If a CMB photon traveled for 13.7 billion years (- 374,000 years) to reach me. How far away was the source of that CMB photon when it first emitted it?
My attempt to solve this question was to use the following assumptions:
Temperature of CMB photon today is 2.725 K (will use value of 3 K here)
Temperature of CMB photon when it was first emitted is 3000 K
A factor of x1000 in temperature decrease results in a factor of x1000 in wavelength increase. (According to Wien's displacement law)
Does this mean that the source of the CMB photon that just reached me today, was actually 13.7 billion light years / 1000 = 13.7 million light years away from me when it first emitted the photon?