Lifetime of states and

An alternative approach to chemical kinetics uses the broadening of spectral lines to determine lifetimes of states and thus kinetics. In NMR, exchange processes can be used to determine lifetimes in the range of sec while in optical spectra, lifetimes can be determined which are on the order of picoseconds. Puls NMR techniques can be used to determine lifetimes which are on the order of nanoseconds. A recent review of the possibilities of NMR and references are given in the chapter on NMR and some in the chapter on ESR in the Techniques in Chemistry volumes (Swift 1974). 

Here, t is the time taken for to fall to 1 /e of its initial value (where e is the base of natural logarithms) and is referred to as the lifetime of state n. If spontaneous emission is the only process by which M decays, comparison with Equation (2.9) shows that... 

Lifetimes of upper and lower states are governed by collisions and that of the upper is always longer than that of the lower in the gas mixtures used. 

The use of emission (fluorescence and phosphorescence) as welt as absorption spectroscopy. From these spectra the presence of as well as the energy and lifetime of singlet and triplet excited states can often be calculated. 

Where is the Hamiltonian for the interaction of the nucleus with the photon, /> is the initial (excited) state of the nucleus, g the final (ground) state and T the inverse of the natural lifetime of state /). We introduce an integral form of the denominator of Eq. (92) by ... 

Distinguish between the excited lifetime and radiative lifetime of Si and Ti states. 

Consider a sensor in dynamic equilibrium between phases or states A and B as illustrated in Figure 9.5. This situation may occur in pH sensors in which the lifetime of the ionized molecule is different from the lifetime of the neutral molecule. In this case a distinction needs to be made between the lifetimes of the individual states and the lifetimes measured. Let xA and xb be the lifetimes of states A and B, respectively. The measured lifetime values, t and n, are then given by the following equation 12 ... 

The time course of the charge-separated intermediate I can be measured in a flash photolysis experiment that monitors the (I — A) transient absorbance difference at a ground state/triplet state isosbestic point (e.g., 432 nm for Mg, and 435 nm for Zn). We have observed this intermediate for the [M, Fe] hybrids with M = Mg, Zn representative kinetic progress curves are shown in Fig. 3 [7a]. In a kinetic scheme that includes Eqs. (1) and (2) as the only electron-transfer processes, when the I A step is slow (kb < kp) the intermediate builds up (exponentially) during the lifetime of A and exponentially disappears with rate constant kb (Fig. 4A). This behavior is not observed for the hybrids, where the I - A process is more rapid than A - I, with kb > kp. In this case, I appears exponentially at early times with rate-constant kb and is expected to disappear completely in synchrony with A in an exponential fall with rate-constant kp (Fig. 4B). 

The Si excited-state lifetimes of cyclohexane and alkyl cyclohexanes are relatively short, all around 1-2 nsec however, their radiative rate coefficient —8 x 10 sec h R is the largest for the di- and trimethylcyclohexane group, —1.2 x 10 sec . 

Time-Resolved IR Spectroscopy. More recently, time-resolved IR (TRIR) experiments have been used to characterize species with lifetimes of micro-and even nanoseconds. Since IR spectra provide structural information in more detail than UV, this technique will be more powerful than TRUV-vis if one can find a carbene that can be detected and studied by this technique. To date, however, only one carbene has been studied by using TRIR. The matrix IR study shows that the planar triplet and twisted singlet states of 2-naphthyl(methoxycartbonyl) carbenes (NMC, 17) show distinctly different IR bands (see Section 3.1.4). Both NMC and NMC are detected by TRIR in solution and their kinetics have been studied. Such experiments provide clear cut data for the reaction kinetics as well as energetics of both states (see Sections 4.2 and 4.3... 

There are established techniques for the determination of and np (Section 10.2). In this expression, kf and kp are reciprocals of the radiative lifetimes of flucrescene and phosphorescence states, respectively, kf can be obtained experimentally from the integrated area under the absorption curve and kp is obtained from the measured decay rates for phosphorescence at 77K in EPA. In Table 5.3 the observed quantities, their symbols, relation to rate constants and sources of studies are summarized. 

The coefficient Am tn is related to the lifetime of state m. Suppose we initially have Nm0 molecules in the excited state m and let no radiation be present. Assume that state n is the only available state to which the excited molecules can decay. Then the rate of decay is dNmf dt= — Am nNm. This equation integrates to... 

We have seen that in the statistical limit simultaneous nonradiative and radiative processes proceed independently. The lifetimes and quantum yields characteristic of these several processes are then defined in terms of the relevant densities of states and matrix coupling elements connecting the initial state with the appropriate con tin ua and quasicontinua. 

Lifetimes of/43n, /> +, and c n have been measured by various workers and are given in Table V I0A. The dependence of lifetime on rotational and vibrational levels of, 43n and c n states has been observed by Smith et al. (916). 

An electronically excited molecule may, under some conditions, absorb another quantum and be raised to a higher excited state. Usually the population of excited species is so low that the probability of this occurrence is very slight. However, in recent years the technique of flash photolysis has been developed, which allows us to investigate the absorption properties of excited states. An extremely high intensity laser, which has approximately one million times the power of a conventional spectroscopic lamp, is turned on for a tiny fraction of a second, and a large population of excited species is produced. Immediately after this photolysis flash is turned off, a low-power spectroscopic flash may be turned on and the absorption spectrum of the already-excited system determined. By varying the delay between photolysis and spectroscopic flashes, much can be learned about the absorption and lifetime of singlet and triplet excited states. 

Complex reactions invariably involve intermediates which are formed in some steps, removed in others, and have a wide range of lifetimes. Longer lifetimes can result in build-up to significant intermediate concentrations during reaction, but these intermediates must also be sufficiently reactive to allow the subsequent reactions to occur. Intermediates can also be so short lived that they are removed almost as soon as they are formed, resulting in very, very low steady state concentrations. The lifetimes of intermediates and their concentrations have profound effects on the analysis of the kinetics of the reactions in which they occur. 

The inflection point of the fluorescence intensity curves against acidity gives a first approximation to the p/f/Sj )-value but this involves the assumption that the protolytic equilibrium is established within the lifetime of the S state and that the fluorescence lifetimes of B and BH+ are equal. These assumptions are less likely to hold when only one form is fluorescent and Lasser and Feitelson (1973)... 

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