The integrals can be solved in a closed form

Example 3-34 Photoisomerisation by irradiation at the isosbestic point In the case of a simple photoisomerisation, an irradiation at the wavelength of the isosbestic point results in 

The second integral contains the time function, since at the position z = 0 one obtains 

Therefore the relative concentration in the newly defined time axis x is given by 

In Fig. 3.11 a comparison is given between the photoisomerisation in viscous media and in a stirred solution. Furthermore another graph demonstrates the difference between a viscous medium and a stirred solution. In Fig. 3.12 the reaction time of a stirred solution Tr is calculated by iterative procedures for an equivalent of the turnover in viscous medium as a function of its irradiation time. 

According to eq. (3.9) the following equation is valid for the chemically sensitised photoaddition discussed in Example 3.12. 

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In Fig. 3.17 a different presentation is chosen. One assumes at turnover = 0.95 at= 0 and the corresponding time (t = 3.00) is kept constant. Assuming different values of r the turnover is given as a function of ij. These values can be obtained by numerical integration according to eq. (3.117) for a constant lower limit and a variable upper limit. The values for r—>oo ( =0) cannot be obtained by numerical integration. Under these conditions the exceptional case happens where the integral can be solved in a closed form. 

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