Qs re average and peak wavelength of Planck distribution

In summary, the conversation is discussing a thread that was prompted by a closed thread that did not answer the original question about the ratio of wavelengths in the Planck's Law distribution. The OP is asking for confirmation and a reference for this ratio, as well as the value of 1.84 that was given by the previous thread. They also mention the Wien wavelength displacement law constant and provide its value. After five days, the OP was able to derive the answers for themselves and confirmed that the ratio is 1.84 and the value they calculated is 0.73624. They offer to share their analysis with anyone interested.
  • #1
Buzz Bloom
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This thread is prompted by a closed thread which left it’s OP’s original question unanswered.
->https://www.physicsforums.com/threads/average-wavelength-for-blackbody-radiation.423536/
The original question asked:
is the ratio, of (a) the wavelength corresponding to the average energy in the Planck’s Law distribution
PlancksLaw-lambda.png

to (b) the wave length corresponding to the peak (maximum value) of this distribution, independent of temperature?​

I am guessing that the answer to this question is YES, but I am hopeful someone can cite a reference that confirms this. Also, the OP gave 1.84 as the value of this ratio for some unspecified temperature, but did not provide any references, so I would also like see a reference that will validate that this value is correct. If someone who can’t provide a citation knows with confidence that YES is correct or not, and/or that the ratio 1.84 is correct or not, I would much appreciate your letting me know this.

The OP also gave the value 0.29 for the product of peak wavelength and temperature, but gave no units. I found that this product is called the
Wien wavelength displacement law constant,​
and it is represented by “b” and has the value
-b = 2.8977729(17) x 10^-3 m K.
http://physics.nist.gov/cgi-bin/cuu/Value?bwien​
 

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  • #2
Although I have been hoping someone would save me the effort of calculating my own answers to the questions in the previous post, I was finally, after five days, able to derive the answers for myself.

I have confirmed that the answer to the first question
Buzz Bloom said:
is the ratio, of (a) the wavelength corresponding to the average energy in the Planck’s Law distribution
planckslaw-lambda-png.112253.png

to (b) the wave length corresponding to the peak (maximum value) of this distribution, independent of temperature?
is YES.

The second question was to confirm (or not) that the value of this ratio is 1.84. The value I calculated is 0.73624.

I will post my analysis leading to either of both of these answers if anyone would like to see it.

Regards,
Buzz
 

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FAQ: Qs re average and peak wavelength of Planck distribution

1. What is the Planck distribution?

The Planck distribution, also known as the Planck black body radiation curve, is a mathematical function that describes the emission of electromagnetic radiation by a black body at a given temperature. It is named after German physicist Max Planck who first proposed the theory in 1900.

2. What is the average wavelength in the Planck distribution?

The average wavelength in the Planck distribution is known as the Wien displacement law and is given by the expression λ_avg = 4.965 x 10^-3 / T, where T is the temperature of the black body in Kelvin. This means that as the temperature increases, the average wavelength decreases, and vice versa.

3. What is the peak wavelength in the Planck distribution?

The peak wavelength, also known as the peak of the black body radiation curve, is the wavelength at which the intensity of electromagnetic radiation emitted by a black body is at its maximum. It is given by the expression λ_max = 2.898 x 10^-3 / T, where T is the temperature of the black body in Kelvin.

4. How does the peak wavelength change with temperature in the Planck distribution?

According to Wien's displacement law, as the temperature of the black body increases, the peak wavelength decreases. This means that as the temperature increases, the emitted radiation shifts towards shorter wavelengths, such as from red to blue in the visible spectrum.

5. Why is the Planck distribution important in physics?

The Planck distribution is important in physics because it describes the fundamental relationship between the temperature of a black body and the intensity of radiation it emits. This concept is used in various fields of physics, such as astrophysics, thermodynamics, and quantum mechanics, to understand and analyze the behavior of electromagnetic radiation in different systems.

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