One of the principal methods for obtaining the electronic spectra of unstable radicals

Chapter 14, Problem 14.29

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One of the principal methods for obtaining the electronic spectra of unstable radicals is to study the spectra of comets, which are almost entirely due to radicals. Many radical spectra have been found in comets, including that due to CN. These radicals are produced in comets by the absorption of far ultraviolet solar radiation by their parent compounds. Subsequently, their fluorescence is excited by sunlight of longer wavelength. The spectra of comet HaleBopp (C/1995 O1) have been the subject of many recent studies. One such study is that of the fluorescence spectrum of CN in the comet at large heliocentric distances by R.M. Wagner and D.G. Schleicher (Science 275, 1918 (1997)), in which the authors determine the spatial distribution and rate of production of CN in the coma. The (00) vibrational band is centred on 387.6 nm and the weaker (11) band with relative intensity 0.1 is centred on 386.4 nm. The band heads for (00) and (01) are known to be 388.3 and 421.6 nm, respectively. From these data, calculate the energy of the excited S1 state relative to the ground S0 state, the vibrational wavenumbers and the difference in the vibrational wavenumbers of the two states, and the relative populations of the v = 0 and v = 1 vibrational levels of the S1 state. Also estimate the effective temperature of the molecule in the excited S1 state. Only eight rotational levels of the S1 state are thought to be populated. Is that observation consistent with the effective temperature of the S1 state?