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

In summary, Wikipedia explains that the Cosmic Microwave Background Radiation (CMBR) has a thermal black body spectrum at a temperature of 2.725 K. The peak frequency is at 160.2 GHz in the microwave range, with a corresponding wavelength of 1.873 mm when measured per unit frequency using Planck's law. However, when measured per unit wavelength using Wien's law, the peak is at 283 GHz with a wavelength of 1.06 mm. This difference in peak frequencies is due to the need to transform the differential element between the two laws rather than simply substituting in the corresponding expression from the dispersion relation.
  • #1
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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?
 
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  • #2
In short, the difference is because you have to transform the differential element [itex]d\lambda[/itex] to [itex] d \nu [/itex] (or vice-versa) rather than just substituting in the corresponding expression from the dispersion relation.
 

1. What is the CMB peak frequency and how is it calculated?

The CMB (Cosmic Microwave Background) peak frequency is the frequency of the electromagnetic radiation that corresponds to the peak of the blackbody radiation curve of the CMB. It is calculated using Planck's law, which describes the distribution of energy emitted by a blackbody at a given temperature. This law takes into account the temperature of the CMB and the speed of light to determine the peak frequency.

2. What is the difference between Planck's law and Wein's law?

Both Planck's law and Wein's law describe the distribution of energy emitted by a blackbody at a given temperature, but they use different approaches. Planck's law takes into account the entire spectrum of electromagnetic radiation, while Wein's law only considers the peak of the spectrum. Planck's law also takes into account the speed of light, while Wein's law does not.

3. How do the CMB peak frequencies predicted by Planck's law and Wein's law differ?

Planck's law predicts a slightly higher CMB peak frequency compared to Wein's law. This is because Planck's law takes into account the speed of light, which results in a slight shift in the peak frequency towards higher values.

4. Which law is more accurate in predicting the CMB peak frequency?

Planck's law is considered to be more accurate in predicting the CMB peak frequency. This is because it takes into account more factors, such as the speed of light, and has been validated through observations and experiments.

5. How does the CMB peak frequency affect our understanding of the early universe?

The CMB peak frequency provides valuable information about the temperature of the universe during the period of recombination, when the first atoms were formed. This temperature is a crucial factor in understanding the evolution and expansion of the universe, and can also shed light on the nature of dark matter and dark energy. Additionally, the CMB peak frequency can help validate current theories and models about the early universe.

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