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I'm reading about molecular spectra on Resnick-Eisberg, particularly the Rotational Spectra chapter. I'm wondering how come that the emission (absorption) lines are equally spaced by a constant factor while energy differences between allowed state are paced with a non-uniform factor dependent by the energy level involved r *(2πh)^2 / I, where r is the value of the modulus of the angular momentum during the transition r -> r - 1.

If we regard those equally spaced lines as energies released (absorbed) between transitions, we will find out that they came from equally spaced energies too, right? With the relation ΔE = hc/λ we should be able to find equally spaced energy interval if wavelength are equally spaced too.

here the picture from Resnick-Eisberg

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