Life-time, excited state

For fluorescent compounds and for times in die range of a tenth of a nanosecond to a hundred microseconds, two very successftd teclmiques have been used. One is die phase-shift teclmique. In this method the fluorescence is excited by light whose intensity is modulated sinusoidally at a frequency / chosen so its period is not too different from die expected lifetime. The fluorescent light is then also modulated at the same frequency but with a time delay. If the fluorescence decays exponentially, its phase is shifted by an angle A([) which is related to the mean life, i, of the excited state. The relationship is... 

Because luciferyl adenylate emitted a red chemiluminescence in the presence of base, coinciding with the red fluorescence of 5,5-dimethyloxylucferin, the keto-form monoanion Cl in its excited state is considered to be the emitter of the red light. Thus, the emitter of the yellow-green light is probably the enol-form dianion C2 in its excited state, provided that the enolization takes place within the life-time of the excited state. Although the evidence had not been conclusive, especially on the chemical structures of the light emitters that emit two different colors, the mechanism shown in Fig. 1.12 was widely believed and cited until about 1990. 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

For nuclear y-resonance absorption to occur, the y-radiation must be emitted by source nuclei of the same isotope as those to be explored in the absorber. This is usually a stable isotope. To obtain such nuclei in the desired excited meta-stable state for y-emission in the source, a long-living radioactive parent isotope is used, the decay of which passes through the Mossbauer level. Figure 3.6a shows such a transition cascade for Co, the y-source for Fe spectroscopy. The isotope has a half-life time //2 of 270 days and decays by K-capmre, yielding Fe in the 136 keV excited state ( Co nuclei capmre an electron from the K-shell which reduces the... 

For a two-level EPR system this reads as follows when the life time of a molecule in the excited state is known accurately, then the energy of the excited state is uncertain. In other words, if spin-lattice relaxation from the excited state to the ground state would be infinitely fast, then the excited state life time would be exactly equal to zero seconds, and the uncertainty in the excited state energy would be maximal, which would lead to an EPR spectrum broadened beyond detection. Lowering the... 

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

The life-time of the photo chemically generated excited state should be shorter than the dissociation of the ligand-receptor complex, but long enough to spend sufficient time in a close proximity to a target site for covalent linkage. 

The excited states used as the photoreductant in the CoPc are difficult to determine. No long-lived excited state is known for CoPc, and, therefore, we are unable to identify the states involved in the electron transfer reaction. The longest living excited state in CoPc is expected to have a life time on the neuiosecond time scale by analogy with other first row (open shell) transition metal phthalocyanines (33). 

The lowest energy excited triplet state of FePc is known to have a life time of about 45 nanoseconds (33) and we expect the life time of the lowest energy excited triplet state of FePc(Im )2 Also to be in the same time scale. Electrochemical oxidation at the phthalocycuiine ligand oxidation... 

In the decay chain of let Ni = N2 = Th, and /V3 = Pa, derive how the concentration of /V3 would change with time. You may ignore different excitation states of Pa, and simplify the decay of Pa as one-step decay to with a half-life of 1.1 7 min. 

The level pi/2 is coimected with the ground level f7/2 by an E4 transition and with the low-lying level ps/2 by an E2 transition. The levels ps/2 and fj/2 are coimected by the E2 transition. One could also consider the magnetic transitions between these levels. The life-time for the isolated nucleus in the excited states is of the order of 10. Following papers [3, 20], let us assume that a proton moves in an effective field of the core ... 

Neutral hydrogen in the magnetic fields in interstellar space may have excited state life times that is measured in years—in contrast hydrogen in liquid water at room temperature display excited state lifetimes of 3 seconds. Why is this How come that the liquid water can lead to a more efficient relaxation of the proton... 

Consider now a one-dimensional lattice of parameter /. The distance of each atomic jump depends on the rate of de-excitation once the adatom is excited and is translating along the lattice. This de-excitation process can be described by a characteristic life time r in the symmetric random walk, as in many other solid state excitation phenomena. The initial position of the adatom is taken to be the origin, denoted by an index 0. The adatom accomplishes a jump of distance il if it is de-excited within (i — i)l and (i + i)l, where / is the lattice parameter, or the nearest neighbor distance of the one-dimensional lattice, and i is an integer. The probability of reaching a distance il in one jump is given by... 

Life times of excited electronic states of atoms and... 

The energy of a single photon is obviously insufficient to ionize an organic compound. As early as the nineteen forties (3, 4), however, it -was observed that Wurster blue cation radical is produced by photoirradiation of 3-methylpentane glass containing N,N-tetramethyl p-phenylenediamine (TMPD) at 77° K. The recent detailed study of this system by electric conductivity measurement (5, 6) and electronic spectroscopy (7) provided conclusive evidence that the ionization is brought about via excitation to the triplet state followed by successive photoabsorption at the triplet state. This mechanism is supported by the facts that the life-time of the photochemical intermediate is identical with that of phosphorescence and the formation of Wurster blue, and that phosphorescence is inhibited in the presence of triplet scavengers. 

PAD (perturbed angular distribution) is a variation of PAC with nuclear excitation by a particle beam from an accelerator. QMS is quasielastic MdBbauer-spectroscopy, QNS is quasielastic neutron spectroscopy. For MOBbauer spectroscopy (MS), perturbed angular correlation (PAC), and /J-nuclear magnetic resonance (/3-NMR), the accessible SE jump frequencies are determined by the life time (rN) of the nuclear states involved in the spectroscopic process. Since NMR is a resonance method, the resonance frequency of the experiment sets the time window. With neutron scattering, the time window is determined by the possible energy resolution of the spectrometer as explained later. 

Finally, another mode of line broadening is due to the motion of the nucleus, reflecting the mobility (or diffusivity) of the resonant atom. That is, if the nucleus emits or absorbs a y ray while the nucleus is undergoing a movement from site A to site B, then a broadening of the y-ray distribution results if the time scale for this motion is of the order of the nuclear decay time (79). The time scale for the y-ray emission or absorption process is the life time of the excited state, rn ( 10-8 sec) the resolution of the y ray is its wavelength k ( 0.1 nm) thus, effective diffusivities of order k2/r ... 

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