Cosmic microwave background radiation

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Homework Statement



The cosmic microwave background radiation has a blackbody type spectrum. Determine its max frequency and the correspondent wavelenght. Verify if found frequency is a microwave frequency and compare with the following curve:


Untitled(2).jpg




Homework Equations



Using the Wien Law displacemente, and knowing that CMBR has a thermal black body spectrum at a temperature of 2.725 K. We can easily calculate the wavelength peak and its frequency.

λmax = 1,06mm

frequency = λmax/c = 2,83E11HZ


We can verify that the frequency that we obtained corresponds to the microwave frequency.

But when i am comparing with this curve
Untitled(2).jpg
, i did not find any relation...

I just do not know what is the relation of the graphic with the obtained results.

Anybody to help? Help is always appreciated.!!!
 
Last edited:

Answers and Replies

  • #2
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That is a tricky problem.

The curve shows the frequency-dependence of the intensity (waves/cm is proportional to frequency) - you can calculate the wavelength which corresponds to its peak, and it will not agree with your wavelength.

This is not an error on your side, it is a surprising mathematical result: If you switch between wavelength and frequency dependence, you get different positions of the peaks, as "per wavelength" on the y-axis is different from "per frequency".
 
  • #3
83
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That is a tricky problem.

The curve shows the frequency-dependence of the intensity (waves/cm is proportional to frequency) - you can calculate the wavelength which corresponds to its peak, and it will not agree with your wavelength.

This is not an error on your side, it is a surprising mathematical result: If you switch between wavelength and frequency dependence, you get different positions of the peaks, as "per wavelength" on the y-axis is different from "per frequency".

So, the difference is the switching from wavelength to frequency dependence. The results are "mathematically" equal?
 
  • #4
35,441
11,872
The intensity maximum of the wavelength is different from intensity maximum of the frequency - even if the curves correspond to the same spectrum.
 
  • #5
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Understood!

Thanks a lot for the help!
 

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