Lifetime between collisions

Figure Y shows the H NMRD profiles of water solutions of Fe(H20)g in 1 M perchloric acid at 298 K and in a glyceroTwater mixture (36). Only one dispersion is observed at about Y MHz. It corresponds to a correlation time Tc 3 X 10 s. The small increase of relaxivity above 20 MHz indicates that a field dependent is influential in the determination of at high field (see also Section II. C). From the fit to the SBM theory, is estimated to be around 5 x 10 s at room temperature, a value commonly found for small complexes in water solution and of the order expected for the mean lifetime between collisions with solvent molecules. The fit also provides a value for A = 0.095 cm , so that t o is calculated to be 9 x 10 s at room temperature. By increasing the viscosity through glycerol water mixture, it is shown that the relative influence of tb on with respect to becomes lower and lower with the increase in relaxivity in the high-field region being more and more evident. The fit of the profile acquired in the glycerol solution, performed by assuming that r, Ag, and A are not affected by the presence...

For an intrinsic semiconductor with refractive index n, where the mean lifetimes between collisions are rn and 77 for electrons and holes, respectively, it leads to an energy-dependent free-carrier absorption coefficient Kfc given by the contribution of the free electrons and holes ... 

Spectral lines are fiirther broadened by collisions. To a first approximation, collisions can be drought of as just reducing the lifetime of the excited state. For example, collisions of molecules will connnonly change the rotational state. That will reduce the lifetime of a given state. Even if die state is not changed, the collision will cause a phase shift in the light wave being absorbed or emitted and that will have a similar effect. The line shapes of collisionally broadened lines are similar to the natural line shape of equation (B1.1.20) with a lifetime related to the mean time between collisions. The details will depend on the nature of the intemrolecular forces. We will not pursue the subject fiirther here. 

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... 

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 ... 

By lifetime we mean the average time that an excess carrier exists before annihilation by a carrier of the opposite sign. This is as opposed to relaxation time, the average time between collisions, or trapping time, the average time in a band before being trapped. We have used the same symbol, t, to represent both the lifetime and the relaxation time because this symbol... 

To take one example, let us consider the effects of rotational relaxation in BrF. The excited 53FI(0+) state in BrF is crossed by another 0+ state which leads to predissociation of the B state in vibrational levels 7 and 6. The initial study of the dynamics of the B state was carried out in a discharge flow system where the minimum operating pressure was 50 m Torr. The gas-kinetic collision rate coefficient at 298 K for He + BrF(B) collisions is 4.4 x 10-10 cm3 molecule-1 s-1. Thus, at the minimum pressure of 50 m Torr, the average time between collisions of excited BrF molecules and helium buffer gas is 1.5/us. This time is short compared with the radiative lifetime of BrF (42—56/ns [43]) and therefore significant redistribution in the excited state can occur before it radiates. 

Drude [3] proposed an equation of motion for free electrons of mass m, charge — e, and classical electron momentum p, moving in a constant electrical field E, and undergoing collisions with each other and/or the ionic cores, with a lifetime (t) between collisions ... 

Sigal studied the benzene d-6 sensitized isomerization of butene-2 at pressures below 0.1 mm., where the interval between collisions is long relative to the fluorescence lifetime. The butene-2 isomer concentration was monitored by long-path infrared spectrometry. The data are consistent with a kinetic scheme based on collisions being rate determining for intersystem crossover at low pressures. 

In 1953 Dicke [18] proposed the use of an inert buffer gas such as helium to reduce the first order Doppler width of a radiating system by partially averaging the velocities when the times between collisions are short compared to the radiative lifetime. 

Time, lifetime between strong collisions H-bond energy... 

Collisions between molecules are the greatest cause of line broadening at the pressures normally employed for MMW spectrometry. In the Lorentz theory (ref 2, p. 338) the lifetime of the rotational state involved in the transition is ended abruptly by collision with another molecule which stops the rotation. When the molecule starts to rotate again, its phase with respect to the other molecules is random. For an assembly of molecules this will give rise to an absorption line profile with a FWHM of Xjlm, where r is the mean time between collisions. This is the linear sum of two terms, one for the upper and one for the lower state, having the shape of the Lorentz function (Figure 1.4) when Av [Pg.12]

The first sum 2 describing the gain is restricted to the discrete levels below Eq. Eq is defined by the fact that all states with , > E ar negligibly populated in the low pressure limit, because the dissociative lifetimes are shorter than the time between collisions. The second sum also includes transitions from discrete states < < Eg to states above the energy threshold. 

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