Lifetime of excited

It can be assumed that in cycloadditions only one reactant is electronically excited, in view of the short lifetimes of excited species in solution and the consequently low probability of a collision between two excited molecules. Also, the cycloadditions are conducted with light of wavelengths above 2800 A... 

Direct evidence for the competition of two counteracting contributions to the transient absorption changes stems from the temporal evolution of the transmission change at 560 nm. From Figure 10-3 it can be seen that the positive transmission change due to the stimulated emission decays very fast, on a time scale of picoseconds. On the other hand the typical lifetime of excitations in the 5, slate is in the order of several hundred picoseconds. Therefore, one has to conclude that the stimulated emission decay is not due to the decay of the. Sj-population (as is typically the case in dye solutions). The decay is instead attributed to the transiei.i build up of spatially separated charged excitations that absorb at this wavelength. 

Iq/I — t — KgI0 [Q], in which Kg is the bimolecular rate constant of interaction of quencher Q with the excited states of the PCS, t is the lifetime of excited molecules with no quencher, I0 is the quantum yield of fluorescence in the absence of the quencher, and I is the quantum yield of fluorescence in the presence of the quencher. 

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... 

Solutions of surfactant-stabilized nanogels share both the advantage of gels (drastic reduction of molecular diffusion and of internal dynamics of solubilizates entrapped in the micellar aggregates) and of nonviscous liquids (nanogel-containing reversed micelles diffuse and are dispersed in a macroscopicaUy nonviscous medium). Effects on the lifetime of excited species and on the catalytic activity and stability of immobilized enzymes can be expected. 

The ratio F/Eq of width F and the mean energy of the transition Eo defines the precision necessary in nuclear y-absorption for tuning emission and absorption into resonance. Lifetimes of excited nuclear states suitable for Mossbauer spectroscopy range from 10 s to s. Lifetimes longer than 10 s produce too... 

Upon illumination, photons having energy higher than the band gap (eg = ec — v) are absorbed in the semiconductor phase and the electron-hole-pairs (e //i+) are generated. This effect can be considered equivalent to the photoexcitation of a molecule (Fig. 5.57) if we formally identify the HOMO with the ec level and LUMO with the v level. The lifetime of excited e //i+ pairs (in the bulk semiconductor) is defined analogously as the lifetime of the excited molecule in terms of a pseudo-first-order relaxation (Eq. 5.10.2). 

Of the different kinds of forbiddenness, the spin effect is stronger than symmetry, and transitions that violate both spin and parity are strongly forbidden. There is a similar effect in electron-impact induced transitions. Taken together, they generate a great range of lifetimes of excited states by radiative transitions, 109 to 103 s. If nonradiative transitions are considered, the lifetime has an even wider range at the lower limit. 

Recognise features which relate to the elucidation of the nature, energy and lifetime of excited-state species. 

A lifetime of 27 ns at room temperature (in the absence of quencher, but in the presence of 0.025 M OH ) has been calculated from a linear Stem-Volraer plot using 9-fluorenone as quencher i >. In general, lifetimes of excited substrates are dependent on the nucleophile concentration. Quenching of the excited state by the nucleophile probably takes place by either formation of a a-complex or simply return to ground state starting material. 

With this method lifetimes of excited states in diatomic alkali molecules have been measured 122,123) means of the apparatus in Fig. 6. 

Another technique for measuring the lifetime of excited activator atoms in solid-state lasers has been published by Gilrs h If the pulsed laser is operated close above threshold, only a single spike (i.e. a short pulse of induced emission) appears, whereas many spikes are emitted when the laser ist running well above threshold. This... 

A study by Petrich et al. (1987) on the fluorescence lifetimes of excited tryptophans in azurin has proved exceptionally interesting, especially in light of the studies to be reviewed below on ascorbate oxidase. By comparing the lifetimes of tryptophan fluorescence of three azurins— Az-Pae (only one tryptophan, Trp-48), A.faecalis [Az-Afe (one tryptophan, Trp-118)] and A. denitrificans [Az-Ade (two tryptophans, Trp-48), and Trp-118)] in both holo and apo forms—the authors found that (1) there is virtually no fluorescence quenching in the apo forms (2) the decay of... 

It has further tacitly been assumed that photocurrents can only be induced by excited dye molecules in the absorbed state on the electrode surface. Although one would expect that excited dye molecules in solution should be able to exchange electrons with the electrode by approach from the solution 2e>, the lifetime of excited molecules is too short and the excess of adsorbed molecules over the amount of dissolved ones in a layer of > -7 cm thickness is too high as to detect charge injection from dissolved molecules, besides that from adsorbed ones. 

LIFETIMES OF EXCITED ELECTRONIC STATES OF ATOMS AND MOLECULES... 

Since the lifetimes of excited states are small, by applying the steady state approximation, respective concentrations are obtained,... 

Determination of decay constants or lifetimes of excited states. Decay... 

The natural broadening which results from the finite lifetime of excited states. The energy of a state and its lifetime are related by the principle of uncertainty (section 2.2) which implies a minimal spread of the actual energy of any excited state of finite lifetime this gives an absolute limit to the width of atomic spectral lines. 

In a rigid system such as a glass or a polymer, the molecules M and Q are distributed at random and do not move, at least within the lifetimes of excited states. The distance distribution follows the Perrin law which is based on a very simple model. Take any excited molecule M, and ask if one quencher molecule Q happens to be within the volume of action defined by the centre-to-centre distance r. Should any molecule Q be found within this action volume, the molecule M is quenched instantaneously, but if there is no quencher Q within this space, then M emits as if no quenchers at all were present. Figure 3.39 gives a picture of the Perrin model. The mathemat-... 

The situation for reactions in solids is much more complex and is treated in a separate section (4.7.4, p. 153). Physical diffusion of molecules can be neglected within the lifetimes of excited states, but exciton interactions can become important. These have no counterpart in dark reactions and can lead to unusual photochemical properties in crystals and polymers. 

Diffusion of molecules in rigid glasses is negligible within the lifetimes of excited molecules, so that the main reactions are unimolecular dissociations and isomerization. These are rather similar to liquid state reactions, but the fragments cannot separate through diffusion and often recombine to restore the reactants. There are exceptions when the photoproducts are in fact more stable than the reactants, as in the case of photoeliminations. 

Although actual diffusion in solids is not significant within the lifetimes of excited molecules, bimolecular reactions can take place when molecules are kept in close contact in a polymer or crystal lattice. In some crystals the molecules are ideally spaced for cycloaddition, as in the example of cinnamic acid (Figure 4.80). The geometrical requirements are quite stringent and the reaction cannot proceed if the interplane separation of the molecules exceeds about 4A. 

Obviously, the various electronically excited states of an atomic or molecular ion vary in their respective radiative lifetime, t. The probability distribution applicable to formation of such states is thus a function of the time that elapses following ionization. Ions in metastable states, which have no allowed transitions to the ground state, are most likely to contribute to ion-neutral interactions observed under any experimental conditions since these states have the longest lifetimes. In addition, the experimental time scale of a particular experiment may favor some states over others. In single-source experiments, short-lived excited states may be of greater relative importance than in ion-beam experiments, in which there is typically a time interval of a few microseconds between ion formation and the collision of that ion with a neutral species, so that most of the short-lived states will have decayed before collision. There are several recent compilations of lifetimes of excited ionic states.lh,20 ,2,... 

The energy levels and eigenfunctions, obtained in one or other semi-empirical approach, may be successfully used further on to find fairly accurate values of the oscillator strengths, electron transition probabilities, lifetimes of excited states, etc., of atoms and ions [18, 141-144]. 

MBPT significantly improves the electron transition wavelengths, line and oscillator strengths, transition probabilities as well as the lifetimes of excited levels. Therefore, it seems promising to generalize such an approach to cover the cases of more complex electronic configurations having several open shells, even with n > 2. 

There are numerous needs for precise atomic data, particularly in the ultraviolet region, in heavy and highly ionized systems. These data include energy levels, wavelengths of electronic transitions, their oscillator strengths and transition probabilities, lifetimes of excited states, line shapes, etc. [278]. 

Expressions for a number of main moments of the spectrum may be utilized to develop a new version of the semi-empirical method. Evaluation of the statistical characteristics of spectra with the help of their moments is also useful for studying various statistical peculiarities of the distribution of atomic levels, deviations from normal distribution law, etc. Such a statistical approach is also efficient when considering separate groups of levels in a spectrum (e.g. averaging the energy levels with respect to all quantum numbers but spin), when studying natural widths or lifetimes of excited levels, etc. 

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