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I Qs re average and peak wavelength of Planck distribution

  1. Jan 29, 2017 #1
    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
     

    Attached Files:

  2. jcsd
  3. Feb 3, 2017 #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
    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
     

    Attached Files:

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