13. Look at the spectrum of the Sun below. What type of spectrum (continuous, emission line or absorption line spectrum) does the Sun produce? a. absorption b. emission c. continuous The next few problems will be much easier if you review how to use scientific notation (see also http://www.ifa.hawaii.edu/~barnes/ast110_06/sosat.html#[20] ) 14. Hydrogen has a spectral line that is observed at a wavelength of 656 nm (656x10 9 meters). Recalling that the speed of light is 3x10 8 meters/sec and the relationship between wavelength and frequency, what is the frequency of the photons observed as this spectral line? a. 4.6x10 14 Hz b. 2.2x10 15 Hz c. 100 MHz d. 4.6 Hz e. Cannot be computed 2
15. The photons producing the hydrogen line in question 14 also have energy. Review the relationship between energy and frequency given in the Jan 29 lecture. Use h=planck s constant = 6.6x10 34 Joules/Hz to compute the photon s energy which is Joules. a. 3 b. 3.0x10 19 c. 24 d. 24x10 19 e. 7x10 47 16. If you observed the hydrogen line discussed in questions 14 and 15, what color would it have? a. purple b. green c. white d. all the colors of the rainbow e. red A. B. Examine the two spectra above. Go to http://www.amateurspectroscopy.com/color spectra ofchemical elements.htm and compare the spectra shown there with these spectra. 17. The spectrum labeled A. above is produced by which element? a. lithium b. Hydrogen c. Helium d. carbon e. no way to tell 18. The spectrum labeled B. above is produced by which element? a. lithium b. Hydrogen c. Helium d. carbon e. no way to tell A. B. C. D. 3
19. The spectra of four stars are shown on the previous page. Which star s spectrum is dominated by spectral lines from hydrogen? A. B. C. D. E. none are 20. The spectrum plotted above is from a real star, Vega. The spectrum is also shown in color as it might appear to your eye. What element s absorption lines are prominent in Vega s spectrum? a. lithium b. hydrogen c. helium d. carbon e. no way to tell The plot at the right shows a magnified section of the Vega spectrum in black. You may assume that Vega is not moving. The red plot is part of the spectrum from another star very similar to Vega except for its Doppler shift. The numbers show the location of the spectral line. You will find It helpful to review the end of the Feb 1 lecture. Use c=300,000 km/sec 410.2165 410.4216 21. In what direction is the star producing the red spectrum moving? a. Toward us b. Away from us c. Cannot be figured out from this plot 4
22. How fast is the star producing the red spectrum moving? a. 300,000 km/sec b. 150 km/sec c. 15000 km/sec d. 0.205 km/sec e. 61,500 km/sec 23. This figure is similar to the previous one but the blue plot is the spectrum from a third star with a different Doppler shift. In what direction is the star producing the blue spectrum moving? a. Toward us b. Away from us c. Cannot be figured out from this plot 409.9293 410.2165 24. How fast is the star producing the blue spectrum moving? a. 300,000 km/sec b. 210 km/sec c. 21000 km/sec d. 0.287 km/sec e. 86,160 km/sec 25. The graph on the next page shows the output of a black body at a temperature of 5000K, against the wavelength. The peak is at 0.58 microns. How would the output against wavelength change if the temperature were 2500K? a. it would stay the same b. it would get fainter but otherwise stay the same c. the shape of the curve of output against wavelength would change d. the peak of the output would appear at 1.1 microns e. the peak of the output would appear at 0.29 microns 5
1.4 1.2 1 0.8 flux 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 wavelength (microns) 26. In the situation described in problem 23, with the temperature going down by a factor of two, how will the total output over the entire range of wavelengths (the luminosity) change? a. stay the same b. get 2 times smaller c. get 4 times smaller d. get 8 times smaller e. get 16 times smaller 27. How low would the temperature have to be for the peak of the output to be in the far infrared, at 100 microns? a. 250K b. near absolute zero c. 29K d. 57C e. None of the above 6