?A transition of particular importance in O2 gives rise to the Schumann–Runge band in

Chapter 11, Problem P11F.4

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A transition of particular importance in O2 gives rise to the Schumann–Runge band in the ultraviolet region. The wavenumbers (in \(\mathrm{cm}^{-1}\)) of transitions from the ground state to the vibrational levels of the first excited state \(\left({ }^{3} \Sigma_{u}^{-}\right)\) are 50 062.6, 50 725.4, 51 369.0, 51 988.6, 52 579.0, 53 143.4, 53 679.6, 54 177.0, 54 641.8, 55 078.2, 55 460.0, 55 803.1, 56 107.3, 56 360.3, 56 570.6. What is the dissociation energy of the upper electronic state? (Use a Birge–Sponer plot, Topic 11C.) The same excited state is known to dissociate into one ground-state O atom and one excited-state atom with an energy 190 kJmol−1 above the ground state. (This excited atom is responsible for a great deal of photochemical mischief in the atmosphere.) Ground-state \(\mathrm{O}_{2}\) dissociates into two ground-state atoms. Use this information to calculate the dissociation energy of ground-state \(\mathrm{O}_{2}\) from the Schumann–Runge data.

Text Transcription:

cm^-1

^3Sigma_u^-

O_2