Lifetime natural

Apart from the natural lifetime due to spontaneous emission, both uni- and bimolecular processes can contribute to the observed value of T. One important contribution comes from coiiisionai broadening, which can be distmguished by its pressure dependence (or dependence upon concentration [M] of tlie collision partner) ... 

Natural linewidths are broadened by several mechanisms. Those effective in the gas phase include collisional and Doppler broadening. Collisional broadening results when an optically active system experiences perturbations by other species. Collisions effectively reduce the natural lifetime, so the broadening depends on a characteristic impact time, that is typically 1 ps at atmospheric pressure ... 

It has been demonstrated that the whole photoexcitation dynamics in m-LPPP can be described considering the role of ASE in the population depletion process [33], Due to the collective stimulated emission associated with the propagation of spontaneous PL through the excited material, the exciton population decays faster than the natural lifetime, while the electronic structure of the photoexcited material remains unchanged. Based on the observation that time-integrated PL indicates the presence of ASE while SE decay corresponds to population dynamics, a numerical simulation was used to obtain a correlation of SE and PL at different excitation densities and to support the ASE model [33]. The excited state population N(R.i) at position R and time / within the photoexcited material is worked out based on the following equation ... 

The 16 ns natural lifetime of excited Na is much shorter than the 140 /rs mean time between collisions, thus the fine broadening due to collision-induced... 

D2 natural lifetime 16 ns Saturation intensity per velocity group 64 W/m ... 

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 ... 

From spectroscopic measurements, we can estimate the fluorescence lifetime, t [. = (PpTi. where the natural lifetime, rN, can be calculated from the Strickler-Berg equation in CGS units [60] ... 

In (8), the solvent-independent constants kr, kQnr, and Ax can be combined into a common dye-dependent constant C, which leads directly to (5). The radiative decay rate xr can be determined when rotational reorientation is almost completely inhibited, that is, by embedding the molecular rotor molecules in a glass-like polymer and performing time-resolved spectroscopy measurements at 77 K. In one study [33], the radiative decay rate was found to be kr = 2.78 x 108 s-1, which leads to the natural lifetime t0 = 3.6 ns. Two related studies where similar fluorophores were examined yielded values of t0 = 3.3 ns [25] and t0 = 3.6 ns [29]. It is likely that values between 3 and 4 ns for t0 are typical for molecular rotors. 

Table 6.2 lists some of the physical data for the hydrated electron. Most of these data are experimental. The molar volume is calculated, as experimental measurements are not reliable. The oscillator strength and the natural lifetime against reaction with water molecules are lower bounds, whereas the salvation time is possibly an upper bound. 

This reaction is important, because it gives the natural lifetime of eh, has an isotope effect (the rate in D20 being a factor -13 times less than that in H20), and it can give us the reduction potential of eh. The forward reaction is hard to observe because of the low rate, and special precautions are necessary (Hart and Anbar, 1970). Using the utmost care, Hart et al. (1966) established that rate as kf = 16 1... 

In general, most converters are tested on the bench with the electronic load set to constant current (CC mode). True, that s not benign, nor as malignant as it gets. But the implied expectation is that converters should at least work in CC mode. They should, in particular, have no startup issues with this type of load profile. But even that may not be the end of the story Some loads can also vary with time. For example, an incandescent bulb has a resistive profile, but its cold resistance is much lower than its hot resistance. That s why most bulbs fail towards the end of their natural lifetime just when you throw the wall switch to its ON position. And if the converter is powering a system board characterized by sudden variations in its instantaneous supply current demand, that can cause severe problems to the converter, too. The best known example of this is an AC-DC power supply inside a computer. The 12V rail goes to the hard disk, which can suddenly demand very high currents as it spins up, and then lapse back equally suddenly into a lower current mode. 

If the only way of de-excitation from Sj to S0 was fluorescence emission, the lifetime would be l/krs this is called the radiative lifetime (in preference to natural lifetime) and denoted by rf. The radiative lifetime can be theoretically calculated from the absorption and fluorescence spectra using the Strickler-Berg relation6 . 

ISOTOPE EXCHANGE KINETICS COMPARTMENTAL ANALYSIS Natural lifetime,... 

Class (3) reactions include proton-transfer reactions of solvent holes in cyclohexane and methylcyclohexane [71,74,75]. The corresponding rate constants are 10-30% of the fastest class (1) reactions. Class (4) reactions include proton-transfer reactions in trans-decalin and cis-trans decalin mixtures [77]. Proton transfer from the decalin hole to aliphatic alcohol results in the formation of a C-centered decalyl radical. The proton affinity of this radical is comparable to that of a single alcohol molecule. However, it is less than the proton affinity of an alcohol dimer. Consequently, a complex of the radical cation and alcohol monomer is relatively stable toward proton transfer when such a complex encounters a second alcohol molecule, the radical cation rapidly deprotonates. Metastable complexes with natural lifetimes between 24 nsec (2-propanol) and 90 nsec (tert-butanol) were observed in liquid cis- and tra 5-decalins at 25°C [77]. The rate of the complexation is one-half of that for class (1) reactions the overall decay rate is limited by slow proton transfer in the 1 1 complex. The rate constant of unimolecular decay is (5-10) x 10 sec for primary alcohols, bimolecular decay via proton transfer to the alcohol dimer prevails. Only for secondary and ternary alcohols is the equilibrium reached sufficiently slowly that it can be observed at 25 °C on a time scale of > 10 nsec. There is a striking similarity between the formation of alcohol complexes with the solvent holes (in decalins) and solvent anions (in sc CO2). 

As described in Chapter 5, the natural lifetime for acetaldehyde with respect to photolysis under these conditions can be calculated from kp for the overall reaction. The natural lifetime, t, is defined as the time for the concentration of CH3CHO to fall to 1/e of its initial value, where e is the base of natural logarithms. The natural lifetime of acetaldehyde under these conditions is therefore given by r = 1 /kp = 5.5 X 106 s = 63 days. Of course, these conditions do not exist for 63 days, so the lifetime is hypothetical. However, it does provide a sort of back-of the envelope method of assessing the relative rapidity of loss of the compound by photolysis compared to other processes, such as reaction with OH. 

A rate constant is a quantitative measure of how fast reactions proceed and therefore is an indicator of how long a given set of reactants will survive in the atmosphere under a particular set of reactant concentrations. However, the rate constant per se is not a parameter that by itself is readily related to the average length of time a species will survive in the atmosphere before reacting. More intuitively meaningful parameters are the half-life (/l/2) or the natural lifetime (r), the latter usually referred to simply as lifetime, of a pollutant with respect to reaction with a labile species such as OH or NO-, radicals. 

To pare the list of VOC oxidations down to the most important processes, we can calculate the effective lifetimes of organics with respect to reactions with each of the oxidants listed in the previous section. Since these natural lifetimes are defined as r = 1 / [X], we also need to assume an average concentration for the oxidant, [X]. We can therefore take a typical organic from each of the major classes (alkane, alkene, aromatic, etc.) and compare the individual lifetimes for reaction with OH, 03, N03, etc. Those reactions having very long lifetimes are insignificant with respect to their contribution to tropospheric chemistry and hence can be ignored for the purposes of this discussion. 

Schwartz and Freiberg (1981) have calculated the rates of these processes for S02 and expressed them in terms of characteristic times t, which for Step 5, chemical reaction, is the natural lifetime discussed in Section 5.A.I.C. For Steps 1-4, the characteristic time is the time to establish the appropriate steady state or equilibrium for the process involved for example, for Step 1, it is the time to establish a steady-state concentration of the gas in the air surrounding the droplet. Seinfeld (1986) discusses in detail calculation procedures for these characteristic times. A brief summary of the results of Schwartz and Freiberg (1981) for Steps... 

To consider gas molecules as isolated from interactions with their neighbors is often a useless approximation. When the gas has finite pressure, the molecules do in fact collide. When natural and collision broadening effects are combined, the line shape that results is also a lorentzian, but with a modified half-width at half maximum (HWHM). Twice the reciprocal of the mean time between collisions must be added to the sum of the natural lifetime reciprocals to obtain the new half-width. We may summarize by writing the probability per unit frequency of a transition at a frequency v for the combined natural and collision broadening of spectral lines for a gas under pressure ... 

If the exposure had been much smaller, the risk calculation would have been less direct and less certain. For purposes of risk reduction in public health, we may choose to err on the pessimistic side in risk estimations. For purposes of attribution, however, we want to make best estimates. Most of the numbers in Ikble 8.4 are overestimates of the risks. For radiation-induced leukemia, as described in Section 6.1.2, the best dose-incidence model might be lineai>quadratic and not linear. Thus, someone exposed to 50 mSv (5 rem) might be considered, on a linear extrapolation basis, to have a radiation related lifetime risk of cancer mortality of 10 (2 x 10 Sv 2 x 10 rem ), or a lifetime risk of mortality from leukemia of approximately 1.5 x 10 (0.3 x 10" Sv 0.3 X 10 rem ). The natural lifetime risk of mortality from leukemia other than chronic lymphocytic leukemia is approximately 56 x 10 . Therefore, the percent attribution to radiation according to the linear model would be ... 

At — 20 °C. the lifetime in both solvents was approximately the same, as was the lifetime at 77°K. (which was assumed to be the natural lifetime ro). In view of the high viscosity of glycerol at — 20°C., it is reasonable to assume that impurity quenching is negligible, and the same must therefore have been true for ethanol at this temperature. The ratio of ro to r at — 20 °C. is equal to (kp + kh)/kp. The values of the rates of intersystem crossing from triplet to ground state (fa) at —20° were thus derived (see Table I). They are apparently independent of viscosity, a... 

In Chap. 2 and 3, the motion of two reactants was considered and a diffusion equation was derived based upon the equation of continuity and Fick s first law of diffusion (see, for instance, Chap. 2 and Chap. 3, Sect. 1.1). When one reactant (say D) can transfer energy or an electron to the other reactant (say A) over distances greater than the encounter separation, an additional term must be considered in the equation of continuity. The two-body density n (rj, r2, t) decays with a rate coefficient l(r, — r2) due to long-range transfer. Furthermore, if energy is being transferred from an excited donor to an acceptor, the donor molecular excited state will decay, even in the absence of acceptor molecules with a natural lifetime r0. Hence, the equation of continuity (42) becomes extended to include two such terms and is... 

Wilemski and Fixman [51] have also discussed the excitation of the fluorophor with steady-state light, at a rate F per second. When the excited fluorophor decays with a natural lifetime, r, the probability that the fluorophor is excited is [Pg.276]

Some fluorescence lifetimes are observed in ps times, although these are unusual cases. In organic molecules the Sj—S0 fluorescence has natural lifetimes of the order of ns but the observed lifetimes can be much shorter if there is some competitive non-radiative deactivation (as seen above for the case of cyanine dyes). A few organic molecules show fluorescence from an upper singlet state (e.g. azulene) and here the emission lifetimes come within the ps time-scale because internal conversion to S and intersystem crossing compete with the radiative process. To take one example, the S2-S0 fluorescence lifetime of xanthione is 18 ps in benzene, 43 ps in iso-octane. 

Since the natural lifetime of emission, r°, is equal to l/key Equation 13.19 may... 

There are two parameters which appear to be of major importance in determining the occurrence and observability of electron solvation. The first is the polarizability of the liquid, as expressed by its dielectric behavior. On the basis of theory, which will be discussed later, a necessary condition for electron solvation appears to be that the static dielectric constant of the liquid be substantially greater than one. The second parameter, which seems at present to be unpredictable, is the natural lifetime of the solvated electron—i.e., its lifetime with respect to reaction with the solvent itself. 

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