Circular distribution electron probability

The electron probability density along the line passing through the nuclei is graphically represented as in Fig. 4.5 for H2 and the isoprobability contours for a plane containing the intemuclear axis are similar to those of Fig. 4.7 for the same ion. If we seek a distribution similar to the radial probability distribution for atoms. Fig. 6.1 is obtained (ref. 65). It shows the circular distribution of electron density for different distances from the inter-nuclear axis. It is found that the electronic charge is concentrated in a circular doughnut around the H-H axis, with a maximum at about 37 pm from the axis and about 50-55 pm from each nucleus. 

Fig. 6.1 Circular distribution of the electronic probability for the bonding m.o. of H2 for increasing distances from the internuclear axis, and corresponding contours in a plane containing that axis (adapted with permission from ref. 65, Journal of Chemical Education, 68, 743 (1991) copyright 1991, Division of Chemical Education Inc.).

The solution for the energy is the same as for the Bohr model, which is good because Bohr got that part right. But now, with the explicit wavefunction, we can draw the probability distributions of the electron and see that they differ considerably from the classical, circular orbits. 

Such structures are known as porous electrodes and they behave quite differently from the effectively planar electrodes used in most other areas of applied electrochemistry. The porous electrode is a mass of particulate reactants (sometimes with additives) with many random and tortuous electrolyte channels between. Real porous electrodes cannot be modelled but their behaviour can be understood qualitatively using a simplified model shown in Fig. M.5 in fact, there are two distinct situations which arise. In the first (Fig. 11.5(a)) the electroactive species is a good electronic conductor (e.g. a metal or lead dioxide here, the electrode reaction will occur initially on the face of the porous electrode in contact with the electrolyte but at the same time, and probably contributing more to the total current, the reaction will occur inside the pore not, however, along the whole depth of the pore because of the fR drop in solution. The potential and current distribution will depend on both the kinetics of electron transfer and the resistance of the electrolyte phase. A quantitative treatment of the straight, circular pore approximation allows a calculation of the penetration depth (the distance down the pore where reaction occurs to a significant extent) and it is found to increase linearly with electrolyte conductivity and the radius of... 

Another way to visualize the probability distributions is by the use of density plots in Figures 2.6 and 2.7. The highest probability density for both the Is and the 2s states is spherically distributed as shown in Figure 2.5a and b. From these plots, one is tempted to think of the electrons in circular orbits around the nuclei. But remember, the electron in an... 

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