Suppose when we look in one half of the sky, the CMBR appears to be at a temperature of 2.72K. What is the peak wavelength in that direction? Are we moving toward or away from the region of space? What is our velocity with respect to the CMBR?
Physics - bobpursley, Tuesday, April 24, 2012 at 11:16am
Since decoupling, the temperature of the background radiation has dropped by a factor of roughly 1,100 due to the expansion of the universe. As the universe expands, the CMB photons are redshifted, making the radiation's temperature inversely proportional to a parameter called the universe's scale length. The temperature Tr of the CMB as a function of redshift, z, can be shown to be proportional to the temperature of the CMB as observed in the present day (2.725 K or 0.235 meV):
Tr = 2.725(1 + z)
So answer the last question first, your temperature is not precise enough to determine, you only have three significant digits.
Peak wavelength:<<The CMBR has a thermal black body spectrum at a temperature of 2.725 K, which peaks at the microwave range frequency of 160.2 GHz, corresponding to a 1.873 mm wavelength. This holds if measured per unit frequency, as in Planck's law. If measured instead per unit wavelength, using Wien's law, the peak is at 1.06 mm corresponding to a frequency of 283 GHz.>>