Electron ladders

These vertical cuts are called electron ladders. Rungs are placed on them at the proper E values, and proper species are indicated below and above the rungs. These are shown in Figure 3.3. The exact values of E for the HOH ladder have been calculated from the equations given above, and that for the Mg ladder from E = —2.36 + 0.030 log [Mg+ ], which is the equation that describes the line between Mg+ and Mg on the Mg E-pH diagram. 

Figure 3.3 Electron ladders for Mg and H2O at pH = 2.0. Soluble species concentrations (except H+) = 10° ° M.

The consequent electron ladder is shown in Figure 3.5. The reaction which results by the combination of the lower species at the lower rung with the upper species at the upper rung to give the intermediate species is ... 

The pertinent equations for the rungs on the electron ladder are as follows ... 

The electron ladder which shows these interrelationships is pictured in Figure 3.6. And the reaction which takes place along with its potential is... 

Figure 3.11 Combined electron ladder for Mn, Fe, and H2O at pH = 1.0. Mn soluble species concentrations = 10° ° M. Fe soluble species concentrations = 10 ° ° M.

Consider the electron ladder in Figure 3.13. This ladder was abstracted from the E-pH diagrams of HOH and Cr with all soluble species at 10°-° M and a... 

In Figs. 42b, c the ionic excited states have the full molecular symmetry and by including diagonal hole-hole and hole-electron ladders in analogy with Figs. 42d,e will... 

Light-Induced Electron Spin Resonance laddered poly(p ra-phenylene) lowest unoccupied molecular orbital molecular beam epitaxy... 

Concerning the nature of electronic traps for this class of ladder polymers, we would like to recall the experimental facts. On comparing the results of LPPP to those of poly(para-phenylene vinylene) (PPV) [38] it must be noted that the appearance of the maximum current at 167 K, for heating rates between 0.06 K/s and 0.25 K/s, can be attributed to monomolecular kinetics with non-retrapping traps [26]. In PPV the density of trap states is evaluated on the basis of a multiple trapping model [38], leading to a trap density which is comparable to the density of monomer units and very low mobilities of 10-8 cm2 V-1 s l. These values for PPV have to be compared to trap densities of 0.0002 and 0.00003 traps per monomer unit in the LPPP. As a consequence of the low trap densities, high mobility values of 0.1 cm2 V-1 s-1 for the LPPPs are obtained [39]. 

We are now ready to build a quantum mechanical model of a hydrogen atom. Our task is to combine our knowledge that an electron has wavelike properties and is described by a wavefunction with the nuclear model of the atom, and explain the ladder of energy levels suggested by spectroscopy. 

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