Quantum true integral

The effect of nitrate on the photochemical degradation kinetics of hydrophilic was studied by Sorensen and Frimmel (1997). A number of common pollutants were examined, including amino-polycarboxylates and aromatic sulfonates. Kinetic experiments were performed with or without H202. Quantum yield was used as a tool for examining whether a substance acts as an inner filter. Under the assumption that water compounds do not take part in the chemical reaction but exert influence only in a physical way by the absorption of light, the true integral quantum yield (Oaj ) is independent of the concentration of the inner filter. 0.a , is expressed as ... 

Whereas Si and s2 are true one-electron spin operators, Ky is the exchange integral of electrons and in one-electron states i and j (independent particle picture of Hartree-Fock theory assumed). It should be stressed here that in the original work by Van Vleck (80) in 1932 the integral was denoted as Jy but as it is an exchange integral we write it as Ky in order to be in accordance with the notation in quantum chemistry, where Jy denotes a Coulomb integral. 

First, we note that the number of photons absorbed rather than the number of incident photons has to be taken into account. Second, integrations over extended time periods most likely bear substantial errors because the intensity of the source may fluctuate or drift. As a consequence of this, the only exact measure for the efficiency of a photochemical reaction is the true differential quantum yield, which needs to be determined for each step of the reaction. Similar to thermal reactions, photochemical reactions may be complex. Accordingly, the only correct measure is the so-called partial (true differential photochemical) quantum yield, which is defined for each linearly independent step of the reaction. 

One of the most important features of a photoreaction is the value of the quantum yield ( )i of compound i, which is the quantifying answer to the question How effective In principle, the quantum yield is the ratio of the number of reacting molecules to the number of quanta absorbed. In praxis there are several definitions of the quantum yield true (only light absorbed by the reactant is considered) and apparent (there are other absorbers present), differential (at the moment ) and integral (mean). In the previous rate equation, ( )e and (j) are the true differential yields. The monoexponential kinetics of Equation, 1.2 or 1.4 allow one to determine the yields in systems where the starting solution is already a mixture of E- and Z-forms (which can happen easily if the E-form is not prepared under strict exclusion of light). It turns out, however, that the yalues of the Z —> E quantum yield are especially sensitive to small errors in the E values. 

In this communication I wish to show, first for the simplest case of the non-relativistic and unperturbed hydrogen atom, that the usual rules of quantization can be replaced by another postulate, in which there occurs no mention of whole numbers. Instead, the introduction of integers arises in the same natural way as, for example, in a vibrating string, for which the number of nodes is integral. The new conception can be generalized, and I belieVe that it penetrates deeply into the true nature of the quantum rules. 

The true differential quantum yields can no longer be localised in the integrated equations of photokinetics. The different rate constants are distributed to different terms in the equation. On the other hand one can correlate quantum yields in the differential equations. If the quantum yield does not depend on the intensity of the irradiation source on finds according to eq. (3.35)... 

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