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 find the peak wavelength in the direction where the CMBR (Cosmic Microwave Background Radiation) appears at a temperature of 2.72K, we can use Wien's Displacement Law. This law states that the wavelength at which the peak intensity of radiation occurs is inversely proportional to the temperature. The formula for Wien's Displacement Law is:
λ = (c / T)
Where:
λ is the peak wavelength
c is the speed of light (approximately 3 x 10^8 m/s)
T is the temperature (in Kelvin)
Plugging in the given temperature of 2.72K into the formula, we can calculate the peak wavelength:
λ = (3 x 10^8 m/s) / 2.72K
Calculating this value gives us the peak wavelength in meters.
To determine whether we are moving toward or away from the region of space, we need to consider the concept of redshift or blue shift. If the observed radiation has a longer wavelength (redshifted), it suggests that we are moving away from the region of space. Conversely, if the observed radiation has a shorter wavelength (blueshifted), it indicates that we are moving towards the region of space.
The CMBR is a result of the Big Bang, and it is observed to be very uniform in all directions. This means that on average, the CMBR should not be significantly redshifted or blueshifted. Therefore, our velocity with respect to the CMBR should be negligible, indicating that we are not moving significantly towards or away from the observed region of space.