Selection rules atomic spectra

Figure Bl.4.9. Top rotation-tunnelling hyperfine structure in one of the flipping inodes of (020)3 near 3 THz. The small splittings seen in the Q-branch transitions are induced by the bound-free hydrogen atom tiiimelling by the water monomers. Bottom the low-frequency torsional mode structure of the water duner spectrum, includmg a detailed comparison of theoretical calculations of the dynamics with those observed experimentally [ ]. The symbols next to the arrows depict the parallel (A k= 0) versus perpendicular (A = 1) nature of the selection rules in the pseudorotation manifold.

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

When you consider the selection rules, which are not particularly restrictive (see Section 7.1.6), governing transitions between these states arising from each configuration, it is not surprising that the electronic spectrum of an atom such as zirconium consists of very many lines. (Remember that the Laporte rule of Equation (7.33) forbids transitions between states arising from the same configuration.)... 

As a result of the atomic nature of the core orbitals, the structure and width of the features in an X-ray emission spectrum reflect the density of states in the valence band from which the transition originates. Also as a result of the atomic nature of the core orbitals, the selection rules governing the X-ray emission are those appropriate to atomic spectroscopy, more especially the orbital angular momentum selection rule A1 = + 1. Thus, transitions to the Is band are only allowed from bands corresponding to the p orbitals. 

The ro-vibronic spectrum of molecules and the electronic transitions in atoms are only part of the whole story of transitions used in astronomy. Whenever there is a separation between energy levels within a particular target atom or molecule there is always a photon energy that corresponds to this energy separation and hence a probability of a transition. Astronomy has an additional advantage in that selection rules never completely forbid a transition, they just make it very unlikely. In the laboratory the transition has to occur during the timescale of the experiment, whereas in space the transition has to have occurred within the last 15 Gyr and as such can be almost forbidden. Astronomers have identified exotic transitions deep within molecules or atoms to assist in their identification and we are going to look at some of the important ones, the first of which is the maser. 

However, in the sodium atom, An = 0 is also allowed. Thus the 3s —> 3p transition is allowed, although the 3s —> 4s is forbidden, since in this case A/ = 0 and is forbidden. Taken together, the Bohr model of quantized electron orbitals, the selection rules, and the relationship between wavelength and energy derived from particle-wave duality are sufficient to explain the major features of the emission spectra of all elements. For the heavier elements in the periodic table, the absorption and emission spectra can be extremely complicated - manganese and iron, for example, have about 4600 lines in the visible and UV region of the spectrum. 

In polymers the infrared absorption spectrum is generally very simple, considering the large number of atoms that are involved. This simplicity is due to the fact that many of the normal vibrations have almost the same frequency and so appear in the spectrum as one absorption band and, also from the strict selection rules that avoid many of the vibrations from causing absorptions. 

The SAM was obtained by immersing the clean substrate for 48 h in an ethanol solution of ferrocenylhexyl isocyanide. The strong v(N=C) peak at 2147cm" observed in FTIR spectra of free ferrocenylalkyl isocyanide (on a KBr plate) is not present in the RAIR spectra of this isocyanide on a nickel surface. Considering the surface selection rules for RAIR spectroscopy, the absence of a v(N=C) peak in the RAIR spectrum indicates that the chemisorbed isocyanides are bonded through both their carbon and nitrogen atoms, and they adopt an orientation in which the N=C bond is parallel to the surface. 

Let us conclude this section with the intriguing observation of the absence of the a (7t(ag, b f)) contribution in the Nls NEXAFS spectra of both neutral TCNQ and TTF-TCNQ. Let us recall the absence of precisely the Og and b u contributions in the CI5 spectra of TTF discussed above. However, the Cls NEXAFS spectrum of TCNQ shows some intensity in the a (7r(ag, b f)) region [between n a , bif) and TT (jr(b3g, af>) + a n b g, 2u))]- This is due to the signihcant 6 -contribution from carbon for neutral TCNQ while nitrogen contributes negligibly. Thus, it seems that in addition to the intra-atomic selection rules there are additional restrictions apparently symmetry-related in MOMs like those discussed here. This unexplained phenomenon certainly calls for both theoretical and experimental future work. 

The Selection Rule for L - The energy-level diagram for lithium as. shown in Figure 2-6 has been obtained by analysis of the spectrum of the lithium atom. Lines are observed in the spectrum of lithium corresponding to the transition from one of the states indicated in the diagram to another state. The lines that are observed in the spectrum do not represent all combinations of the energy levels, however, but... 

Lines, corresponding to different transitions from initial states with vacancy in the shells with the same n, compose a series of spectra, e.g. K-, L-, M-series etc. Main diagram lines correspond to electric dipole ( 1) transitions between shells with different n. The lines of 2-transitions also belong to diagram lines. Selection rules of 1-radiation as well as the one-particle character of the energy levels of atoms with closed shells and one inner vacancy cause, as a rule, a doublet nature of the spectra, similar to optical spectra of alkaline elements. X-ray spectra are even simpler than optical spectra because their series consist of small numbers of lines, smaller than the number of shells in an atom. The main lines of the X-ray radiation spectrum, corresponding to transitions in inner shells, preserve their character also for the case of an atom with open outer shells, because the outer shells hardly influence the properties of inner shells. 

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