?The vibrational wavenumber of the oxygen molecule in its electronic ground state is

Chapter 11, Problem P11F.3

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The vibrational wavenumber of the oxygen molecule in its electronic ground state is 1580 \(\mathrm{cm}^{-1}\), whereas that in the excited state \(\left(\mathrm{B}^{3} \Sigma_{\mathrm{u}}^{-}\right)\), to which there is an allowed electronic transition, is 700 \(\mathrm{cm}^{-1}\). Given that the separation in energy between the minima in their respective potential energy curves of these two electronic states is 6.175 eV, what is the wavenumber of the lowest energy transition in the band of transitions originating from the v = 0 vibrational state of the electronic ground state to this excited state? Ignore any rotational structure or anharmonicity.

Text Transcription:

cm^-1

B^3Sigma_u^-