Cosmic microwave background radiation

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SUMMARY

The cosmic microwave background radiation (CMBR) exhibits a blackbody spectrum with a peak wavelength of 1.06 mm and a corresponding frequency of 2.83E11 Hz, calculated using Wien's Law at a temperature of 2.725 K. This frequency falls within the microwave range. A discussion arose regarding the discrepancy between the obtained wavelength and the intensity peaks shown in a frequency-dependent curve, highlighting that switching between wavelength and frequency dependence results in different peak positions. This mathematical phenomenon is crucial for understanding the relationship between frequency and wavelength in blackbody radiation.

PREREQUISITES
  • Understanding of Wien's Law for blackbody radiation
  • Familiarity with the concepts of wavelength and frequency
  • Basic knowledge of thermal radiation and its spectrum
  • Ability to interpret graphical data related to intensity and frequency
NEXT STEPS
  • Study the implications of Wien's Law in astrophysics
  • Explore the mathematical relationship between frequency and wavelength in blackbody radiation
  • Investigate the properties of cosmic microwave background radiation
  • Learn about the significance of intensity curves in thermal radiation analysis
USEFUL FOR

Astronomers, physicists, and students studying cosmology or thermal radiation, particularly those interested in the properties and implications of cosmic microwave background radiation.

Fabio010
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Homework Statement



The cosmic microwave background radiation has a blackbody type spectrum. Determine its max frequency and the correspondent wavelength. 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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