Physics 401 Homework1---Due September 9


  1. In class it was stated that the spectral density for black-body radiation was given by Planck’s formula:   


a)      We argued in class that for low frequencies ( 1 <<kT/(hn)  )  this should reduce to the classical statistical mechanical result of Rayleigh and Jeans----


Show that it does.


b)      Well before  the discovery of the Planck formula data for black-body radiation was restricted to relatively high frequencies

( 1 >> kT(hn)  ) and was found to empirically be fit by Wien’s law



where a and b are parameters. Starting with the Planck law, find the parameters a and b in terms of fundamental constants.


  1. The universe as a whole is at a temperature of 2.7° as a result of the big bang cooling.  Use the Planck radiation formula to determine the frequency and wavelength at which the spectrum has maximum energy.