If the cosmic microwave background radiation (CMBR) is at a temperature of 2.7K, what is its peak wavelength?
To determine the peak wavelength of the cosmic microwave background radiation (CMBR) given its temperature, you can use Wien's displacement law. According to this law, the peak wavelength (λ_max) is inversely proportional to the temperature (T) of the radiation.
Wien's displacement law can be expressed as:
λ_max = b / T
Where:
λ_max is the peak wavelength
T is the temperature in Kelvin
b is Wien's displacement constant, which is approximately equal to 2.898 × 10^(-3) meter-kelvin
In this case, the temperature of the CMBR is given as 2.7 Kelvin.
Substituting the values into the formula, we have:
λ_max = (2.898 × 10^(-3) m·K) / 2.7 K
Calculating this equation, we find:
λ_max ≈ 1.072 × 10^(-3) meters
Therefore, the peak wavelength of the cosmic microwave background radiation (CMBR) is approximately 1.072 millimeters (mm).