1) Assume an atom has an energy level diagram like the one shown below.

a) (6 pts) List all of the possible energies that can be absorbed by this atom if its electron is in the energy level corresponding to E = 5. List only energies absorbed for electrons beginning in the level E = 5. You may assume the atom is in an environment where ionization is possible. No explanation needed.

b) (8 pts) Atoms that absorb energy are more likely to be ionized when they are in high temperature environments. Name and explain two reasons why this is true.

2) 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) Refutable beliefs can be (and usually are) disproven through scientific observations that serve as tests of the theories' predictions. Why, then, are refutable beliefs thought to be a better basis for knowledge among scientists?

3) Spectral line widths, when analyzed carefully along with other information about stars, can reveal information about the radius (size) of a star.

a) (8 pts) Explain how and why both the temperature and the size of a star affect the width of its spectral lines.

b) (6 pts) Assuming you know the spectral line width for a star (as well as other information), how would you use this to determine the star's size?

4) The "solar neutrino problem" has raised questions about our ideas of how the Sun generates energy.

a) (7 pts) Suppose the core of the Sun were to increase its energy output due to some sort of temporary instability, would we expect the number of neutrinos counted on Earth to increase, decrease or remain the same? Explain.

b) (7 pts) Despite the fact that we count fewer neutrinos than most theorists expected originally, scientists have not abandoned the theory of nuclear fusion as the proper explanation for the Sun's energy source. Instead, the theory has been modified a bit after the fact. Explain why the theory was modified instead of abandoned.

5) According to some theorists, there is an instability in the Sun's core related to one of the atomic nuclei involved in the fusion process, Helium-3.

a) (7 pts) Briefly explain how this instability can lead to a temporary decrease in the energy output of the core.

b) (7 pts) Suppose the core temperature drops temporarily due to this instability. What would happen to the boundary between the radiative and convective zone in the Sun's envelope? Would it remain in place, move outward or move inward? As part of your answer, explain why this boundary exists in the first place.

6) Two stars, A and B, have the same apparent luminosity and the same temperature (which we determine from their color, among other things). Both stars are close enough to Earth so that we can measure their parallax angles, and we find that, using the same baseline for both, star A has a parallax angle twice as large as star B. Which of these two stars probably has a larger size (radius)? Explain your answer. Note well that I am *not* talking about angular size in this problem.

7) Suppose a sun-like star is seen in the sky. This star is extremely far away from the Earth, but we can measure it's apparent luminosity and other properties (such as its absorption lines, peak wavelength, line widths, line strengths, composition, etc). When we measure these other properties, we find that this star is identical to the Sun in all respects.

a) (7 pts) Explain why it is impractical to use the parallax technique to estimate distances to stars that are extremely distant from the Earth.

b) (7 pts) Explain how you could use the inverse square law to estimate the distance to this star with reasonable accuracy.

8) The process that generates energy in the core of the Sun is believed to be nuclear fusion, the combining together of Hydrogen nuclei to form Helium. The mass lost during this process is converted into energy.

a) (8 pts) Explain why nuclear fusion is thought to require both high temperatures (and thus, high nuclear speeds) and high densities in order to occur. It is not sufficient to simply say that high temperature leads to high speed, for example. You need to explain why high speeds are necessary. Similarly, *why* is high density necessary?

b) (6 pts) An alternative form of energy recently in the news here on Earth is "cold fusion", a process that supposedly uses fairly simple lab apparatus to achive fusion of atoms. Name and briefly explain two reasons why the experimental results from cold fusion researchers have not been accepted by the general scientific community.