Introduction to Astrophysics I, 29:119
Fall, 2006
Ninth Homework Set...December 1, 2006.
Due December 7, 2006
`` A homework set that will live in infamy ...''

Show calculations and give reasons for your answers. Don't go around confused and despondent; if you do not know how to get started, ask me for help. All problem numbers refer to the first edition of the book.

(1) Verify the statement made in class that the main sequence lifetime of the Sun would be about 200 years, if it operated with a chemical reaction fuel cycle, which has an energy yield of $\simeq 10^{10}$ ergs/gm.

(2) What is the potential energy released if the Sun contracted from its present size to that of a white dwarf star? Approximate the stars in both cases by uniform spheres.

(3) The ``Triple Alpha Process'' is a nuclear reaction sequence by which $^4He$ fuses to form $^{12}C$ (see eq 10.55). Calculate the energy yield in ergs/gram obtainable from this fusion reaction.

(4) Problem 10.1 from textbook

(5) Problem 10.4 from textbook

(6) Problem 10.6 from textbook

(7) Use the chemical abundances of the Sun in Table 9.2. Demonstrate the truth of the statement in the textbook (p326) that

$$\left< \frac{1+z}{A}\right>_i \simeq \frac{1}{2}$$ (1)

(8) Given the result from problem # 7 and the data in Table 9.2, calculate the mean molecular weight for fully-ionized solar material.