Selection rules alkali atoms

So far we have considered only hydrogen, helium, the alkali metals and the alkaline earth metals but the selection rules and general principles encountered can be extended quite straightforwardly to any other atom. 

The operation of the selection rule for l for hydrogen and hydrogenlike ions can be seen by the study of the fine structure of the lines. The phenomena are complicated, however, by the influence of electron spin.1 In alkali atoms the levels with given n and varying l are widely separated, and the selection rule for l plays an important part in determining the nature of their spectra. Theoretical calculations have also been made of the intensities of lines in these spectra with the use of wave functions such as those described in Chapter IX, leading to results in approximate agreement with experiment. 

In the triplet spectrum, the series lie in the longer wavelength region, ranging from the visible to the infrared. Each line in the triplet spectrum consists of a number of closely spaced lines the separation between these lines increases rapidly as the atomic number increases in the two-electron species He, Be, Mg, Ca, Sr, Ba, Zn, Cd, Hg. Consider the first line in the sharp series in calcium, corresponding to the transition from 5 S to 4 P. Since the 5 S level is a single level while the 4 P level is split into three levels, the line consists of three closely spaced lines A = 610.272 nm, 612.222 nm, and 616.218 nm. The transition from 4 D to 4 P yields a group of six closely spaced lines. In contrast to the alkali metal case in which the levels were not split, in calcium the levels are split into three levels. If each level of could combine with each level of P, nine lines would be expected. In fact, the selection rule, AJ = 0, + 1, rules out three of these possibilities so that only six lines appear. This situation is illustrated in Fig. 24.11. The transitions J = 2 -> 0, 3 - 1, and 3 -> 0 are forbidden. 

The alkali metals all have a lone electron in an outermost s atomic orbital. The transition from the higher p atomic orbital in the excited state to this s orbital corresponds to an energy difference AE that can be attributed to release of a photon whose energy is hv. Quantum mechanical selection rules... 

These angular momentum selection rules figure prominently in the fine structure of alkali atom spectra. The filled-shell core electrons have zero net orbital and spin angular momentum, so the term symbols 2 Si/2,... 

We now briefly consider the magnetic dipole (Ml) selection rules for transitions in hydrogenlike and alkali atoms. The relevant matrix element is (not as has sometimes been implied, because the... 

The selection rule AL = 0 needs a little further explanation since transitions of this type are not observed in the spectra of most one- and two-electron atoms. For one-electron systems such as hydrogen and the alkalis, we have L = and the selection rule Al- = -1 effectively... 

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