On Wien’s peaks


  • Ernesto Marin Instituto Politécnico Nacional
  • Antonio Calderón Instituto Politécnico Nacional




Thermal radiation, Planck’s Law, Jacobian’s transformation, Wien´s peak


Most Modern Physics Books contain a chapter on the Laws of Black Body radiation when introducing the principles of Quantum Mechanics. These laws govern many phenomena that we encounter in daily life, technological developments, and scientific research. For that, this old subject is still of great importance, and even now some issues require our attention. This work addresses one of these topics. We describe why it has no sense to think that the wavelength at which Planck’s black-body spectral radiance distribution plotted as a function of the wavelength has its maximum value, must be the same that the wavelength calculated from the peak value obtained when the distribution is plotted as a function of another variable, such as the energy of the photons. We will show how the issue lies in using the correct form to calculate this wavelength from measured quantities.


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One trivial example of a narrow distribution function is the Dirac Delta, δ(λ − λ0), which is centered at λ=λ0. For this function, the average wavelength is hλi = R λδ(λ − λ0)dλ/ R δ(λ − λ0)dλ = λ0 = R (hc/E)δ(E − E0)dE/ R δ(E − E0)dE = hch1/Ei = hc/E0 = hc/hEi. It is obvious to see that, for δ(λ − λ0), λmax = hc/Emax is also fulfilled.




How to Cite

E. Marin and A. Calderón, “On Wien’s peaks”, Rev. Mex. Fis. E, vol. 21, no. 1 Jan-Jun, pp. 010501 1–, Jan. 2024.