The alkali model

One of the most instructive energy level diagrams in the whole of atomic physics is plotted in fig. 2.4, which shows the comparison between the energy levels of the ground and first excited states of the alkali atoms and the excited states of H. 

All of these facts need to be explained, but the alkali model does not attempt to account for all of them. In particular, (v) requires principles beyond the simple alkali model which will be dealt with in section 5.5. Also, the alkali model does not seek to provide absolute magnitudes of pi- Rather, it should be regarded as a conceptual framework within which 

The fundamental assumption of the alkali model (which is vindicated by its success in interpreting fig. 2.4) is the following the space in which the electrons move can be partitioned into two regions (a) a (small) inner region called the electronic core, within which the wavefunction of an electron is subjected to a complicated potential due to the presence of all 

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We here anticipate that one consequence of the alkali model is the introduction of a minimum radius7 ro at which solutions of the Schrodinger equation for the inner and outer reaches of the alkali atom can be joined (this idea will be useful in chapter 3). 

This terminology is derived from the Bohr model of the atom, which was used in early descriptions of the alkali model, most notably by White [26]. 

It will not have escaped the reader that the alkalis are not the only elements with one external electron. If the alkali model had general validity, then it should be possible in principle to draw a similar diagram for the elements Cu, Ag and Au.9 An attempt to do so is shown in fig. 2.8. 

As a provisional conclusion, let us merely note that the alkali model works best for optical electrons when the Rydberg spectrum occurs far away in energy from any spectrum involving excitation out of the core. 

To demonstrate how useful the alkali model is for d subshell excitation in Zn, Cd and Hg, consider the effective quantum numbers n listed in table 2.2 for np and nf orbitals. The behaviour of these numbers is closely similar to that for alkali spectra, with the most hydrogenic states (near integral n ) being those of greatest , while the n values indicate that the outermost np electron, in its lowest available state, occurs at a binding energy (referred to a core-excited threshold) intermediate between the values for n = 1 and n = 2 of H. 

It is perhaps interesting to note that this problem is exactly the opposite of the alkali model, presented above, in which the electron is free to move outside a radius ro-... 

The alkali model and its extensions are fundamental to the development of atomic physics, and will be referred to several times in the course of the present monograph. 

Rasaiah J C 1970 Equilibrium properties of ionic solutions the primitive model and its modification for aqueous solutions of the alkali halides at 25°C J. Chem. Phys. 52 704... 

It is also possible to explain, from hydration models, the differences between equally-charged cations, such as the alkali metals = 73,5, = 50,1 land 38.68, all in units of mor cm ). From atomic... 

The alkali metals tend to ionize thus, their modeling is dominated by electrostatic interactions. They can be described well by ah initio calculations, provided that diffuse, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ah initio calculations on the heavier elements. 

The material evaporated by the laser pulse is representative of the composition of the solid, however the ion signals that are actually measured by the mass spectrometer must be interpreted in the light of different ionization efficiencies. A comprehensive model for ion formation from solids under typical LIMS conditions does not exist, but we are able to estimate that under high laser irradiance conditions (>10 W/cm ) the detection limits vary from approximately 1 ppm atomic for easily ionized elements (such as the alkalis, in positive-ion spectroscopy, or the halogens, in negative-ion spectroscopy) to 100—200 ppm atomic for elements with poor ion yields (for example, Zn or As). 

The interpretation of these remarkable properties has excited considerable interest whilst there is still some uncertainty as to detail, it is now generally agreed that in dilute solution the alkali metals ionize to give a cation M+ and a quasi-free electron which is distributed over a cavity in the solvent of radius 300-340 pm formed by displacement of 2-3 NH3 molecules. This species has a broad absorption band extending into the infrared with a maximum at 1500nm and it is the short wavelength tail of this band which gives rise to the deep-blue colour of the solutions. The cavity model also interprets the fact that dissolution occurs with considerable expansion of volume so that the solutions have densities that are appreciably lower than that of liquid ammonia itself. The variation of properties with concentration can best be explained in terms of three equilibria between five solute species M, M2, M+, M and e ... 

An example of a modem instrument of this type is the Coming Model 410 flame photometer. This model can incorporate a lineariser module which provides a direct concentration read-out for a range of clinical specimens. Flame photometers are still widely used especially for the determination of alkali metals in body fluids, but are now being replaced in clinical laboratories by ion-selective electrode procedures (see Section 15.7). 

It is obvious that one can use the basic ideas concerning the effect of alkali promoters on hydrogen and CO chemisorption (section 2.5.1) to explain their effect on the catalytic activity and selectivity of the CO hydrogenation reaction. For typical methanation catalysts, such as Ni, where the selectivity to CH4 can be as high as 95% or higher (at 500 to 550 K), the modification of the catalyst by alkali metals increases the rate of heavier hydrocarbon production and decreases the rate of methane formation.128 Promotion in this way makes the alkali promoted nickel surface to behave like an unpromoted iron surface for this catalytic action. The same behavior has been observed in model studies of the methanation reaction on Ni single crystals.129... 

The possibility of a barrier which inhibits a reaction in spite of the attractive ion-dipole potential suggests that one should make even crude attempts to guess the properties of the potential hypersurface for ion reactions. Even a simple model for the long range behavior of the potential between neutrals (the harpoon model ) appears promising as a means to understand alkali beam reactions (11). The possibility of resonance interaction either to aid or hinder reactions of ions with neutrals has been suggested (8). The effect of possible resonance interaction on cross-sections of ion-molecule reactions has been calculated (25). The resonance interaction would be relatively unimportant for Reaction 2 because the ionization potential for O (13.61 e.v.) is so different from that for N2 (15.56 e.v.). A case in which this resonance interaction should be strong and attractive is Reaction 3 ... 

Figure 15. Isotherms of internal mobilities in alkali-alkaline earth nitrate mixtures. The mobility of the alkali ion is always greater than that of the alkaline earth ion. (Reprinted from T. Koura, H. Matsuura, and I. Okada, "A Dynamic Dissociation Model for Internal Mobilities in Molten Alkali and Alkaline Earth Nitrate Mixtures,"/ Mol. Liq. 73-75 195, Fig. 4, Copyright 1997 with permission from Elsevier Science.)...

Most metals (other than the alkali and alkaline-earth metals) are corrosion resistant when cathodically polarized to the potentials of hydrogen evolution, so that this reaction can be realized at many of them. It has thus been the subject of innumerable studies, and became the fundamental model in the development of current kinetic concepts for electrochemical reactions. Many of the principles... 

With respect to the thermodynamic stability of metal clusters, there is a plethora of results which support the spherical Jellium model for the alkalis as well as for other metals, like copper. This appears to be the case for cluster reactivity, at least for etching reactions, where electronic structure dominates reactivity and minor anomalies are attributable to geometric influence. These cases, however, illustrate a situation where significant addition or diminution of valence electron density occurs via loss or gain of metal atoms. A small molecule, like carbon monoxide,... 

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