Issued Wed, Jan 24 Due Wed, Jan 31

Extra Credit problem

a) The energy density function given in problem 4a has a maximum at some frequency . (You saw this graphically in the MMA exercise). Find as a function of temperature.

(You should find that it is proportional to the temperature. What is the proportionality constant?)

b) (You don't need part a to do this one:) Given your answer to problem 4b: What is the numerical value of the energy density (in eV/m^3) in a cavity at 2.7 K? (Note: our universe is a black cavity at 2.7 K right now!) At 2.7 K, the spectrum peaks for photons very roughly around =1 mm (microwaves): if you make the further crude assumption that ALL the photons in the cavity have that same , how many photons are there in each m^3 of outer space?

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