Competitive unimolecular decay

I. Competitive unimolecular decay. Consider an excited species A that can decay in two different ways A —PandA —Q. Write kinetic rate equations and thereby show that the rate constant for the decay of the concentration of A is k = k +k2, [A ](r) = [A ](0) exp(-A i). As discussed, in quantum mechanics we can reproduce a unimolecular decay by endowing the energy of the state with an imaginary part that we call the width. Hence, in the absence of interference effects, the widths add up. 

This expression is known as the Stern-Volmer equation and Ksv as Stern-Volmer constant. Ksv is the ratio of bimolecular quenching constant to unimolecular decay constant and has the dimension of litre/mole. It implies a competition between the two decay pathways and has the ch".acter of an equilibrium constant. The Stern-Volmer expression is linear in quencher concentration and Ksv is obtained as the slope of the plot of 4>f°If vs [Q], if the assumed mechanism of quenching is operative. Here, t is the actual lifetime of the fluorescer molecule in absence of bimolecular quenching and is expressed as... 

The fact that plots of reciprocal of quantum yield of photoaddition vs. olefin concentration are linear with positive slope (Table 5) suggests that olefin quenches the singlet state and that all triplets formed are captured by olefin in the olefin concentration range examined in competition with unimolecular decay. Inefficiency... 

Thus R may be calculated from the depletion of the bare cluster ion signal. The ratio in parentheses on the right-hand side of Eq, (4) represents the competition between collisional stabilization and unimolecular decay of [M A ]. The collisional stabilization rate slowly rises with an increase in the geometric size of the cluster. This rise is small compared with that for k , as indicated by a simple RRK calculation. 

In fact, quenching effects can be evaluated and linearized through classic Stem-Volmer plots. Rate constants responsible for dechlorination, decay of triplets, and quenching can be estimated according to a proposed mechanism. A Stern-Volmer analysis of photochemical kinetics postulates that a reaction mechanism involves a competition between unimolecular decay of pollutant in the excited state, D, and a bimolecular quenching reaction involving D and the quencher, Q (Turro N.J.. 1978). The kinetics are modeled with the steady-state approximation, where the excited intermediate is assumed to exist at a steady-state concentration ... 

Another less likely alternative, but one which cannot be ruled out from the evidence given, is that the apparent temperature independence reflects the presence of an electronically excited species X. Equation 3b represents a possible reaction of such a species, namely unimolecular decay in competition with a bimolecular reaction with RNO and 02. This would explain the falloff of G(RNO) at low solute concentrations. 

The fate of G in the absence of any additive is as yet unknown. It decays bimo-lecularly with a rate constant of some 108 dm3 mol-1 s 1 (Faraggi et al. 1996), but there is increasing evidence that in competition, at least at elevated pH [pKa(G-) = 10.8], its radical anion also decays unimolecularly [k = 5 x 103 s 1 at pH 11 in the case of Guo and dGuo Faraggi and Klapper 1994 Faraggi et al. 1996]. The nature of this unimolecular transformation is as yet unknown. 

Some years ago Cornelisse reported that deuteration of alkyl benzenes results in a deuterium isotope effect upon the quantum yield of the meta photocycloaddition reaction with alkenes. In a new report the same group has published an analysis describing how the observed isotope effect upon the reaction quantvun yield can be ascribed to a kinetic deuterium isotope effect on the excited state reaction and distinguished from an effect upon the unimolecular photophysical modes of decay of the excited state. In addition, it is reported that when the quantum yield of meta photocycloaddition of cyclopentene to alkyl benzenes is measured using a mixture of deuterated and non-deuterated benzenes, the quantum yield is arene concentration dependent.The authors argue that this arises from competition between cycloaddition and the formation of mixed excimers between deuterated and non-deuterated alkyl benzenes which dissociate to yield excited deuterated alkyl benzene and ground state non-deuterated alkyl benzene preferentially. 

We saw in Section 1.2(i) that the position of the fall-off on the pressure scale is determined by the competition between the rates of decay to products and of deexcitation of the reactive molecules. Also, we will see shortly that the calculation of the unimolecular rate constant through the use of equations (2.26), (3.4) and (4.9) gives a virtually exact representation of the shape of the fall-off, but that the pressure at which the fall-off occurs is only reproduced correctly if the relaxation rate g is chosen to be about an order of magnitude smaller than the collision rate Z[M], For this reason, Nordholm introduced the idea of an effective strong collision whose rate constant is given by [78.N]... 

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