Exponential decay law

While it is not feasible to measure exponential decay of resonance states in the environment of a molecular beam experiment, in theoretical work the exponential decay law provides a necessary condition that a proposed state, generated by some method, is in fact a resonance state. Furthermore, the rate of exponential decay provides probably the most accurate method for the numerical determination of the lifetime. 

For 8,9,10,11-tetrahydro-BA the lifetimes measured with and without DNA are the same within experimental error ( 2 nsec). Without DNA the decay profile of trans-7,8-dihydroxy-7,8-dihydro-BP follows a single-exponential decay law. With DNA the decay profile has a small contribution from a short-lived component (x = 5 nsec) which arises from DNA complexes. This indicates that Equation 1 is not strictly valid. However, the analysis of the decay profile with DNA also indicates that the short lifetime component contributes less than 11% to the total emission observed at [POa ] 5 x 10 M. Under these conditions Equation 1 still yields a good approximate value to the association constant for intercalation. 

In fact, an important advance in the phosphorescence theory was realized by Wiedemann in 1889, stating that a phosphor exists in two forms, a stable one, A, and an unstable one, B. Light absorption brings along conversion of form A to B, which then returns to A emitting light. This hypothesis was in agreement with the exponential decay law as postulated years before by Becquerel, but who did not provide any information about the nature of both forms [5],... 

Suppose one has a fluorescent system whose emissions follow a simple exponential-decay law and is excited with a periodic function 7(r). 

Fits to single (one floating parameter) and double (three floating parameters) exponential decay laws are always poorer as judged by the x2 and residual traces. In the case where we assume that there is some type of excited-state process (e.g., solvent relaxation) we find that the spectral relaxation time is > 20 ns. This is much, much greater than any reasonable solvent relaxation process in supercritical CF3H. For example, in liquid water, the solvent relaxation times are near 1 ps (56). 

It is known that Silicalite in particular, and zeolites in general contain several different sites (24) the inhomogeneity of adsorption sites is largely responsible for the non-exponential decay law. Figure 2 illustrates the decay observed in the case of 8-phenylpropiophenone in Silicalite. 

The waiting time distribution can be analyzed in a simple model, assuming each channel obeys a simple exponential decay law for its switching between the open and closed states. Consider a single channel and let Po(t) and Pi (t) be the probability that the channel is open and closed, respectively, at a certain point t in time. Then Po and Pi evolve according to ... 

This method is commonly used with radioisotope tracers that undergo radioactive decay. The tracer concentration will decrease over time following an exponential decay law ... 

We recorded the EL decay patterns when a voltage pulse of 10 /u.sec duration was applied to the sample at room temperature (Figure 7.6A). We found that decay patterns of turn-on and turn-off EL spikes are similar initial fast-decay part followed by slower decay. The observed curves were fitted to bi-exponential decay law with characteristic times t = 0.07 xsec and t2 = 1.15 /rsec (Figure 7.6B). The drastic difference in time scales indicates the presence of two different mechanisms playing role in transient EL. Thus we may consider two different time scales for counter-field build-up, which presumably controls the EL spike decay. However, these time scales should be the same for the turn-on and turn-off spikes. 

In theory, the removal of fine particles by collision processes results in chemical concentrations in the air mass following an exponential decay law. In actual clouds, both collision and nucleation may contribute to particle removal, and their combined effects often are lumped into a single scavenging coefficient, A [T 3] ... 

Using the standard Wigner-Weisskopf procedure [Cohen-Tannoudji 1992 Landau 1997], we find that the decay rate of the initial state, obeying the exponential decay law bi(t) 2 = exp(—Wt), is equal to... 

The efficiency of long-distance energy transfer and its gradual decrease with intercomponent distance is usually described by an exponential decay law of the type Fab = F) exp (-yJtAe), where y is denoted the attenuation factor and 1 ab is the spatial separation between the redox sites. In the case of ligand-bridged complexes is set as the distance between the metal centres. 

The Beer-Lambert exponential decay law for conventional (singlephoton) absorption results from the elementary relation... 

Although no convincing proof, either experimental or theoretical has been given for the exponential decay law, it is universally used,... 

It was implicit in the last section and indeed in all the discussion so far that the decay of an autoionising resonance should be exponential in time. This may seem to be obvious, and is indeed verified with good accuracy in experiments, but there are also fundamental reasons for believing that it is not strictly correct [280] according to quantum mechanics, the exponential decay law is violated for very long times, where the probability of nonexponential decay eventually prevails, a fact which has been recognised in nuclear and particle theory [282], but has not so far been verified experimentally. 

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