Physics 401 Homework1---Due September 9
- 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.
- 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.