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?
To determine the peak wavelength of the Cosmic Microwave Background Radiation (CMBR) in the given direction, we can use Wien's displacement law. This law states that the peak wavelength (λ) of radiation emitted by an object is inversely proportional to its temperature (T). The formula is written as:
λ = (constant) / T
In this case, we know that the temperature of the CMBR is 2.72K. The constant in the equation is known as Wien's displacement constant, equal to approximately 2.898 x 10^(-3) meters kelvin (m*K).
By substituting these values into the formula, we can calculate the peak wavelength:
λ = (2.898 x 10^(-3) m*K) / 2.72K
Calculating this expression gives us the peak wavelength in the given direction.
To determine whether we are moving toward or away from the region of space, we need to consider the concept of cosmological redshift. The expansion of the universe causes light to be redshifted as it travels through space. If the universe is expanding, the galaxies and regions of space are moving away from us, and their light is shifted towards longer (redder) wavelengths.
If the CMBR appears to have a temperature of 2.72K, which is the expected temperature of the CMBR throughout the universe, it means we are at rest relative to the CMBR. This is because if we were moving away from the CMBR, we would observe it at a lower temperature (cooler) due to the cosmological redshift. Similarly, if we were moving towards the CMBR, we would observe it at a higher temperature (warmer).
Therefore, in this specific scenario, we are considered to be at rest relative to the CMBR.
As for our velocity with respect to the CMBR, since we are considered to be at rest relative to it, our velocity will be zero.