Introduction to Astrophysics I, 29:119
Fall, 2008
Fourth Homework Set...October 2, 2008.
Due October 9, 2008

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) Positronium is an atom consisting of an electron and a positron in bound states (like hydrogen, but with the positron taking the place of the proton). What is the wavelength of the $n=3 \rightarrow n=2$ transition?

(2) Use equations and numbers to explain why the Compton effect is more pronounced at x-ray than optical wavelengths.

(3) Consider the $n=2$ state of a hydrogen atom. If a magnetic field is applied to a hydrogen atom, the energy of the state is changed by

$$\Delta E = \mu_B m B$$ (1)

where $\mu_B$ is a set of fundamental constants (the ``Bohr magneton''), $B$ is the strength of the magnetic field, and $m$ is the quantum number corresponding to the z component of angular momentum. How many energetically-distinct states occur when the magnetic field is turned on?

(4) A binary star system consists of star A, with a mass of $2 M_{\odot}$ ($1 M_{\odot}$ is one solar mass), and star B with a mass of $1 M_{\odot}$. The centers of the stars are separated by $20 R_{\odot}$ (20 solar radii).
(a) What is the orbital period?
(b) What kind of binary star could it be? Explain your reasons.
(c) Assuming circular orbits, what is the orbital speed of star B?
(d) If we are observing this star in the plane of its orbit, what is the maximum change in wavelength we would observe for the H$\alpha$ line of hydrogen?

(5) Problem 5.15 from textbook

(6) Problem 7.3 from textbook

(7) Problem 7.4(a) from textbook

(8) Problem 7.5 from textbook