CMB Peak Fregenucy (Planck's law vs. Wein's law)

  • Context: Graduate 
  • Thread starter Thread starter redrum419_7
  • Start date Start date
  • Tags Tags
    Cmb Law Peak
Click For Summary
SUMMARY

The discussion centers on the difference in peak frequencies of the Cosmic Microwave Background Radiation (CMBR) when analyzed using Planck's law versus Wien's law. According to Planck's law, the CMBR peaks at a frequency of 160.2 GHz (1.873 mm wavelength) at a temperature of 2.725 K. In contrast, Wien's law indicates a peak frequency of 283 GHz (1.06 mm wavelength). This discrepancy arises from the necessity to transform the differential element dλ to dν, rather than merely substituting values from the dispersion relation.

PREREQUISITES
  • Understanding of Planck's law and its application in black body radiation.
  • Familiarity with Wien's law and its implications for thermal radiation.
  • Basic knowledge of frequency and wavelength conversions in physics.
  • Concept of differential calculus as it applies to physical equations.
NEXT STEPS
  • Study the derivation and applications of Planck's law in thermal radiation.
  • Explore Wien's law and its relevance in astrophysics and cosmology.
  • Learn about the mathematical transformations between frequency and wavelength.
  • Investigate the implications of CMBR measurements on cosmological models.
USEFUL FOR

Astronomers, physicists, and students of cosmology who are interested in understanding the properties of cosmic microwave background radiation and the mathematical principles underlying thermal radiation laws.

redrum419_7
Messages
58
Reaction score
0
wikipedia says:
"The CMBR has a thermal black body spectrum at a temperature of 2.725 K, which peaks at the microwave range frequency of 160.2 GHz, corresponding to a 1.873 mm wavelength. This holds if measured per unit frequency, as in Planck's law. If measured instead per unit wavelength, using Wien's law, the peak is at 1.06 mm corresponding to a frequency of 283 GHz."

How come there is a difference in the peak frequencies, between using Planck's law vs. Wein's law?
 
Space news on Phys.org
In short, the difference is because you have to transform the differential element d\lambda to d \nu (or vice-versa) rather than just substituting in the corresponding expression from the dispersion relation.
 

Similar threads

Undergrad The CMB has a thermal black body spectrum
  • · Replies 18 ·
Replies
18
Views
2K
Graduate Why Do Graphs of the Cosmic Microwave Background Show a Peak at 2mm, Not 1mm?
  • · Replies 8 ·
Replies
8
Views
6K
Undergrad Some questions about Cosmic Microwave Background radiation
  • · Replies 13 ·
Replies
13
Views
7K
Undergrad Physics of colors and our perception
  • · Replies 18 ·
Replies
18
Views
3K
Graduate Why does Planck's Law have different peaks?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Planck's law in wavenumber vs. wavelength
  • · Replies 20 ·
Replies
20
Views
5K
Graduate Current CMB photon number density?
  • · Replies 1 ·
Replies
1
Views
12K
Graduate Untangling the Implications of CMB for the Cosmological Model
  • · Replies 19 ·
Replies
19
Views
5K
Graduate Why is the peak frequency of the Cosmic Microwave Background 160 GHz?
  • · Replies 2 ·
Replies
2
Views
9K
Undergrad Qs re average and peak wavelength of Planck distribution
  • · Replies 1 ·
Replies
1
Views
2K