Radiative lifetime, natural

Just as with quantum yields, there are basically two different kinds of lifetimes, one a result of direct experimental measurement, and the other a derived quantity. These have not always been carefully distinguished. Moreover, the same quantity has been labeled by a variety of names and symbols. For example, radiative lifetime, true radiative lifetime, natural lifetime, intrinsic lifetime, and inherent lifetime all mean the same thing the lifetime a molecule in an excited state would have if there were no steps competing with that of spontaneous emission of radiation. 

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 . 

Table 2 Fluorescence lifetimes ti, natural radiative lifetimes tr, and calculated fluorescence lifetimes for compounds 3, 5, and 11 in different solvents... 

Therefore the lifetime is defined as the time aken for the radiation intensity to decay to 1 [eth qf its original value (Figure 3.14). Thus the natural radiative lifetime is inversely related to the rate constant for the spon-... 

The natural radiative lifetime gives an upper limit to the lifetime of an excited molecule and can be calculated from the integrated absorption intensity. The quantity to be plotted is e vs v if (3.96) is used and... 

The natural radiative lifetime is independent of temperature, but is susceptible to environmental perturbations. Under environmental perturbation, such as collisions with the solvent molecules or any other molecules present in the system, the system may lose its electronic excitation energy by nonradiative processes. Any process which tends to compete with spontaneous emission process reduces the life of an excited state. In an actual system the average lifetime t is less than the natural radiative lifetime as obtained from integrated absorption intensity. In many polyatomic molecules, nonradiative intramolecular dissipation of energy may occur even in the absence of any outside perturbation, lowering the inherent lifetime. 

In general, the natural radiative lifetimes of fluorescence and phosphorescence should be independent of temperature. But the emission intensities may vary due to other temperature dependent and competitive rate constants. 

The rate constant kt for fluorescence emission is related to natural radiative lifetime xN as... 

This is similar to a first-order reaction in chemical kinetics and follows the same law as radioactive decay. The rate constant kv defined in this manner is the natural radiative rate constant which also defines the natural radiative lifetime... 

The natural radiative lifetime is the longest (average) lifetime of an excited molecule. This lifetime is seldom observable in practice because there are other deactivation processes which compete with the luminescence emission. These can be intramolecular, non-radiative transitions (internal conversion or intersystem crossing) or intermolecular quenching processes these are considered in the next sections. 

Since the transition Si — T0 is strongly spin forbidden in such a light molecule, the gas phase lifetime of 02 reaches some 45 min ( ) and is then still shorter than the natural radiative lifetime. In solution the lifetime decreases as a result of quenching actions to somewhere between a few ps and a few ms, depending on the solvent water 2 ps ethanol 5 ps cyclohexane 15 ps chloroform 60 ps. 

Confusion reigns when one examines the definitions of fluorescence and phosphorescence in different areas of the literature of the natural sciences. Many physicists in particular prefer the operational definition in which fluorescence is described as short-lived emission and phosphorescence is long-lived emission (4,15). However, the question arises as to what constitutes short-lived. A possible transition point may be radiative lifetimes, r0 (vide infra), of the order of 10-s to 10 6 sec. 

Dahne and associates (243) assumed that the natural radiative lifetime of the J-aggregates in aqueous solution is the same as that of the dyes adsorbed on silver halide, and used values obtained for solution to estimate the rate constant for sensitization by the adsorbed dye. Based on the data of Muenter and Cooper, they obtained rate values for the adsorbed J-aggre-... 

The analog of Equation 13.20, then, is Equation 13.22, where r is the actual lifetime (as opposed to natural radiative lifetime) of D in the absence of A. 

In the case of 27-29, with the exception of the borderline 28, the radiative rate constant is one order of magnitude lower than the value found for 24-26. This observation, together with the longer values obtained for the natural radiative lifetime (see t°f = tf/< )f)/ is clearly compatible with the forbidden nature of the lowest lying transition/state. The nature of this transition seems to be a 71,71 symmetry forbidden transition/state. 

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