On the fine structure of the band-spectra of sodium, potassium and sodium-potassium vapours

It has become of importance to analyse the fine structure of band spectra since it has been shown that, by the application of the quantum theory, certain information can be obtained concerning the molecules which give rise to these spectra. It is assumed that the fine lines of which these bands are composes are due to simultaneous changes in the electronic configuration of the molecule in the oscillation of the nuclei along the line joining them, and in the rotation of the molecule about its centre of gravity. It can then be shown that the frequencies of the lines in a group of bands are given byν =νe +nνn + (h /8π 2 I´ ±mh /4π 2 I´) +m 2 h /8π 2 (1/I´ – 1/I) wheren andm are integers. In this formulaνe is a frequency depending on the change in electronic configuration; to each value ofνe characteristic of the molecule corresponds a complete group of bands.νa depends on the oscillation of the nuclei, and the remaining terms depend on the rotation of the molecule, I´ and I being the moments of inertia in the initial and final states. This shows that the wave-numbers of the fine lines of a single band, when plotted against the series of integers, fall on the three parabolas Q(m ) = A + Cm 2 P(m ) = A + B – 2Bm + Cm 2 R(m ) = A + B + 2Bm + Cm 2 where A =νe +n νn /c , B =h /8π 2 c I´ C =h /8π 2 c (1/I´ – 1/I). When this notation, which is that of Sommerfeld, is used, all three series of a normal band are given by three constants.