Hydrogen spectrum, fine structure

The oscillating part of the secondary electron spectrum fine structure in the expression obtained is determined by two interference terms resulting from scattering of secondary electrorrs of final and intermediate states (the latter are due to the second-order process only). Here intensities of oscillating terms are determined by the amplitudes and intensities of electron transitions in the atom ionized. In this section we make estimations of these values within the framework of the simple hydrogen like model using the atomic unit system as in the preceding section. This section s content is based on papers [20,22,29-31,33,35,37,45-47]. 

The hydrogen atom and one-electron ions are the simplest systems in the sense that, having only one electron, there are no inter-electron repulsions. However, this unique property leads to degeneracies, or near-degeneracies, which are absent in all other atoms and ions. The result is that the spectrum of the hydrogen atom, although very simple in its coarse structure (Figure 1.1) is more unusual in its fine structure than those of polyelectronic atoms. For this reason we shall defer a discussion of its spectrum to the next section. 

W. E. Lamb (Stanford) the fine structure of the hydrogen spectrum. 

This simplified treatment does not account for the fine-structure of the hydrogen spectrum. It has been shown by Dirac (22) that the assumption that the system conform to the principles of the quantum mechanics and of the theory of relativity leads to results which are to a first approximation equivalent to attributing to each electron a spin that is, a mechanical moment and a magnetic moment, and to assuming that the spin vector can take either one of two possible orientations in space. The existence of this spin of the electron had been previously deduced by Uhlenbeck and Goudsmit (23) from the empirical study of line spectra. This result is of particular importance for the problems of chemistry. 

C-NMR refers to recording another NMR-spectrum but of the C-13 atoms rather than the hydrogen atoms. In actual practice, however, - these spectra are recorded in such a manner that each chemically distinct carbon gives rise to single peak, without any coupling or fine structure . 

Fine structure. Evidently the set of term values is exactly the same as on the usual theory but the quantum numbers are different, making new transitions possible and changing the intensities of the fine structure. The hydrogen fine structiure is so obscured by the natural breadth of the lines that no information can be obtained from it, and we must turn to the spectrum of ionized helium. For Paschen s data the reader is referred to Sommerfeld, figures 89-92. The only measurements of value for the... 

Fig. 1 shows an early saturation spectrum of the hydrogen Balmer-a line, recorded in this way at Stanford [4], together with the seven theoretically predicted fine structure components and the Doppler-... 

The 1 1 complex of water and hydrogen fluoride was also studied by Thomas 79), from 4000 to 400 cm-1. This is an experimentally difficult task in view of the low volatility of the H2O.HF complex. The analysis of the spectrum shows that the complex is coplanar, C2v. This splits the degeneracy of vb and vp the two bridge deformation vibrations which are degenerate in the linear or C3v complexes. Vj has some structure consisting of a sharp band at 3608 cm-1, a broader band split into two at 3623 and 3626 and a broad band at 3644 cm-1 followed by continuous absorption (Fig. 10). The free-associated separation is 354 cm-1 for H2O.HF while it is 420cm-1 for dimethylether. HF. (Arnold and Millen20. ) As in the previous cases the fine structure can be interpreted as a series of hot bands, (vt + n vp — n"vp). 

This constant explains far more than the appearance of the hydrogen atom s spectrum, however. The fine-structure constant is recognized as one of the most important constants in physics. We know, for example, that the fine-strucmre constant is a measure of the strength of the interaction between photons and electrons. Thus, this constant will appear in all simations that reveal quantum and relativistic properties of electrically charged particles. If electrons and light did not interact, the fine-structure constant would be zero. 

The hydrogen atom is the simplest one in existence, and the only one for which essentially exact theoretical calculations can be made on the basis of the fairly well confirmed Coulomb law of interaction and the Dirac equation for the electron. Such refinements as the motion of the proton and the magnetic interaction with the spin of the proton are taken into account in rather approximate fashion. Nevertheless, the experimental situation at present is such that the observed spectrum of the hydrogen atom does not provide a very critical test either of the theory or of the Coulomb law of interaction between point charges. A critical test would be obtained from a measurement of the fine structure of the n = 2 quantum state. 

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