Download Ch. 3

Astronomy 120
HOMEWORK - Chapter 3
Radiation
Use a calculator whenever necessary.
For full credit, always show your work and explain how you got your answer in full, complete
sentences on a separate sheet of paper.
Be careful about units!
Please CIRCLE or put a box around your final answer if it is numerical.
If you wish, you may discuss the questions with friends, but please turn in your own hand-written
solutions, with questions answered in your own way.
1. Chaisson Review and Discussion 3.3
What is the relationship between wavelength, wave frequency, and wave velocity? (3 points)
If speed is constant, the longer the wavelength, the lower the frequency; the shorter the
wavelength, the higher the frequency. Thus, wavelength and frequency are inversely
related. The product of the wavelength and frequency is the velocity of the wave.
2. Chaisson Review and Discussion 3.4
What is diffraction, and how does it relate to the behavior of light as a wave? (2 points)
Diffraction is the ability of waves to bend around corners. A sharp-edged gap in a wall
produces a fuzzy shadow due to diffraction. Diffraction would not occur if light were strictly
made of particles – the shadows would be very sharp.
3. Chaisson Review and Discussion 3.8
Compare and contrast the gravitational force with the electric force. (4 points)
The electric force is similar to the gravitational force in that it drops off by the inverse
square of the distance. It is different in that it can be either attractive or repulsive; dislike
charges attract and like charges repel. If the numbers of positive and negative charges are
equal in an object, it appears to be neutral and has no electric force. Gravity is always
present and cannot be neutralized. Gravity is also always attractive regardless of the
circumstances.
4. Chaisson Review and Discussion 3.11
What do radio waves, infrared radiation, visible light, ultraviolet radiation, X rays, and
gamma rays have in common? How do they differ? (3 points)
Radio waves, infrared radiation, visible light, ultraviolet radiation, x-rays, and gamma
rays are all electromagnetic radiation and move at the speed of light in a vacuum. They
differ only by their wavelengths (or frequencies), from longest wavelength (radio waves) to
shortest wavelength (gamma rays).
5. Chaisson Review and Discussion 3.12
In what regions of the electromagnetic spectrum is the atmosphere transparent enough to
allow observations from the ground? (2 points)
The parts of the electromagnetic spectrum for which the Earth’s atmosphere is transparent
are the visible (when it isn’t cloudy!), parts of the infrared, and radio waves between about
one centimeter to ten meters.
6. Chaisson Review and Discussion 3.13
What is a blackbody? What are the main characteristics of the radiation it emits? (4 points)
A blackbody is an idealized object that absorbs all radiation falling on it. It also re-emits all
this radiation. The radiation emitted occurs at all wavelengths but peaks at a wavelength that
depends on the temperature of the blackbody. The hotter the temperature, the shorter the
wavelength of the peak radiation.
7. Chaisson Review and Discussion 3.14
What does Wiens’ law reveal about stars in the sky? (3 points)
Wien’s Law states that the wavelength at which a body emits the peak amount of radiation in
its blackbody curve depends inversely on the temperature of the body; no other factors are
involved. By observing the wavelength at which this peak radiation occurs, the temperature
of a star can be determined.
8. Chaisson Review and Discussion 3.15
What does Stefan’s law tell us about the radiation emitted by a blackbody? (3 points)
Stefan’s Law relates the amount of radiation emitted by a blackbody to its temperature. The
amount at all wavelengths depends upon the fourth power of the temperature.
9. Chaisson Review and Discussion 3.16
In terms of its blackbody curve, describe what happens as a red-hot glowing coal cools. (3
points)
As the coal cools off, its temperature decreases. According to Wien’s Law, more and more
of its radiation will be emitted at longer and longer wavelengths. According to Stefan’s
Law, it will emit less and less radiation as it cools. The net result is that it gets fainter and
redder with time.
10. Chaisson Review and Discussion 3.18
How do astronomers use the Doppler Effect to determine the velocities of astronomical
objects? (3 points)
The Doppler Effect can make the radiation we receive from objects display a different
wavelength than what we expect. By measuring the amount of this “shift” in the wavelength,
astronomers can determine whether an object is moving towards or away from us. The
greater the shift appears, the greater the relative speed. So by measuring the Doppler shift,
the size and direction of the relative velocity along the line of sight can be determined.
11. Chaisson Problem 3.3
Estimate the frequency of an electromagnetic wave having a wavelength equal to the size of
the period at the end of this sentence. In what part of the electromagnetic spectrum would
such a wave lie? (3 points)
Assume a 0.1 mm diameter period. Thus, λ = 0.1 mm = 10-4 m. We know that f = v/ λ, so f =
3x108 m/sec / 10-4 m. f = 3x1012 Hz. This is a far infrared wave or microwave.
12. Chaisson Problem 3.4
Normal human body temperature is about 37oC. What is this temperature in kelvins? What is
the peak wavelength emitted by a person with this temperature? In what part of the spectrum
does this lie? (3 points)
Using the Celsius to Kelvin conversion, 37 + 273 = 310 K. Using Wien’s law, λmax = 0.29/T,
with T in Kelvins and the wavelength in centimeters. For 310 K, this gives λmax = 0.00094
cm = 9.4 µm. This is in the infrared portion of the spectrum.
13. Chaisson Problem 3.7
The sun has a temperature of 5800 K, and its blackbody emission peaks at a wavelength of
approximately 500 nm. At what wavelength does a protostar with a temperature of 1000 K
radiate most strongly? (3 points)
Using Wien’s Law, λmax= 0.29 cm /T(1000 K) = 0.00029 cm or 2.9 μm, which is in the
infrared.
14. Chaisson Problem 3.8
Radiation from the nearby star Alpha Centauri is observed to be reduced in wavelength (after
correction for Earth’s orbital motion) by a factor of 0.999933. What is the recession velocity
of Alpha Centauri relative to the sun? (3 points)
Use the Doppler formula. v = (300,000 km/s ) (1 – 0.999933) = 20 km/s. Because the
wavelength is reduced, this is toward the Sun.
15. Frequency and wavelength of light are related by:
f   c
where f is the frequency in units of cycles per second (Hertz)
 is the wavelength in meters
c is the speed of light in meters/second
c  3  108 m s
a) The wavelength of red visible light is   7  10 7 meters. What is its frequency?
(3 points)
f = c/ =
m
3 x 108 s
7 x 10-7m
= 4.29 x 1014 Hz
b) The frequency of X-rays are about 3  1018 Hertz. What is the
wavelength of X-rays in angstroms if 1 angstrom (Å)  1  10 10
meters?
(3 points)
 = c/f =
m
3 x 108 s
3 x 1018Hz
= 1 x 10-10m = 1 Å