BUCKNELL UNIVERSITY

Astronomy 102

First Hour Exam

1998 February 27

This Exam will be scored on a 100 point scale and has two parts: a multiple choice section of 18 questions each worth 2 points and a problem section with 3 problems, each worth 20 points. You earn four points for writing your name on the exam.

Here are some quantities and relationships that you might find useful:

for a sphere:
- surface area = 4 x pi x radius²
distances:
- 1 Astronomical Unit = 1.495 x 10¹¹ m
- 1 parsec = 3.09 x 10¹⁶ m
for a wave:
- speed = wavelength x frequency
for light waves:
- energy = h x frequency = h x c/wavelength
- the speed of light --- c = 3 x 10⁸ m/sec
- Planck's constant --- h = 6.626 x 10^-34 J s
for blackbody emitters:
- intensity = sigma x temperature⁴
- luminosity = intensity x surface area
- wavelength of spectrum peak =(0.003 m K)/temperature
- Stefan-Boltzmann constant--- sigma = 5.67 x 10-8 W/(m² K⁴)

Doppler formula:

                   speed of emitter      change in frequency
              ---------------------- = ----------------------
	            speed of wave         rest frequency

magnitude scale: difference of one magnitude corresponds to a factor of 2.512 in flux
flux = luminosity/(4 x pi x distance²)
The observer's triangle relation:
alpha/57.3^o = w/R (a in degrees)

Multiple Choice Questions:

1) Water waves travel across the surface of a pond with a speed of 12 m/s. If the waves lap up against the far shore at a rate of 3 per second, what is the wavelength of the waves?

a) 36 m
b) 4 Hz
c) 4 m
d) 36 Hz
e) 3 Hz

2) The chromospheric "flash" spectrum seen just before a total solar eclipse is an example of

a) blackbody emission
b) spectral line absorption
c) spectral line emission
d) blackbody absorption
e) thermal emission

3) The astronomer who correctly deduced that stars are composed mainly of hydrogen was

a) Henry Norris Russell
b) Cecilia Payne
c) Max Planck
d) Henrietta Leavitt
e) Annie Jump Cannon

4) The most convincing piece of evidence indicating that stars are really as luminous as the Sun is

a) stellar spectra are well-fit by a blackbody model.
b) stars have colors similar to those of the Sun.
c) stars have very small parallaxes.
d) stars rise and set just like the Sun.
e) the absorption seen in stellar spectra indicates that stars have chemical compositions very similar to that of the Sun.

5) Photons with energies slightly lower than the energies of visible light photons are

a) infrared photons.
b) radio photons.
c) ultraviolet photons.
d) x-ray photons.
e) photon torpedoes.

6) Rigel has an apparent magnitude of 0.1 and Polaris has an apparent magnitude of 2.1. What is the ratio of the fluxes from these two stars?

a) 2.0
b) 2.512
c) 5.024
d) 6.31
e) 100

7) Which of the following spectral types corresponds to the hottest Main Sequence stars?

a) O
b) M
c) K
d) G
e) F

8) Which of the following spectral types corresponds to the Main Sequence stars of the lowest mass?

a) O
b) M
c) K
d) G
e) F

9) The temperature of an object is a measure of

a) its total energy content.
b) the average amount of energy per gram.
c) the average amount of energy per particle.
d) the total energy contained in the motions of all of the particles.

10) A star with a surface temperature of 6000 K will emit a blackbody spectrum which peaks at what wavelength?

a) 6000 m
b) 5 x 10^-7 nm
c) 18 nm
d) 5 x 10^-7 m
e) 1.8 x 10^-7 nm

11) In the above sketch, the Bohr model of an atom is represented with a black nucleus and three acceptable electron orbits. If an electron in this atom were initially in state 2 and moved to state 1, this would result in

a) the emission of a light photon whose energy is equal to the energy of state 1.
b) the absorption of a light photon whose energy is equal to the difference in energy between states 1 and 2.
c) the emission of a light photon whose energy is equal to the difference in energy between states 1 and 2.
d) the emission of a light photon whose energy is equal to the energy of state 2.
e) the absorption of a light photon whose energy is equal to the energy of state 2.

12) Still referring to the above sketch, which electronic transition would produce the shortest wavelength photon?

a) the transition from state 2 to state 1
b) the transition from state 3 to state 1
c) the transition from state 3 to state 2
d) the transition from state 1 to state 3
e) the ionization of the electron from state 1

The following six questions refer to the Hertzsprung-Russell Diagram below:

13) Please indicate, by marking an "X" in the above diagram, the position of the Sun.

14) Please write down the letter indicating the position of a star on the Main Sequence (there are several correct answers; pick one) D, C, E

15) Please write down the letter indicating the position of White Dwarfs in this diagram A

16) Please write down the letter corresponding to the stars with the largest radii in this diagram B

17) Please write down the letter corresponding to the stars which would appear the most red if you were to look at them in the night sky B,E

18) Of all of the lettered choices, find the most luminous star. What is its surface temperature? 30000 K

Problems:

(Show your work!! I will be very generous with partial credit!!!)

Problem 1) A giant star of spectral type M0 has a luminosity 300 times larger than a typical Main Sequence M0 star. A Main Sequence M0 star has a radius of 1.0 x 10⁸ m.

Part 1) What is the ratio of the intensities of the two stars?

(5 points)

Solution

Part 2) What is the radius of the M0 giant?

(15 points)

Solution

Problem 2) Sirius is a Main Sequence star with a surface temperature of 8000 K and a luminosity of 8.61 x 10²⁷ W. It has a parallax of 1.053 x 10^-4 degrees.

Part 1) Calculate its distance.

(10 points)

Solution

Part 2) Calculate the flux (in W/m²) from this star, when viewed from the Earth.

(10 points)

Solution

Problem 3) Stars alpha gamma globulin and beta gamma globulin are members of an eclipsing spectroscopic binary system. Both stars have the same mass and orbit their common center of mass with velocity 3.0 x 10⁵ m/s. An optical spectrum of the light from the binary system shows the following "w" shaped absorption line:

Part 1) Both absorption lines have been identified as due to the transition from the N=2 to N=3 energy levels of the hydrogen atom. The difference in energy between these two levels is 3.03 x 10^-19 Joules. Calculate the rest frequency of the photons absorbed by this process.

(10 points)

Solution

Part 2) Calculate the maximum frequency separation between the two absorption lines in the above spectrum due to the motions of the stars .

(10 points)

Solution