Mean lifetime

The Mean Lifetime of the Active Metal-Polymer Bond... 

The mean lifetime of the active metal-polymer bond in one-component catalysts is limited by the following transfer processes (69, 76, 159) ... 

The mean lifetime of the metal-polymer can be evaluated by the values of the polymerization degree (Pw) and Kp ... 

Marcus cross relation, 243-246 Marcus theory, 239-248 Mean lifetime (see Lifetime)... 

Where the mean lifetimes of the growing chains are short, narrower MWD s are produced than in a batch or plug flow reactor but the minimum Dp is 1.5 or 2.0 according to the mechanism of termination. Dp independent of Up and... 

Resonant y-ray absorption is directly connected with nuclear resonance fluorescence. This is the re-emission of a (second) y-ray from the excited state of the absorber nucleus after resonance absorption. The transition back to the ground state occurs with the same mean lifetime t by the emission of a y-ray in an arbitrary direction, or by energy transfer from the nucleus to the K-shell via internal conversion and the ejection of conversion electrons (see footnote 1). Nuclear resonance fluorescence was the basis for the experiments that finally led to R. L. Mossbauer s discovery of nuclear y-resonance in ir ([1-3] in Chap. 1) and is the basis of Mossbauer experiments with synchrotron radiation which can be used instead of y-radiation from classical sources (see Chap. 9). 

Fig. 2.2 Intensity distribution /( ) for the emission of y-rays with mean transition energy Eq. The Heisenberg natural line width of the distribution, F = S/t, is determined by the mean lifetime T of the excited state (e)...

The energy q of a nuclear or electronic excited state of mean lifetime t cannot be determined exactly because of the limited time interval At available for the measurement. Instead, q can only be established with an inherent uncertainty, AE, which is given by the Heisenberg uncertainty relation in the form of the conjugate variables energy and time,... 

The relevant time interval is on the order of the mean lifetime, At x. Consequently, ground states of infinite lifetime have zero uncertainty in energy. 

Weisskopf and Wigner [2] have shown that the natural width of the emission and the absorption line is readily determined by the mean lifetime x of the excited state because of the relation (note the equal sign) ... 

Nuclear resonance absorption for the 136 keV transition has been established by Steiner et al. [174]. The authors used a metal source and an absorber of metallic tantalum to determine the mean lifetime of the 136 keV level from the experimental line width ( 52.5 mm s for zero effective absorber thickness) and found a value of 55 ps. This has been the only report so far on the use of the 136 keV excited state of Ta for Mossbauer experiments. 

Typically, the insertion induces sharp variation of the membrane profile at the distances 0.5-1.0nm from the membrane-peptide interface [79-82]. The steepness of this perturbation indicates that the short-A, behavior of membrane moduli must be important in the estimates of the elastic energy. In addition, a peptide inserted in a membrane almost certainly perturbs the membrane s elastic moduli in the immediate vicinity of the inclusion. Both these effects, membrane nonlocality and nonuniform modification of elastic properties by insertions, might play an important role in resolving the contradiction between the local calculations [80] and the experimental data for the mean lifetime of a gramicidin channel [81,109,110]. ... 

Henry constant F can be evaluated by the method of Tsvitering and Krevelyn (see [105]) based on the concept of mean lifetime of a molecule absorbed on a surface proposed by De Boer [106]. The number of molecules adsorbed on a surface is... 

Fig. 1. Mean lifetimes of a single water molecule in the first coordination sphere of a given metal ion, th2o> and the corresponding water exchange rate constants, h2o- The tall bars indicate directly determined values, and the short bars indicate values deduced from ligand substitution studies. References to the plotted values appear in the text.

As defined here, kex is also the rate constant for the exchange of all n solvent molecules because each particular solvent molecule (for example, solvent molecule number 2, if the solvent molecules are numbered from 1 to n) exchanges at the same rate. The mean lifetime of a particular solvent molecule in the first coordination sphere, rex = llke%, is the same for each of the n coordinated solvent molecules. Thus, the probability of exchange of each particular solvent molecule is the same as the probability of exchange for all n solvent molecules, but is n times smaller than the probability of exchange of one unspecified solvent molecule. 

Closed periods due to channel blockages have, from the same rule, a mean lifetime of ... 

Hint The reciprocal of the mean lifetime of an individual state is the sum of the rates (in sec1) for leaving that state. 

NS (general population) Developmental Impaired motor developmental status in 6-year-old children (Cincinnati cohort) 2 9.0 (mean lifetime) Dietrich et al. 1993b... 

Photophysical Processes in Pi butyl 4,4 -Sulfonyldibenzoate (4,4 -SD). The UV absorption spectra of dibutyl 4,4 -sulfonyl-dibenzoate (4,4 -SD) in both HFIP and 95% ethanol showed similar absorptions. The corrected excitation and emission fluorescence spectra of 4,4 -SD in HFIP at 298°K showed a structured excitation with band maxima at 236, 286, and 294 nm and a structured emission exhibiting band maxima at 322, 372, and 388 nm. The uncorrected excitation and phosphorescence spectra of 4,4 -SD in a 95% ethanol glass at 77°K displayed excitation band maxima at 268, 282, and 292 nm with strong phosphorescence emission with band maxima at 382, 398, and 408 nm with a mean lifetime (t) of 1.2 sec. 

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