1) One of the reasons limb darkening occurs in the photosphere of the Sun is because of the relationship between color, intensity and temperature in continuous radiation.

a) (7 pts) Explain why the peak wavelength of emission in continuous radiation is inversely proportional to the object's temperature. In other words, why do the spectra of hotter objects tend to have their peak intensity occur at shorter wavelengths?

b) (7 pts) Suppose the solar photosphere were at a constant temperature throughout, from top to bottom, instead of the current temperature distribution. Would we still see the limb darkening effect? Explain your answer.

2) Astronomers know that in order to find the abundance of a certain element in a cloud of gas, one must determine the absorption or emission line strength of that element's "spectral fingerprint" in the spectrum of light from the cloud. However, line strength does not depend only on the abundance but also on temperature.

a) (7 pts) Explain why, for Hydrogen atoms, the line strength is very weak at low temperatures even though there might be a very large abundance of Hydrogen present.

b) (7 pts) Explain why the line stregth for Hydrogen atoms is very weak at extremely high temperatrues even though there might be a very large abundance of Hydrogen present.

3) At high temperatures, we see two major changes in the spectrum of light coming from a cloud of gas. One example is with Helium. At moderature temperatures, Oxygen I (neutral Oxygen) lines can be seen. At much higher temperatures, we see the spectral fingerprint of Oxygen II (but no longer do we see Oxygen I lines). At still higher temperatures, we see Oxygen III, but no Oxygen II or Oxygen I lines.

a) (7 pts) Explain why, as temperatures in a gas rise, the level of ionization of a typical atom tends to rise.

b) (7 pts) Another change that occurs is that the spectral line width of these lines gets broader. Explain why temperature and line width are related in this way.

4) Below is an energy level diagram for an atom of element X:

E = 2 ________________

E = 7 ______________

E = 3 ________________

E = 9 ______________

E = 5 ________________

E = 10 ______________

5) Irrefutable beliefs can be very compelling. The fact that these beliefs can't be disproven can be comforting, providing us with a basis of unchanging truths about the way the world works. However, this isn't the whole story.

a) (7 pts) Explain the major weakness of irrefutable beliefs when used as a basis for a system of knowledge.

b) (7 pts) One might argue that because our theory for how nuclear fusion in the Sun generates energy is still believed (despite evidence to the contrary) that this theory somehow qualifies as an irrefutable belief. Explain why scientists still consider nuclear fusion to be the correct explanation despite its flaws.

6) Our understanding of energy generation in the Sun via nuclear fusion has led to the development of an entire industry based on research into nuclear power, both fission and fusion, but it has also led to some difficult questions.

a) (8 pts) In order for nuclear fusion to occur, the temperature and density of the gas must be extremely high. Explain why each of these two properties of the gas must be so high.

b) (6 pts) If nuclear fusion is indeed the energy source at work in the core of the Sun, then a certain number of neutrinos should be detected here on Earth, and we only detect about a third of the predicted number. Briefly explain one possible theory as to why we might be detecting fewer neutrinos while still remaining consistent with nuclear fusion theory.

7) Explain how energy is transported in the Sun's envelope, starting with the energy leaving the core and entering the lower part of the envelope. How does energy travel in each part of the envelope? How does the energy leave the Sun? For each of the three forms of energy transport, explain in 1-2 sentences why energy moves in that fashion rather than some other way.

8) The most advanced telescopes these days having large reflecting mirrors to focus the light on the detector, and some even use fancy technology to correct for the effects of the Earth's atmosphere.

a) (7 pts) Explain why reflecting telescopes are more popular with professional astronomers than refracting telescopes.

b) (7 pts) Explain how Adaptive Optics works to help us see stellar images more clearly through the blurring effects of the Earth's atmosphere.