Sodium potential energy curves

However, because of the avoided crossing of the potential energy curves the wave functions of Vq and Fi are mixed, very strongly at r = 6.93 A and less strongly on either side. Consequently, when the wave packet reaches the high r limit of the vibrational level there is a chance that the wave function will take on sufficient of the character of Na + 1 that neutral sodium (or iodine) atoms may be detected. 

Figure 11. Comparison of potential energy curves for dehydration of sodium hexahydrate and monohydrate using DFT and effective potentials developed in this work.

By considering the shapes of the potential energy curves for the reactions of sodium atoms with alkyl halides, Evans and Polanyi [384] deduced, for a series of related reactions, that... 

An example of the Diabatic potential energy curves for the NaCl molecule is shown in Figure 3.39(a). This suggests that as the Sodium atom/ion separates from the Chlorine atom/ion, the potential curves representing the neutral and charged... 

Figure 3.39 Potential energy curves of (a) the NaCl dimer in the gas phase as explained by the Landau, Zener, and Stnckelberg model and (b) a Sodium atom departing an NaCl snrface.

Figure 9.11 (Left) Potential energy curves for the covalent (Nal) and ionic (Na l ) forms of sodium iodide. AE is the nominal (i.e., asymptotic) energy gap between the two states, i.e., the difference between the ionization potential of Na and the electron affinity of I. Thus, from A o (eV) S 14.35// x (A) (Eq. (3.18)), / x = 7 A. It is known that for this system the actual electronic energy gap as discussed below is the much smaller value of = 0.025 eV. Note that the curves shown are "diabatic" ones. The electronic state is frozen and is not allowed to adjust to the position of the nuclei. The Born-Oppenheimer or adiabatic states do not cross. (Right) Cross-section for collisional ionization, in reduced units, logarithmic scale vs. the velocity in reduced units. The velocity Vm is defined in Eq. (9.24). The thresholds are indicated. Points experimental. Adapted from Moutinho etal., Physica, 53, 471 (1971) and Baede (1975).

Both the dynamics of the transition state [Na... 1] and the kinetics of formation of the reaction product (Na atom) were detected by the LIF method. Figure 4.8 demonstrates the time plots of the fluorescence intensity I(t) for the transition state and for the free Na atom. It is seen that the nuclear motion in the transition state has an oscillatory character with considerable decay (Fig. 4.8, b). This decay is due to the fact that some molecules jump on another potential energy curve to form the products, viz., the Na and I atoms. The energy of the transition state is not enough to form ions of the sodium and iodine atoms. 

Fig. 6.11 The structural-energy differences between bcc and fee (full curves) and hep and fee (dashed curves) as a function of the relative atomic volume, fl/Q f°r sodium, magnesium, and aluminium. The curves in the upper panel (a) were predicted by Moriarty and McMahan (1982) using their first principles interatomic potentials. The curves in the middle and lower panels (b) and (c) were predicted by Pettifor and Ward (1984) using three terms (<1, + 2 + 3) and one term 3 respectively in their analytic interatomic potentials.

Several investigations were carried out to study the above transitions from CF to common black film, and finally to Newton black film. For sodium dodecyl sulphate, the common black films have thicknesses ranging from 200 nm in very dilute systems to about 5.4 nm. The thickness depends heavily on the electrolyte concentration, while the stability may be considered to be caused by the secondary minimum in the energy distance curve. In cases where the film thins further and overcomes the primary energy maximum, it will fall into the primary minimum potential energy sink where very thin Newton black films are produced. The transition from common black films to Newton black films occurs at a critical electrolyte concentration which depends on the type of surfactant... 

Sodium and other alkali metals are easily ionized and need special caution. Early instruments were usually fitted with an air-propane burner that yielded a cooler flame, that is, less energy rich, hence giving rise to lesser ionization. Modern instruments do not usually have this facility rather, they use an air-acetylene flame that results in a standard upward curve as the ionization decreases with increasing concentration of the analyte. In such cases, ionization has to be counteracted by modifying the sample solution. Another metal with a high ionization potential is added in large quantities, for example, 1000 pg g-1, to the... 

It follows from Table 6 that the shape of anodic curves obtained by several authors for sodium salt solutions in hexamethylphosphotriamide is indicative of oxidation of two different kinds of localized electrons in the solution (cf. e.g.. Fig. 9). The first wave conforms to the oxidation of solvated electrons proper and the second to the oxidation of non-paramagnetic associates containing one cation and two electrons. It is seen that the reactivity of monoelectrons far exceeds that of the complexes with respect to the anodic oxidation reaction. Potentials at which they oxidize differ by more than 0.5 V this is consistent with the large difference in the energies of the optical absorption peaks for these particles. 

The same picture is presented in Figure 9.6 (below) however, here the distance between atoms corresponds to the shortest interatomic distance in sodium metal (a = 4.3 A). Firstly, the potential curves in a crystal form a unique periodic potential with the maxima located appreciably below the zero level of energy. Secondly, an upper occupied 3s-electron level has risen above the potential barriers and a corresponding electron spears capable of moving along the whole crystal. It is usually said that collectivization of valence electrons has occurred. Such collectivized electrons form an ensemble of quasi-particles that has lost part of their initial properties (see Section 9.2.2). The overlapping of the outer 3s orbits has occurred. 

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