Question

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 2.7 K.The peak frequency of this radiation is 1.6 x 10^11 Hz.

What is the wavelength that corresponds to the peak frequency?

Answer 1

the wavelength that corresponds to the peak frequency is 1.875x10⁻³m

Step-by-step explanation:

The wavelength that corresponds to the peak frequency is:

`\lambda =(c)/(f)`

where

c = speed of light = 3x10⁸m/s

f = 1.6x10¹¹Hz = peak frequency

So, replacing:

`\lambda =(3x10^(8) )/(1.6x10^(11) ) =1.875x10^(-3) m`

Answer 2

The cosmic background radiation is electromagnetic radiation, principally in the microwave region. The wavelength of an electromagnetic wave is defined as:

`\lambda=(c)/(f)`

Where c is the speed of light in vaccum and f the frequency of the wave. Replacing the known values, we can calculate the wavelength that corresponds to the peak frequency:

`\lambda=(3*10^8(m)/(s))/(1.6*10^(11)Hz)\\\lambda=1.87*10^(-3)m`