Questions

Review Questions

1. When Jupiter is undergoing retrograde motion as seen from Earth, would you expect the eclipses of Jupiter’s moons to occur several minutes early, several minutes late, or neither? Explain your answer.

2. Approximately how many times around Earth could a beam of light travel in one second?

3. How long does it take light to travel from the Sun to Earth, a distance of 1.50 × 10⁸ km?

4. How did Newton show that a prism breaks white light into its component colors but does not add any color to the light?

5. For each of the following wavelengths, state whether it is in the radio, microwave, infrared, visible, ultraviolet, X-ray, or gamma-ray portion of the electromagnetic spectrum. Explain your reasoning. (a) 2.6 μm, (b) 34 m, (c) 0.54 nm, (d) 0.0032 nm, (e) 0.620 μm, (f) 310 nm, (g) 0.012 m

6. What is meant by the frequency of light? How is frequency related to wavelength?

7. A cellular phone is actually a radio transmitter and receiver. You receive an incoming call in the form of a radio wave of frequency 880.65 MHz. What is the wavelength (in meters) of this wave?

8. A light source emits infrared radiation at a wavelength of 1150 nm. What is the frequency of this radiation?

9. (a) What is a blackbody? (b) In what way is a blackbody black? (c) If a blackbody is black, how can it emit light? (d) If you were to shine a flashlight beam on a perfect blackbody, what would happen to the light?

10. What does it mean for a material to be opaque? Can water molecules form an opaque object in some forms and a transparent substance in others? (Hint: Think of clouds.)

11. Describe how the thermal energy changes at a microscopic level as a blacksmith heats a piece of iron. If the iron is then removed from the furnace and glows bright red, what effect does this have on the thermal energy?

12. Why do astronomers find it convenient to use the Kelvin temperature scale in their work rather than the Celsius or Fahrenheit scales?

13. Explain why astronomers are interested in blackbody radiation.

14. In what way is the Sun’s spectrum similar to a blackbody spectrum? In what way does it differ from a blackbody spectrum?

15. Using Wien’s law and the Stefan-Boltzmann law, explain the color and intensity changes that are observed as the temperature of a hot, glowing object increases.

16. If you double the Kelvin temperature of a hot piece of steel, how much more energy will it radiate per second?

17. The bright star Bellatrix in the constellation Orion has a surface temperature of 21,500 K. What is its wavelength of maximum emission in nanometers? What color is this star?

18. The bright star Antares in the constellation Scorpius (the Scorpion) emits the greatest intensity of radiation at a wavelength of 853 nm. What is the surface temperature of Antares? What color is this star?

19. (a) Describe an experiment in which light behaves like a wave. (b) Describe an experiment in which light behaves like a particle.

20. How is the energy of a photon related to its wavelength? What kind of photons carry the most energy? What kind of photons carry the least energy?

21. Which part of the electromagnetic spectrum contains light with a higher frequency: microwaves or radio waves?

22. To emit the same amount of light energy per second, which must emit more photons per second: a source of red light or a source of blue light? Explain your answer.

23. (a) Describe the spectrum of hydrogen at visible wavelengths. (b) Explain how Bohr’s model of the atom accounts for the Balmer lines.

24. Why do different elements display different patterns of lines in their spectra?

25. What is the Doppler effect? Why is it important to astronomers?

26. If you see a blue star, what does its color tell you about how the star is moving through space? Explain your answer.

Advanced Questions

Questions preceded by an asterisk (*) involve topics discussed in the Boxes.

27. Your normal body temperature is 98.6°F. What kind of radiation do you predominantly emit? At what wavelength (in nm) do you emit the most radiation?

28. What is the temperature of the Sun’s surface in degrees Fahrenheit?

29. What wavelength of electromagnetic radiation is emitted with greatest intensity by this book? To what region of the electromagnetic spectrum does this wavelength correspond?

30. Can an object convert some of its orbital energy into thermal energy? If yes, describe a context in which this might occur.

31. Black holes are objects whose gravity is so strong that not even an object moving at the speed of light can escape from their surfaces. Hence, black holes do not themselves emit light. But it is possible to detect radiation from material falling toward a black hole. Calculations suggest that as this matter falls, it is compressed and heated to temperatures around 10⁶ K. Calculate the wavelength of maximum emission for this temperature. In what part of the electromagnetic spectrum does this wavelength lie?

32. *Use the value of the solar constant given in Box 5-2 and the distance from Earth to the Sun to calculate the luminosity of the Sun.

33. *The star Alpha Lupi (the brightest in the constellation Lupus the Wolf) has a surface temperature of 21,600 K. How much more energy is emitted each second from each square meter of the surface of Alpha Lupi than from each square meter of the Sun’s surface?

34. *Jupiter’s moon Io has an active volcano named Pele whose temperature can be as high as 320°C. (a) What is the wavelength of maximum emission for the volcano at this temperature? In what part of the electromagnetic spectrum is this? (b) The average temperature of Io’s surface is -150°C. Compared with a square meter of surface at this temperature, how much more energy is emitted per second from each square meter of Pele’s surface?

35. *The bright star Sirius in the constellation of Canis Major (the Large Dog) has a radius of 1.67 R_⊙ and a luminosity of 25 L_⊙. (a) Use this information to calculate the energy flux at the surface of Sirius. (b) Use your answer in part (a) to calculate the surface temperature of Sirius. How does your answer compare to the value given in Box 5-2?

36. Instruments on board balloons and spacecraft detect 511-keV photons coming from the direction of the center of our Galaxy. (The prefix k means kilo, or thousand, so 1 keV = 10³ eV.) What is the wavelength of these photons? To what part of the electromagnetic spectrum do these photons belong?

37. (a) Calculate the wavelength of P_Δ (P-delta), the fourth wavelength in the Paschen series. (b) Draw a schematic diagram of the hydrogen atom and indicate the electron transition that gives rise to this spectral line. (c) In what part of the electromagnetic spectrum does this wavelength lie?

38. (a) Calculate the wavelength of H_η (H-eta), the spectral line for an electron transition between the n = 7 and n = 2 orbits of hydrogen. (b) In what part of the electromagnetic spectrum does this wavelength lie? Use this to explain why Figure 5-21 is labeled
    R I V U X G.

39. Certain interstellar clouds contain a very cold, very thin gas of hydrogen atoms. Ultraviolet radiation with any wavelength shorter than 91.2 nm cannot pass through this gas; instead, it is absorbed. Explain why.

40. (a) Can a hydrogen atom in the ground state absorb an H-alpha (H_α) photon? Explain why or why not. (b) Can a hydrogen atom in the n = 2 state absorb a Lyman-alpha (L_α) photon? Explain why or why not.

41. An imaginary atom has just three energy levels: 0 eV, 1 eV, and 3 eV. Draw an energy-level diagram for this atom. Show all possible transitions between these energy levels. For each transition, determine the photon energy and the photon wavelength. Which transitions involve the emission or absorption of visible light?

42. The star cluster NGC 346 and nebula shown in Figure 5-19 are located within the Small Magellanic Cloud (SMC), a small galaxy that orbits our Milky Way Galaxy. The SMC and the stars and gas within it are moving away from us at 158 km/s. At what wavelength does the red H_α line of hydrogen (which causes the color of the nebula) appear in the nebula’s spectrum?

43. The wavelength of H_β in the spectrum of the star Megrez in the Big Dipper (part of the constellation Ursa Major the Great Bear) is 486.112 nm. Laboratory measurements demonstrate that the normal wavelength of this spectral line is 486.133 nm. Is the star coming toward us or moving away from us? At what speed?

44. You are given a traffic ticket for going through a red light (wavelength 700 nm). You tell the police officer that because you were approaching the light, the Doppler effect caused a blueshift that made the light appear green (wavelength 500 nm). How fast would you have had to be going for this to be true? Would the speeding ticket be justified? Explain your answer.

Discussion Questions

45. The equation that relates the frequency, wavelength, and speed of a light wave, ν = c/λ, can be rewritten as c = νλ. A friend who has studied mathematics but not much astronomy or physics might look at this equation and say: “This equation tells me that the higher the frequency ν, the greater the wave speed c. Since visible light has a higher frequency than radio waves, this means that visible light goes faster than radio waves.” How would you respond to your friend?

46. (a) If you could see ultraviolet radiation, how might the night sky appear different? Would ordinary objects appear different in the daytime? (b) What differences might there be in the appearance of the night sky and in the appearance of ordinary objects in the daytime if you could see infrared radiation?

47. The accompanying visible-light image shows the star cluster NGC 3293 in the constellation Carina (the Ship’s Keel). What can you say about the surface temperatures of most of the bright stars in this cluster? In what part of the electromagnetic spectrum do these stars emit most intensely? Are your eyes sensitive to this type of radiation? If not, how is it possible to see these stars at all? There is at least one bright star in this cluster with a distinctly different color from the others; what can you conclude about its surface temperature?

    

    R I V U X G
    

    (David Malin/Anglo-Australian Observatory)

48. The human eye is most sensitive over the same wavelength range at which the Sun emits the greatest intensity of radiation. Suppose creatures were to evolve on a planet orbiting a star somewhat hotter than the Sun. To what wavelengths would their vision most likely be sensitive?

49. Why do you suppose that ultraviolet light can cause skin cancer but ordinary visible light does not?

Web/eBook Question

50. Search the World Wide Web for information about rainbows. Why do rainbows form? Why do they appear as circular arcs? Why can you see different colors?