Definition of the quantum yield

In thermal kinetics the rate is proportional to concentration in the most simplest mechanism according to eq. (1.1). The proportionality constant is the rate constant k. In photokinetics, the equivalent proportionality constant is, according to eq. (1.2), the so-called photochemical quantum yield. In the literature, some different definitions of quantum yields are discussed but not always clearly distinguished. Therefore the problems with three different definitions are discussed here. Two others related to the partial reactions and independent of the time of the reaction are given in Section 2.1.2. 

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The definition of the quantum yield of a photochemical reaction has been considered in section 4.1 as the ratio of the number of molecules transformed to the number of photons absorbed... 

Tab. 3.7 Definitions of the quantum yield"

One of the most important features of a photoreaction is the value of the quantum yield ( )i of compound i, which is the quantifying answer to the question How effective In principle, the quantum yield is the ratio of the number of reacting molecules to the number of quanta absorbed. In praxis there are several definitions of the quantum yield true (only light absorbed by the reactant is considered) and apparent (there are other absorbers present), differential (at the moment ) and integral (mean). In the previous rate equation, ( )e and (j) are the true differential yields. The monoexponential kinetics of Equation, 1.2 or 1.4 allow one to determine the yields in systems where the starting solution is already a mixture of E- and Z-forms (which can happen easily if the E-form is not prepared under strict exclusion of light). It turns out, however, that the yalues of the Z —> E quantum yield are especially sensitive to small errors in the E values. 

Taking up the photonic efficiency in the form of eq. 5.97, for the case where Q[Cat] (here Q is a constant), i.e. for high loading in photocatalyst Cat, one obtains = R lpox which is precisely the definition of the quantum yield (j) (see... 

In order to measure quantum yields it is necessary to directly measure the intensity of the electromagnetic radiation. From our definitions of the quantum yields, it is important to precisely quantify the number of both the incident and the emitted photons. Devices such as thermistors, thermopiles, bolometers, and photovoltaic cells are available for measuring these photon intensities, but they are not commonly used because of the difficulties encountered when attempting to obtain consistently reliable results. 

Quantum Yield Definitions. Having in mind that the population of the excited state is N (c) or N (0), correspondingly, we can define the absolute values of the quantum yields for these cases as follows ... 

Just as there are a number of different definitions of "primary photochemical processes," so also does "primary quantum yield" have different meanings in the various photochemical references. It may be defined, for example, as the sum of the quantum yields of all of the events which lead to dissociation or reaction of the excited molecule. In Figure 1, these would be events 24, 15, and 14. An alternate definition is that each one of the individual quantum yields in that sum is itself one of the primary quantum yields. 

The result of such a process would be that two electrons are cycled twice through the PQ, and the ratio of H /e between PS II and PS I would be higher than one. This, if definitively confirmed, would be of great importance from the point of view of understanding the coupling of electron transport to the synthesis of ATP, and of the quantum yield of photosynthesis (see discussion under photophosphorylation). 

The definition of a quantum yield for a given process x, (1>x(X) = nx/nv, was given in Equation 2.24, Section 2.1.7. Here nx is the amount of photochemical or photophysical events x that occurred during irradiation and Hp is the amount of photons at the irradiation wavelength X that were absorbed by the reactant. Both nx and Hp are measured in moles or einsteins (1 einstein = 1 mol of photons) and the dimension of [Pg.110]

The efficiency of any photophysical or photochemical process is a function of both the properties of the reaction environment and the character of the excited state species. The fundamental quantity which is used to describe the efficiency of any photo process is the quantum yield (0) it is useful in both quantifying the process and in elucidating the reaction mechanism. Quantum yield has the general definition of the number of events occurring divided by the number of photons absorbed. Therefore, for a chemical process 0 is defined as the number of moles of reactant consumed or product formed divided by the number of einsteins (an einstein is equal to 6.02 X 10 photons) absorbed. Since the absorption of light by a molecule is a one-quantum process, then the sum of the quantum yields for all primary processes occurring must be one. Where secondary reactions are involved, however, the overall quantum yield can exceed unity and for chain reactions reach values in the thousands. When values of 0 are known or can be measured for a specific photochemical reaction the rate can be determined from ... 

Consider a Stern-Volmer-type analysis of a system such as in Figure 16.8, but with one additional process, the conversion of A to photochemical product B with rate constant Show that a plot of relative quantum yield for product formation vs. [Q] is linear and can give a value for the lifetime of A if we assume a value for C,- The definition of relative quantum yield is the quantum yield in the absence of quencher divided by the quantum yield in the presence of quencher. 

For phenomena involving electrons crossing the phase boundary (photocurrents, electron photoemission), the quantum yield j of the reaction is a criterion frequently employed. It is defined as the ratio between the number of electrons, N, that have crossed and the number of photons, that had reached the reaction zone (or, in another definition, the number of photons actually absorbed by the substrate) J=N /N. ... 

The solute-solvent system, from the physical point of view, is nothing but a system that can be decomposed in a determined collection of electrons and nuclei. In the many-body representation, in principle, solving the global time-dependent Schrodinger equation with appropriate boundary conditions would yield a complete description for all measurable properties [47], This equation requires a definition of the total Hamiltonian in coordinate representation H(r,X), where r is the position vector operator for all electrons in the sample, and X is the position vector operator of the nuclei. In molecular quantum mechanics, as it is used in this section, H(r,X) is the Coulomb Hamiltonian[46]. The global wave function A(r,X,t) is obtained as a solution of the equation ... 

The preceding treatment assumed, for simplicity, that the quantum yield of the isolated dipole (i.e., at z= oo) was 100%. Here we assign it a more general value of qQ. The following definitions are useful ... 

Hence the quantum yield of fluorescence 4> n the absence of any external quenching is, from definition, (5.28)... 

Among the still unanswered questions of the scheme in Figure 14 are the number of steps between I w and I 2, a definitive characterization of the chemical nature of all reaction steps, and the elucidation of the relatively slow processes which thermally regenerate Pr from the intermediates and thus cause the difference of 0.35 between the quantum yields of

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Among the several examples of photoelectron producing complexes, Fe(CN)4-has been studied in greatest detail.170-177) The quantum yield for photoelectron production is strongly wavelength dependent, Table 28,177 and shows definitively... 

Using these results for the definition of the relative quantum yield, we obtain the following formula used in Refs. 125 and 200 ... 

Substituting Eq. (3.461) into Eq. (3.455), we obtain the most general definition of the relative quantum yield resulting from the convolution recipe ... 

Note that the condition r>,u — rK(f) — (f M/c2) follows from the definition of p. Quantum conditions further yield r> 2/z. Note the incompatibility between the force defined in Eq. (50) and the energy law defined by the theory of special theory of relativity. One should note here that Einstein, in his studies of the general theory of relativity, started from the force law... 

Scheme 9 shows in fulgide 39, replacement of the isopropylidene group (IPD) by a dicyclopropylidene group (DCP) caused a bathochromic shift in the absorption band of the 7,7a-DHBF, owing to the partial double-bond character of the DCP group. It is obvious that the steric hindrance of R1 and R2 also affected the max of the colored form. There was not a definite role for the substituent effect on the quantum yield of photoreactions. Table 4.8 shows the absorption spectroscopic data and quantum yields of photoreactions of fulgides with different R R2 groups in toluene. 

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