A) Peak wavelength: 1.07 mm
The peak wavelength of the Cosmic Background Radiation can be found by using Wien's displacement law:
[tex]\lambda = \frac{b}{T}[/tex]
where
[tex]\lambda[/tex] is the peak wavelength
[tex]b=2.898\cdot 10^{-3}m\cdot K[/tex] is Wien's displacement constant
T is the absolute temperature
For the Cosmic Background Radiation,
T = 2.7 K
So the peak wavelength is
[tex]\lambda = \frac{2.898\cdot 10^{-3}m\cdot K}{2.7 K}=1.07\cdot 10^{-3} m=1.07 mm[/tex]
B) Peak frequency: [tex]2.8\cdot 10^{11}Hz[/tex]
The peak frequency can be found by using the relationship:
[tex]f=\frac{c}{\lambda}[/tex]
where
[tex]c=3.0\cdot 10^8 m/s[/tex] is the speed of light
[tex]\lambda[/tex] is the peak wavelength
Substituting numbers, we find
[tex]f=\frac{3.0\cdot 10^8 m/s}{1.07\cdot 10^{-3} m}=2.8\cdot 10^{11}Hz[/tex]
