Astronomy 110-03:   Final Exam (Sample)
HTML links within solutions for each problem point to related material from the lecture notes.
SHORT QUESTIONS       (13 × 5 = 65 points)
Please keep your answers brief, and to the point. For multiple choice questions, chose and circle one and only one answer.

1. Draw an atom of neutral helium in an excited state below (we have started the sketch for you). Add an arrow showing what happens when the atom emits a photon.

A small central circle (representing a nucleus) encircles four solid red dots, two labeled n and two labeled p+. The small central circle has three large circles surrounding it (representing electron energy levels). A red dot located on the outermost large circle has an arrow pointing down towards the innermost large circle. A second red dot located on the middle large circle is labeled e-.

2. Sort the following in order of increasing energy: infrared, optical, radio, ultraviolet and x-ray radiation.
      [a] ultraviolet, x-ray, radio, infrared, optical
      [b] radio, optical, ultraviolet, infrared, x-ray
      [c] radio, infrared, optical, ultraviolet, x-ray
      [d] infrared, ultraviolet, x-ray, radio, optical

3, Which is faster, the speed of light or the speed of sound?

4. Which is heavier, the nucleus of a hydrogen atom or the nucleus of a helium atom?

5. Is thermonuclear fission the primary source of the Sun's energy? Why, or why not?
Thermonuclear fission is not the primary source of the Sun's energy, because there is not sufficient radioactive material in the Sun to generate the observed amount of energy.

6. Sketch a continuum spectrum, an absorption spectrum, and an emission spectrum.
The three types of spectra are all defined by the amount of light emitted as a function of wavelength. Continuum spectra show emission at all wavelengths, with no breaks, absorption spectra show emission at most wavelengths with a few discrete dips at particular wavelengths where light has been absorbed, and emission spectra show discrete peaks at particular wavelengths where light has been emitted.

7. For each of the three spectrum, name an object that gives off light in this form. See lecture notes linked below.
      [continuum] Stellar core
      [absorption] Stellar atmosphere
      [emission] Hydrogen gas cloud

8. What is the difference between the progenitor (the star from which it forms) of a white dwarf and the progenitor of a neutron star?
The progenitor of a white dwarf is a low mass (less than 8 solar masses) star, and the progenitor of a neutron star is a high mass star.

9. What substance will a white dwarf star be made up of, at the end of its lifetime? Diamonds!

10. What is the true nature of the spiral nebulae, debated by Shapley and Curtis in 1920?
The spiral nebulae, or island universes, are simply other galaxies beyond the Milky Way.

11. What role did Cepheid variable stars play in their arguments?
They used the known relationship between intrinsic luminosity and period of variation for Cepheid variable stars to determine the distance to Cepheids observed in spiral nebulae, to see whether they were located within the Milky Way or beyond it.

12. If we found a nearby black hole and sent a scientific probe into it, could the probe send back information to us on the contents of the central singularity? Why, or why not?
The probe would not be able to transmit information from within the singularity, because the escape velocity within the singularity is greater than the speed of light and so nothing (mass or light) is able to escape its gravitational pull.

13. What are the three primary components of a spiral galaxy?
The three primary components of a spiral galaxy are the disk, the central bulge, and the diffuse outer halo.

THE BLACKBODY AND ENERGY RELATIONS       (5 × 7 = 35 points)
Please draw a box around your final answer for each question. We will give partial credit, so show your work and attempt every question.

1. The surface temperature of Pluto is 50 K. The surface of Pluto is thus
      [a] colder than the surface of Venus.
      [b] the same temperature as the surface of Venus.
      [c] hotter than the surface of Venus.

2. What is the primary reason for this?
Pluto is much further away from the Sun than is Venus, and so the amount of sunlight per unit area is much lower.

3. What is the wavelength, l, at which Pluto radiates the most energy?
The relationship between wavelength, l, and temperature, T, is as follows:

l (centimeters) = 0.3 / T (K).

We begin with the blackbody relation, relating the temperature T of a blackbody (a body in equilibrium) with the peak wavelength l where it will emit most of its energy.

l (centimeters) = 0.3 / T (K)
 = 0.3 / 50
 = 0.006 centimeters

We can express the wavelength in centimeters, Angstroms, microns, meters, or kilometers, or any other unit of length. For practice in units conversion, let's work through a few of these.

There are 108 Angstroms in a centimeter.
l = 0.006 centimeters
 = 6 × 10-3 centimeters × 108 Angstroms / centimeter
 = 6 × 105 Angstroms.
There are 104 microns in a centimeter.
l = 6 × 10-3 centimeters × 104 microns / centimeter
 = 60 microns.
There are 10-2 meters in a centimeter.
l = 6 × 10-3 centimeters × 10-2 meters / centimeter
 = 6 × 10-5 meters.
There are 10-5 kilometers in a centimeter.
l = 6 × 10-3 centimeters × 10-5 kilometers / centimeter
 = 6 × 10-8 kilometers.

4. Recall that we can define the amount of energy in light by either its wavelength, l, or its frequency, v, and that the speed of light is 3 × 105 kilometers per second. What is the frequency at which Pluto radiates the most energy?
The relationship between wavelength, l, and frequency, v, is as follows:

v (Hz) = c (centimeters per second) / l (centimeters).

We begin with the frequency and wavelength relations, relating the amount of radiated energy E in light to either frequency v or wavelength l.

E=h × v
=h × c / l

This gives us a relationship between v and l.

v=c / l
=3 × 105 kilometers per second / 6 × 10-8 kilometers
=5 × 1012 cycles per second
=5 × 1012 Hertz

5. Light of this wavelength and frequency has:
      [a] a shorter wavelength and higher frequency than optical light.
      [b] a shorter wavelength and lower frequency than optical light.
      [c] the same wavelength and frequency as optical light.
      [d] a longer wavelength and higher frequency than optical light.
      [e] a longer wavelength and lower frequency than optical light, as visible light has a wavelength of 5,000 Angstroms and a frequency of 6 × 1014 Hz.

Extra credit: What is the name for this portion of the electromagnetic spectrum?
A frequency of 5 × 1012 Hertz corresponds to the infrared (IR) portion of the spectrum.