Photokinetic Jacobi matrix

All the equations used above can be taken in principle to describe photochemical reactions also. However, the relationships become more complicated, since the amount of light absorbed has to be considered. Furthermore the quantum yield can depend on the concentration which makes the formulae more complex. Therefore in a simple example of a consecutive photoreaction, the correlation is demonstrated. Details are discussed in Chapter 3. 

Using eq. (1.39), relationships are obtained in the case of Napierian units for the absorption coefficients and the absorbance E at the wavelength of irradiation X.  

Both quantum yields do not depend on the intensity of irradiation. Integration is done with respect to the local volume element. According to eqs. (2.9) and (1.40) the rate law is given by 

It is obvious that thermal and photochemical laws can be treated equivalently (see Table 2.5 for comparison). However, the derivation of the pho-tokinetic equations causes more expenditure, therefore in this chapter thermal equations are chosen for convenience. 

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This mechanism allows the equivalence between thermal and photokinetic rate laws to be demonstrated. If one can assume that the quantum yields do not depend on the concentration of the reactants, the Jacobi matrix given by eq. (2.93) can be written in a similar form according to Section 2.2.1.4 as... 

Since photokinetic equations cannot be solved in a closed form, equations are preferably rearranged due to allow formal (numerical) integration of the integrals. It is best to choose a matrix representation. The elements of the Jacobi matrix ate obtained by... 

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