Question

The Cosmic Background Radiation Outer space is filled with a sea of photons, created in the early moments of the universe. The frequency distribution of this "cosmic background radiation" matches that of a blackbody at a temperature near 2.7K.What is the peak frequency of this radiation in Hz?What is the wavelength that corresponds to the peak frequency in mm?

Answer 1

A) Peak wavelength: 1.07 mm

The peak wavelength of the Cosmic Background Radiation can be found by using Wien's displacement law:

$\lambda = \frac{b}{T}$

where

$\lambda$ is the peak wavelength

$b=2.898\cdot 10^{-3}m\cdot K$ is Wien's displacement constant

T is the absolute temperature

For the Cosmic Background Radiation,

T = 2.7 K

So the peak wavelength is

$\lambda = \frac{2.898\cdot 10^{-3}m\cdot K}{2.7 K}=1.07\cdot 10^{-3} m=1.07 mm$

B) Peak frequency: $2.8\cdot 10^{11}Hz$

The peak frequency can be found by using the relationship:

$f=\frac{c}{\lambda}$

where

$c=3.0\cdot 10^8 m/s$ is the speed of light

$\lambda$ is the peak wavelength

Substituting numbers, we find

$f=\frac{3.0\cdot 10^8 m/s}{1.07\cdot 10^{-3} m}=2.8\cdot 10^{11}Hz$