If the cosmic microwave background radiation (CMBR) is at a temperature of 2.7K, what is its peak wavelength?
To find the peak wavelength of the cosmic microwave background radiation (CMBR), we can use Wien's Law, which states that the peak wavelength of a black body radiation spectrum is inversely proportional to its temperature.
According to Wien's Law, the formula for finding the peak wavelength (λ_max) is:
λ_max = (b / T),
where λ_max is the peak wavelength, b is Wien's constant (approximately 2.898 × 10^(-3) meter-kelvin), and T is the temperature in kelvin.
In this case, the temperature of the CMBR is given as 2.7 Kelvin. Plugging this value into the formula, we get:
λ_max = (2.898 × 10^(-3) m-K) / 2.7 K.
Calculating this expression, the peak wavelength of the CMBR is approximately:
λ_max ≈ 1.073 × 10^(-3) meters.
Therefore, the peak wavelength of the CMBR is approximately 1.073 millimeters.