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Finding mean energy of cosmic microwave background photons

  1. Sep 8, 2008 #1
    Hello all,

    I was recently assigned a problem in my modern physics class regarding finding the mean energy of Cosmic Microwave Background (CMB) photons. The problem reads as follows:

    The universe is permeated with primordial microwave radiation that has a mean wavelength of about 2.5 mm.

    (a) Find the mean energy (in eV) of the CMB photons, given that the energy of a photon is related to its frequency by the relationship E = hf (where f=frequency), where h is Planck's constant.

    (b) Consider a cosmic-ray proton that has total relativistic energy E in the CMB reference frame. Find E such that the Doppler shifted CMB photons striking the proton head-on have a mean energy of 100 MeV.

    I believe I have solved (a), with the solution as follows:
    E = hf = h(c/wavelength)
    E(mean) = h(c/mean wavelength)
    = (4.136x10^-15 eV*s)[(3.0x10^8 m/s)/2.5x10^-3 m]
    = 4.963 x 10^-4 eV

    The second part, (b), I have no idea how to find. Any help would be much appreciated!
  2. jcsd
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