Frequency and Wavelength peak for Wien's displaement law of a blackbody This is a question relating to Wien's displacement law for the Planck function. As we all know frequency and wavelength are related to the speed of light by: ν λ = cHowever, why is it that: ν p e a k λ p e a k ≠ c Any explanations would be very much appreciated.To all of the people wanting to know where this statement came from. It hasn't come from anywhere specific, is it a well known fact of the Planck function. λ p e a k = 0.290 T − 1 cm K and ν p e a k = 5.88 × 10 10 T Hz K − 1

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Frequency and Wavelength peak for Wien&#039;s displaement law of a blackbody This is a question relating to Wien&#039;s displacement law for the Planck function. As we all know frequency and wavelength are related to the speed of light by:  ν  λ  =  cHowever, why is it that:      ν                  p        e        a        k                  λ                  p        e        a        k              ≠      c  Any explanations would be very much appreciated.To all of the people wanting to know where this statement came from. It hasn&#039;t come from anywhere specific, is it a well known fact of the Planck function.       λ                  p        e        a        k              =  0.290      T          −      1       cm K and       ν                  p        e        a        k              =  5.88  ×            10              10              T Hz K                −      1

Arturo Wallace · Accepted Answer

The maximum of the spectral flux per unit wavelength  I  (  λ  ,  T  )does not correspond by   λ  ν  =  c to the maximum of the spectral flux per unit frequency  I  (  ν  ,  T  )since these two functions are related by  I  (  λ  ,  T  )      d    λ  =  I  (  ν  ,  T  )      d    νbut are not the same function, so their maxima are not the same.

Alisa Durham · Accepted Answer

I believe that the issue is with the difference between evaluating the peak in Planck&#039;s law with respect to frequency vs with respect to wavelength. Since this is pointed out on the Wikipedia page, it seems a bit much to replicate the differentiation of the Planck distribution vs wavelength and frequency here. However, the point is that since wavelength and frequency are inversely related, the derivative of the energy density with respect to one or the other can, and will, result in a different answer.

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