Suppose when we look in one half of the sky, the CMBR appears to be at a temperature of 2.725K. What is the peak wavelength in that direction? Are we moving toward or away from the region of space?
To determine the peak wavelength of the CMBR in that direction, we can make use of Wien's displacement law, which states that the peak wavelength of blackbody radiation is inversely proportional to its temperature. The formula is given by:
λpeak = b / T
Where λpeak is the peak wavelength, b is Wien's constant (approximately 2.898 x 10^-3 m·K), and T is the temperature in Kelvin.
Plugging in the given temperature of 2.725K, we can calculate the peak wavelength:
λpeak = (2.898 x 10^-3 m·K) / (2.725K)
λpeak ≈ 1.06 x 10^-3 meters
Therefore, in that direction, the peak wavelength of the CMBR is approximately 1.06 x 10^-3 meters.
To determine if we are moving toward or away from the region of space, from the information provided, we cannot make a definitive conclusion. The CMBR is considered to be isotropic, meaning that it appears relatively the same in all directions. To determine our motion with respect to the region of space, additional information about our relative velocity would be required.