If the cosmic microwave background radiation (CMBR) is at a temperature of 2.7K, what is its peak wavelength?
Wien's displacement law
b =2.9•10^-3
λ= b/T= 2.9•10^-3/2.7 =1.07•10^-3 m
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?
Thank you for all your help!! Could you please help me with this question?
To calculate the peak wavelength of the cosmic microwave background radiation (CMBR), we can use Wien's displacement law. This law states that the wavelength at which an object emits the most radiation is inversely proportional to its temperature.
The formula for Wien's displacement law is:
λmax = (b / T),
where λmax is the peak wavelength, b is Wien's constant (approximately equal to 2.898 x 10^(-3) meters per Kelvin), and T is the temperature in Kelvin.
In this case, the temperature of the CMBR is 2.7 Kelvin. Plugging this value into the formula, we can calculate the peak wavelength:
λmax = (2.898 x 10^(-3) meters per Kelvin) / (2.7 Kelvin)
≈ 1.073 x 10^(-3) meters
≈ 1.073 millimeters.
Therefore, the peak wavelength of the cosmic microwave background radiation is approximately 1.073 millimeters.