First Hour Exam |
1998 February 27 |
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?
Answer: c) 4 m
The key here is to realize that the rate at which the waves lap up against the far shore is the frequency. With the frequency and the wave speed, you can calculate the wavelength: wavelength = speed/frequency.
2) The chromospheric "flash" spectrum seen just before a total solar eclipse is an example of
Answer: c) spectral line emission.
The "flash" spectrum comes from the chromosphere on the limb of the Sun just before it is covered up by the moon in a solar eclipse. This is the only time you can actually see the chromosphere is emission, since when there isn't a solar eclipse, light from the photosphere is so much brighter. The chromosphere is less dense than the photosphere, and absorbs and emits in spectral lines. Since the flash spectrum is measured at the limb of the Sun, there's no continuous source of emission behind that part of the chromosphere, and the result is spectral line emission.
3) The astronomer who correctly deduced that stars are composed mainly of hydrogen was
Answer: b) Cecilia Payne.
Payne realized that the variation in spectral lines from star to star could be explained by temperature variations rather than composition variations. Her analysis of how stellar spectra change with temperature showed that all stars were composed primarily of hydrogen.
4) The most convincing piece of evidence indicating that stars are really as luminous as the Sun is
Answer: c) stars have very small parallaxes.
In order for those wimpy faint little dots in the sky to be bodies as luminous as the Sun, they have to be really far away. The only choice which indicates that stars are far away is c).
5) Photons with energies slightly lower than the energies of visible light photons are
Answer: a) infrared photons.
Look at the electromagnetic spectrum in your book. Lower energy means longer wavelength or lower frequency.
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?
Answer: d) 6.31
Two stars whose apparent magnitudes differ by 1 have fluxes which differ by as factor of 2.512. If they differ by 2 magnitudes, their fluxes must differ by a factor of 2.512 x 2.512, or 6.31. The first factor of 2.512 gets you down one magnitude, and the second factor of 2.512 gets you down the next magnitude.
7) Which of the following spectral types corresponds to the hottest Main Sequence stars?
Answer: a) O
The order of spectral types goes "OBAFGKM" from hottest surface temperatures to coolest.
8) Which of the following spectral types corresponds to the Main Sequence stars of the lowest mass?
Answer: b) M
We know from the H-R diagram that the lowest temperature Main Sequence stars have the lowest luminosity. We also learned from the mass-luminosity relationship that the lowest luminosity Main Sequence stars have the lowest masses. Therefore the coolest Main Sequence stars must have the lowest masses. OBAFGKM -- M stars are the coolest.
9) The temperature of an object is a measure of
Answer: c) the average amount of energy per particle.
This is mostly a definition of the term, but it should be clear that temperature cannot be a measure of the total energy content of an object. Consider two objects -- a paper clip and an I-beam -- heated to the same high temperature. While both have the same temperature, the I-beam has a lot more heat energy. If you don't believe this, drop the hot paper clip in one hand, and the hot I-beam in the other, and let me know which one chars more of your hand.
10) A star with a surface temperature of 6000 K will emit a blackbody spectrum which peaks at what wavelength?
Answer: d) 5 x 10-7 m
This is a straightforward application of Wien's displacement law, which is on the front cover of the exam. The only extra tricky part is to choose the answer with the correct units. You're asked for a wavelength, so you had better pick an answer which has units of length. Then, to narrow it down between nm and m, note that the constant in the Wien displacement law has units of m K, so your answer will have units of m.
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
Answer: c) the emission of a light photon whose energy is equal to the difference in energy between states 1 and 2.
The transition is "downward;" that is, to a lower energy state, since the electron is moving closer to the atom. Therefore, a photon will be emitted, not absorbed. The energy of the emitted photon must be equal to the change in the energy state of the atom; after all, the photon is the "extra" energy the atom no longer needs. So, the photon has energy equal to the difference between the initial and final energy states.
12) Still referring to the above sketch, which electronic transition would produce the shortest wavelength photon?
Answer: b) the transition from state 3 to state 1
In order to produce, rather than absorb, a photon, the atom must make a transition from a high energy state to a lower one. The highest available one is state 3, and the lowest is state 1, so a transition between these two states will free up the most energy.
13) Please indicate, by marking an "X" in the above diagram, the position of the Sun.
The Sun is a Main Sequence star with a surface temperature of about 6000 K, and remarkably enough, a luminosity equal to 1 Lo.
14) Please write down the letter indicating the position of a star on the Main Sequence (there are several correct answers; pick one)
Answer: D, C, or E
The diagonal line running from lower right to upper left defines the Main Sequence, so any choice along this line is acceptable.
15) Please write down the letter indicating the position of White Dwarfs in this diagram
Answer: A
White dwarfs are objects of high temperature and low luminosity. Therefore, they must be on the left (hot) and bottom (low luminosity) part of the H-R diagram.
16) Please write down the letter corresponding to the stars with the largest radii in this diagram.
Answer: B Cool stars with high luminosity must be very big; otherwise they would not be luminous, since cool objects don't generate a lot of intensity. Therefore, the objects with the largest radii must be in the right (cool) and upper (luminous) part of the H-R diagram.
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.
Answer: B or E
Red objects are cooler than blue objects, and cool stars are red. Therefore, the stars on the right (cool) side of the H-R diagram will look red.
18) Of all of the lettered choices, find the most luminous star. What is its surface temperature?
Answer: 30000 K Since the luminosity axis is the vertical axis, the most luminous star is the highest one, which is D. You can read its temperature off of the horizontal axis.