# The frequency distribution of cosmic background radiation matches that of a black body at a temperature near 2.7 K. What is the peak frequency of this radiation? What is the wavelength that corresponds to the peak frequency? (in mm)?

May 2, 2018

#### Explanation:

The temperature is $T = 2.7 K$

Apply Wien's displacement law

${\lambda}_{\max} = \frac{2897.77}{T} = \frac{2897.77}{2.7} = 1073.3 \mu m = 1.073 m m$

The peak wavelength is ${\lambda}_{\max} = 1.073 m m$

The peak frequency is

$\nu = \frac{c}{\lambda} _ \left(\max\right) = \frac{3 \times {10}^{8}}{1.073 \times {10}^{-} 3} = 2.8 \cdot {10}^{11} H z$