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Homework Chapter 4
Due: January 10, 2014
1.
Prof. Menningen
p. 1/2
Name: ______________________________________
How much time does it take light to travel from Jupiter to Earth when the two planets are 5.20 AU apart?
t
2.
ASTRON 311 Introduction to Astronomy
d 5.20 AU  1.50 108 km/AU

 2600 s  43.3 min
c
300,000 km/s
The remote control of a VCR operates with infrared light of frequency 3.55×1014 Hz.. What is the wavelength of the
light wave?

c 3.00 108 m/s

 8.45 107 m  845 nm
f 3.55 1014 Hz
3.
Which one of the following statements is true?
a. Visible light takes up only a very small part of the total range of wavelengths in the electromagnetic
spectrum.
b. Visible light takes up most (but not all) of the total range of wavelengths in the electromagnetic spectrum.
c. Visible light takes up all of the electromagnetic spectrum.
d. Visible light is not part of the electromagnetic spectrum.
4.
Figure 4.7 in Arny’s Explorations, 6th ed., shows that a blackbody with a temperature of 2900 K emits radiation that
peaks at a wavelength much longer than wavelengths in the visible part of the spectrum. This means that
a. the object is not visible but might be detected with equipment sensitive to nonvisible radiation.
b. the object, like all blackbodies, emits no radiation.
c. the object emits visible radiation, but not as intensely as at longer wavelengths.
d. no visible radiation is emitted, but visible radiation would be emitted if the temperature of the object were
increased.
5.
The star P Cygni (in the constellation Cygnus, the Swan) is surrounded by an extensive low-density atmosphere. Its
spectrum consists of a bright, continuous spectrum with many narrow, dark absorption lines and a few bright emission
lines. The dark absorption lines are produced by
a. all parts of the star, the stellar surface and the atmosphere, equally.
b. only the part of the low-density atmosphere that is between us and the surface of the star.
c. the hot, dense, opaque gas of the star's surface.
d. the hot, low-density atmosphere of the star emitting light in all directions.
6.
The spectrum of a star shows an equivalent set of dark absorption lines to those of the Sun, but with one exception:
Every line appears at a slightly longer wavelength, shifted toward the red end of the spectrum. What conclusion can be
drawn from this observation?
a. The star is moving rapidly toward Earth.
b. A cloud of dust surrounds the star and absorbs the light.
c. The star is moving rapidly away from Earth.
d. The temperature of the star's surface is higher than that of the Sun.
7.
Try the “Blackbody Radiation Interactive” under Chapter 4 of the textbook companion website. (a) Use the slide bar in
the lower right to set the temperature to 5800 K, approximately the surface temperature of our Sun. At what
wavelength is the emitted intensity a maximum? Use Wien's law to verify that your estimate from the graph is correct.
(b) Now move the slide bar until the maximum intensity is at about 850 nm, similar to a red giant star. What is the
approximate surface temperature of Betelgeuse?
(a) The peak intensity of the radiation coming from a 5800 K blackbody is at about 500 nm.
(b) The temperature of a blackbody whose maximum intensity is at about 850 nm is
approximately 3400 K.
Homework Chapter 4
8.
ASTRON 311 Introduction to Astronomy
Prof. Menningen
p. 2/2
Suppose your normal body temperature is 98.6°F (310 K). What kind of radiation do you predominantly emit? At what
wavelength (in nm) do you emit the most radiation?
Your body temperature is 37°C: 37 °C + 273 = 310 K. Refering to the “Extending our Reach”
box on p. 100,
max
2.9 106 nm  K
 9350 nm
310 K
 = 9350 nm is infrared radiation, which is why the military’s night vision goggles are
sensitive to this wavelength.
9.
A bright star has a surface temperature of 8700 K. How much more energy is emitted each second from each square
meter of this star's surface than from each square meter of the Sun's surface , if the Sun has a surface temperature of
5800 K? (See p. 345-346 of the text).
The energy flux is proportional to the fourth power of the temperature. The star’s
temperature (8700 K) is greater than the Sun’s (5800 K) by a factor of 8700 /5800 = 1.5. The
flux from the star’s surface is therefore (1.5)4 = 5.1 times greater than that from the Sun’s
surface.
10.
Since the 1970s, instruments on board balloons and spacecraft have detected 511 keV photons coming from the
direction of the center of our Galaxy. (The prefix k means kilo, or thousand, so 1 keV = 10 3 eV.) What is the
wavelength of these photons? To what part of the electromagnetic spectrum do these photons belong?
When working with energies in eV and wavelengths in nm, it is convenient to use hc = 1240 eV·nm:
hc = (4.135 x 10-15 eV·s)(3.00 x 108 m/s)  (109 nm/m) = 1240 eV·nm.
E
hc

 
hc 1240 eV  nm

 0.00243 nm
E
511,000 eV
These are gamma rays. (See Table 4.2 or Figure 4.5).
11.
Try the “Doppler Shift Interactive” exercise under Chapter 4 of the textbook companion web site. Choose “Source
Approaches” and watch the planet approach the spacecraft. (a) What is the detected frequency of the waves as the
planet approaches the spacecraft? (b) What is the frequency as the planet recedes? You’ll have to count the waves
passing the spacecraft in a time interval measured with a stopwatch. Ignore the first few waves that were emitted
while the planet was at rest.
(a) The frequency as the planet approaches is about 1 crest per second, or about 1 Hertz.
(b) The frequency as the planet recedes is about 1 crest per 5 seconds, or about 0.20 Hz.
12.
The nebula NGC 2363 is located within the galaxy NGC 2366 in the constellation Camelopardis (the Giraffe).
Suppose this galaxy and the nebula within it are moving away from us at 252 km/s. At what wavelength does the red
H line (rest wavelength 656.285 nm, see pp. 104-105) of hydrogen (which causes the color of the nebula) appear in
the nebula's spectrum?
Use the Doppler equation, p. 111:

0

V
c
   0
V
c
 252 10 m/s   0.551 nm ,
   656.285 nm 
3 10 m/s 
3
8
 = 656.285 nm + 0.551 nm = 656.84 nm