HOMEWORK 3

Due Thursday, March 8, 2001.

Review session for Homework 3 will be held on Wednesday, March 7 at 6 to 7pm in CPE 2.208.

NOTE: The due date for this homework differs from that on the schedule. The change from Tuesday, March 6 to Thursday, March 8 is made because I am at the McDonald Observatory from March 3 to March 5 and so unavailable for a review on March 5. My office hours will be as advertised except that I am out of the office on Monday, March 5.

Answer all questions in Part A and one from Part B.

Part A questions may be answered on these sheets. As usual, answers to Part B questions mostly require a few complete sentences at a minimum and should be written out on separate sheets.

Part A

A1. The following are names for portions of the wave family to which light belongs.
Arrange them in order of increasing frequency.

FM radio, visible, -rays, infrared, AM radio, X-rays

A2. Photon energy is directly proportional to

a. wavelength
b. frequency
c. velocity
d. brightness

 

A3. How much more energy is carried by a photon of wavelength 5nm (an X-ray) than by
a photon of wavelength 500nm (visible light)?

A4. What color is visible light with the highest frequency?

A5. The theoretical resolving power (i.e., that set by diffraction) of a telescope is proportional to

a. aperture divided by wavelength
b. wavelength divided by aperture
c. (aperture divided by wavelength)²
d. (wavelength divided by aperture)²

 

A6. If diffraction sets the resolving power of telescope, which of the following combinations provides the highest resolving power:

a. a 10cm telescope operated at a wavelength of 5000 Å.
b. a 200cm telescope operated at a wavelength of 5000 Å.
c. a 10cm telescope operated at a wavelength of 2000 Å.
d. a 100cm telescope operated at a wavelength of 1cm.

[Note: 1,000 Å = 10^-5cm]

A7. The Stefan-Boltzmann law states the flux of radiation from a blackbody is
proportional to

a. 1/T b. T⁴ c. 1/T⁴ d. T² e. 1/T²

 

A8. You double both the radius and the temperature of a spherical blackbody. Its luminosity increases by a factor of

a. 4
b. 8
c. 16
d. 32
e. 64

 

A9. The spectrum of radiation is said to be continuous when

a. there are no breaks or gaps in the spectrum, that is, no absorption or emission lines
b. its emission lines are regularly spaced.
c. its absorption lines are regularly spaced.
d. all the spectrum lines of an element are present.

A10. The binary star UT-301 consists of a blue and a red star emitting the same total amount of energy. Which star has the larger radius?

A11. The radial velocity of a body is the velocity

a. perpendicular to the line of sight
b. toward the observer
c. away from the observer
d. either toward or away from the observer
e. either perpendicular to the line of sight or along the line of sight

A12. If we observe a blue laser on a space prove moving away from Earth, we shall find
its wavelength ________compared with the laboratory standard laser of the same type.

a. unchanged
b. shifted toward to red
c. increases in intensity
d. shifted toward the violet

 

A13. The lines of ionized calcium are strongest in stellar spectral class

a. G
b. B
c. O
d. F
e. M

A14. What characterizes the spectrum of an M star?

a. hydrogen
b. singly ionized calcium
c. doubly ionized iron
d. molecules (TiO)
e. ionized helium

A15. Which of the following stars has the strongest Balmer absorption lines in its spectrum?

O6, M2, K5, A0, F1

A16. As an electron of an atom changes from one energy level to a higher energy level by absorbing a photon, the total energy of the atom

a. increases
b. decreases
c. remains the same

A17. Why do we not see bands of the the TiO molecule in the spectra of hot stars?

A18. What is the difference between a neutral atom and a positive ion of the same element?

A19. Stars UT-X and UT-Y are at distances of 10 and 20 light years, respectively. If the stars are equally luminous, how much brighter will UT-X appear than UT-Y?

A20. Star UT-A is 10,000 brighter than an identical star, UT-B. If UT-A is at a distance of 350 light years, what is the distance of UT-B?

Part B [Answer ONE!]

B1.

a. What is the Doppler effect?
b. Explain why the Doppler effect occurs.
c. In January and July you observe a star to have no radial velocity. In Feb-May the star has a positive radial velocity and in Aug-Dec it has a negative radial velocity. What is causing the observed velocity to vary in this way?

B2.

a. State and illustrate the Stefan-Boltzmann law.
b. Stars X and Y have the same size (radius). X has a surface temperature of 50,000 K and Y a temperature of 3,000 K.

Which star emits more energy?
What is the approximate color of X?
What is the approximate color of Y?
Which star emits more blue light?
Which star emits more red light?

c. The color of a blackbody varies with its temperature. The planet Mars has reddish and bluish regions. These Martian regions have very similar surface temperatures seemingly violating the color-temperature relation for blackbodies. Explain!

B3.

a. Explain the difference between 'the brightness' and 'the (absolute) luminosity' of a star.
b. Prove that the brightness (B) of a star, its absolute luminosity (L) and its distance (d) are related as:
B L/d².
c. What is Olber's paradox? Discuss the paradox explaining how it arises from simple assumptions about the Universe.

B4.

a. Give a complete definition of the following 3 types of spectra: continuous, absorption
line, and emission line. Include diagrams showing intensity of light as a function of
wavelength.
b. Why does the spectrum of a normal star contain absorption lines?

B5.

a. Describe the major characteristics of a neutral atom -- size of atom and nucleus, and
constituent particles, distribution of mass and electrical charge.
b. The Rutherford-Bohr model atom is sometimes referred to as a miniature solar system with electrons ( planets) orbiting the nucleus ( Sun). Discuss one way in which this analogy is imperfect and misleading.
c. Write a short section for a junior-high school text describing an atom and explain how an atom of one element differs from that of another element, and include a telling analogy highlighting the very small size of the nucleus within an atom.

B6.

a. Why are the bands of the TiO molecule weak in the spectra of all but the coolest stars?
b. If spectra lines of a certain element are absent from a star's spectrum, may we conclude that the element is absent? Why or why not? (As a specific example, you may wish to discuss the case of the M stars and the absent Balmer lines.)
c. Estimate the temperatures of the following stars based on their spectra. Use Figure 7-14 and Table 7-2.
i) Medium-strength Blamer lines, strong helium lines
ii) Very weak Balmer lines, strong ionized calcium lines

"I read Shakespeare and the Bible and I can shoot dice.
That's what I call a liberal education."
Tallulah Bankhead (1903 -- 1968)

"Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house."
Henri Poincaré (1854 -- 1912)