##
Homework Handout #3

**3.01: What is the luminosity of a star with absolute visual magnitude
M**_{V} = 3.49 and bolometric correction BC = -0.11,
in units of the solar luminosity?
**3.02: Using the information in Table A4-3 of the book, and
assuming the star is Luminosity Class V, what is the approximate spectral
type of the star mentioned in the previous problem? At what wavelength
would its spectrum peak if it were a perfect blackbody?**

**3.03: (a) Derive the Rayleigh-Jeans Law from the expression
for B**_{n} given in the lecture notes,
by using the approximation hn << kT. (The
first-order expansion e^{x} = 1 + x + ... will be useful.)
Notice that Planck's constant is not present in your answer. The
Rayleigh-Jeans Law is a *classical* result, which gives rise to the
*ultraviolet
catastrophe* that we mentioned in lecture. (b) Derive the expression
for the behavior of the Planck function in the Wien Limit, given in the
lecture notes, using the approximation hn >>
kT.

**3.04: Consider a star consisting of a spherical blackbody with a
surface temperature of 28,000 K and a radius of 5.16 x 10**^{9} m.
Let the star be located at a distance of 180 pc from Earth. Determine
the following for the star:

**(a) Luminosity.**

**(b) Absolute bolometric magnitude.**

**(c) Apparent boloemtric magnitude.**

**(d) Distance modulus.**

**(e) Radiant flux at the star's surface.**

**(f) Radiant flux at Earth.**