**Physics
401 Homework1---Due September 9**

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

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

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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**(h**n) * ) and
was found to empirically be fit by Wien’s law

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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.