Multiplets in Three Electron Systems of the First Long Period

Wave-lengths and relative positions of multiplets in the spectra of Sc (I), Ti (II), V (III), and Cr (IV).—Using the regular and irregular doublet laws as guides, it has been found possible, from the corresponding known multiplets in Sc (I) and Ti (II), to identify the triad of multiplets of V (III) designated as ${}_{}{}^4{}_{}{}^{}F_{2,3,4,5}^{}{}_{}{}^{}-{}_{}{}^4{}_{}{}^{}G_{3,4,5,6}^{}{}_{}{}^{}$; ${}_{}{}^4{}_{}{}^{}F_{2,3,4,5}^{}{}_{}{}^{}-{}_{}{}^4{}_{}{}^{}{F}^{\prime }_{2,3,4,5}^{}{}_{}{}^{}$; and ${}_{}{}^4{}_{}{}^{}F_{2,3,4,5}^{}{}_{}{}^{}-{}_{}{}^4{}_{}{}^{}D_{1,2,3,4}^{}{}_{}{}^{}$. For these multiplets the initial state is given by one $4p$ electron and two $3d$ electrons. In the final state the $4p$ electron has shifted to a $4s$ orbit. The separations of the ${}_{}{}^4{}_{}{}^{}F_{2,3,4,5}^{}{}_{}{}^{}$ levels are found to be in the ratio 2.50:3.52:4.50, in very close agreement with Landé's interval rule. The relative intensities of the lines in these multiplets conform to the usual rule. A comparison of the data for one, two, and three electron systems of Sc, Ti, and V shows that the addition of first one and then a second $d$ electron causes not only an increase in the multiplicity but also successive shifts in the radiated lines toward the longer wave-lengths by very nearly the same frequency interval. It has also been found possible to identify the ${}_{}{}^4{}_{}{}^{}F_{2,3,4,5}^{}{}_{}{}^{}-{}_{}{}^4{}_{}{}^{}{F}^{\prime }_{2,3,4,5}^{}{}_{}{}^{}$ multiplet of Cr (IV).