The integrals of simple uniform photoreactions

All the approximations discussed in the previous section might be out of the range of interest, since nowadays numerically powerful electronic calculators can be used. Therefore it is more convenient to solve numerically the integrals, eqs. (3.43) and (3.44). It is useful to present the result in general coordinates. In this case, of all photoreactions which show no dependence of the quantum yields on the intensity of the exciting irradiation, eqs. (1.41) and (3.70) define and F( ). Thus in general coordinates uniform 

The relationship (3.72) can be integrated using numerical methods, e.g., Simpson s [31,33]. On the left-hand side of eq. (3.72) the reciprocal quantum yield is used. Thereby the symbol / includes some reaction constants derived from the reaction scheme and depending on the photophysical mechanism used. The following examples demonstrate this. 

In Section 3.1.1.2 in Example 3.4 the equations for a photoaddition via the triplet state are given. Using eq. (3.3) one derives 

Another example of such a mechanism is the photophysically sensitised photoreaction, which is derived in Section 3.1.1.4. In the following example, the mechanism via the triplet is chosen (see Table 3.3). However, according to Example 3.9 one can set up an equation in general coordinates which differs from eq. (3.74). One finds 

If the quantum yield does not depend on the intensity of the irradiation, many of the photoreactions discussed in Section 3.1.1 can be evaluated using a single program. To achieve this eq. (3.72) is written in a more generalised form as 

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