Internal relaxation rate

We have assumed so far that the electron has sufficient time to relax within the substructure of Sy and therefore reach the lowest state Sy (0) before any decay to the ground state occurs. This is entirely justified if the total decay rate from Sy is much smaller than the typical internal relaxation rate in Sy,... 

Fig. 5.1. Comparison of the theoretical fall-off curve for the thermal isomerisation of cyclopropane at 765 K with the experimental results. The theoretical curve is calculated from the parameters listed in [78.Y2], except that the infinite pressure rate constant is taken to be 3.57 x 10 s rather than 3.41 x lO s as recommended by Falconer, Hunter Trotman-Dickenson [61.F1], see Footnote 4 the internal relaxation rate constant is r, = 5.50x10 Torr s. The experimental data are those of Chambers Kistiakowsky [34.C] (diamonds). Corner Pease [45.C] (crosses), and of Pritchard, Sowden Trotman-Dickenson [53.P2], also Appendix 2 (circles) the dotted line shows the high pressure limit of [61.F1],...

Table 5.1. Apparent internal relaxation rate constants for strong collision reactions...

So what happens if we change our consideration to a molecule of different complexity In practice, there are many variables which complicate the analysis, for not only will the and d change, but /<, and Aoo will also be different. Let us imagine a hypothetical molecule C3D3 which possesses the same internal relaxation rate constant as does cyclopropane, and which reacts to form some product with the same values of and of A. We will also assume that it has the same two moments of inertia as does cyclopropane, so that the only thing different about it is its vibrational frequencies it has 12 normal modes of vibration instead of 21, and for the purposes of this illustration, I have simply made an arbitrary deletion of nine of the original modes of the cyclopropane molecule. 

Fig. 5.10. Comparison of fall-off curves for two of the four reaction products in the thermal isomerisation of monofluorocyclopropane, in the strong collision approximation. The upper theoretical curve corresponds to the rate of formation of (rans-1-fluoropropene, and the lower one to that of 2-fluoropropene. The points are the experimental results of Casas, Kerr Trotman-Dickenson [64.C] see Footnote 14 also the position of these curves is determined by an assumed internal relaxation rate constant r,= 3x 10 Torr s .

Having dispensed with the notion that the observed internal relaxation rate g discriminates between strong and weak collision regimes, we are left with only one criterion for diagnosing a weak collision reaction, the occurrence of a fall-off curve which departs from that predicted by the strong collision expression, equation (5.14). We have seen two examples, that of methyl isocyanide in the previous chapter, and that of nitrous... 

However, when we go on to calculate the internal relaxation rate constant, we find a different value for this quantity from each reaction. 

Show that the magnitude of the feature in Figure 7.3 becomes larger if the internal relaxation rate n is made ten times larger, and that it almost disappears if it is made ten times smaller. 

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