Cosmic microwave background radiation

AI Thread Summary
The cosmic microwave background radiation (CMBR) has a blackbody spectrum with a peak wavelength of 1.06 mm and a frequency of approximately 2.83E11 Hz, confirming it falls within the microwave range. A discussion arose regarding the discrepancy between the calculated wavelength and a provided intensity-frequency curve. It was clarified that the difference arises from the mathematical distinction between wavelength and frequency dependence, leading to different peak positions on the curves. This is not an error but rather a surprising result of how intensity is represented in relation to wavelength versus frequency. Understanding this relationship is crucial for interpreting the CMBR data accurately.
Fabio010
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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:
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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".
 
mfb said:
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?
 
The intensity maximum of the wavelength is different from intensity maximum of the frequency - even if the curves correspond to the same spectrum.
 
Understood!

Thanks a lot for the help!
 
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