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Units of Wavenumbers

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Yet a third spectral unit, commonly used in spectroscopy, is wavenumber, the number of waves per cm: σ = ν /100c  cm-1.  Converting (1) to these units gives





Again, the peak is where the derivative with respect to wavenumber vanishes:





                                                        .                                            (14)


The peak value is



                               .                    (15)



The spectral photon radiance is found by dividing Lσ by the energy of a photon, 100hcσ :


                .      (16)




We next find the wavenumber at the peak of the spectral photon radiance:





and                                                .                                            (17)


The peak spectral photon radiance is



                     .                    (18)


Fig. 3 shows plots of Lσ and LσP for various temperatures.  Note again the important difference between the spectral radiance and spectral photon radiance.






Fig. 3 - Spectral radiance, Lσ , (top) and the spectral photon radiance, LσP, (bottom) as a function of wavenumber, σ, for various temperatures.  The small black dots indicate the wavenumber and value of the peak, at 10 K temperature intervals.  Note that Lσ and  LσP have different wavenumber dependences.  Although the peak wavenumber is proportional to T for both quantities, Lσ peaks at a higher wavenumber than LσP.  Furthermore, the peak value of Lσ increases as 3, whereas the peak value of LσP increases as 2.


Calculation of a Blackbody Radiance
Units of Frequency
Units of Wavelength
Units of Wavenumbers
Radiance: Integrating the Planck Equation
In-band Radiance: Integrating the Planck Equation over a Finite Range
Appendix A: Algorithms for Computing In-band Radiance
Appendix B: The Doppler Effect
Appendix C: Summary of Formulas
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