Einstein equivalence law

Each line iri an x-ray series thus has a common initial state and a different final state. (Note contrast with other spectra.) The initial state is characterized by a hole in an energy level. To create this hole, an electron is expelled by collision with a high-velocity electron in electron excitation, and by the absorption of a photon in x-ray excitation. The Einstein equivalence law must be satisfied in either of these elementary processes. 

This gives the number of molecules observed to undergo chemical transformation per quantum of absorbed energy. The quantum efficiency of a reaction may vary from almost zero to about 106. Nevertheless, no matter how large or small c > may be, the Einstein equivalence law holds good. 

As mentioned, the observation of chemical effects of light is as old as mankind itself. Accounts of the earlier history of photochemistry have been presented by several authors. Long erudite lists of reference are of little usefulness, however. Here, it has been chosen to present a brief historic profile based on a document itself of historic value, the introduction written by a great authority, professor Ivan Plotnikov. This well-known Russian-bom scientist published in 1910 a book on photochemistry which was followed in 1936 by a second, much extended, edition of over 900 pages. The view he had on this science, or at least on some aspects of it, in particular the unconditioned refusal of the Stark-Einstein equivalence law, appeared obsolete at the time of the second edition, as it is discussed in Sect. 2.3. However, Plotnikov can certainly not be accused of insufficient knowledge of the matter or of insufficient exploration of the literature and his book is a rich mine of data and thoughts [7]. 

All of these observations were best accommodated by having an electrMiically excited (Bohr) state as the primary photoproduct, to which the Einstein equivalence law applied, and then considering which chemical processes could occur within the lifetime of the excited state, the role of collisions, and the effect of the environment [40, 41]. 

Consideration of the energy involved in the process and of the energy of the quantum absorbed by chlorophyll showed that interaction with at least three excited molecules was required for each molecule of CO2 formed [186]. The investigations by Emil Warburg, fostered also by the formulation of the Einstein equivalence law (1905 in the first formulation see Chap. 2), and by his son Otto gave a quantitative framework to photosynthesis substituting well-defined chemical measurements to qualitative observations [188]. 

Abnormally high quantum yields may occur in photochemical reactions. Einstein s law of photochemical equivalence is the principle that light is absorbed by molecules in discrete amounts as an individual molecular process (i.e., one molecule absorbs one photon at a time). From optical measurements it is possible to determine quantitatively the number of photons absorbed in the course of a reaction and, from analyses of the product mixture, it is possible to determine the number of molecules that have reacted. The quantum yield is defined as the ratio of the number of molecules reacting to the number of photons absorbed. If this quantity exceeds unity, it provides unambiguous evidence for the existence of secondary processes and thus indicates the presence of unstable intermediates. 

Einstein photochemical equivalence law phys chem The law that each molecule taking part in a chemical reaction caused by electromagnetic radiation absorbs one photon of the radiation. Also known as Stark-Elnstein law. Tn.stTn fod o kem-a-kol i kwivo-lons, 16 ... 

In simple instances, therefore, we should expect to find one molecule transformed for each quantum of light absorbed, provided that the light is active at all. This is Einstein s law of photochemical equivalence. 

Walter Noddack (1893-1960) began studying chemistry, physics and mathematics at the University of Berlin in 1912. Having volunteered during World War I, he received his doctorate in 1920 only, under the direction of Nernst on Einstein s law of photochemical equivalence. He became di-... 

Being able to determine [r ] as a function of elution volume, one can now compare the hydrodynamic volumes Vh for different polymers. The hydrodynamic volume is, through Einstein s viscosity law, related to intrinsic viscosity and molar mass by Vh=[r ]M/2.5. Einstein s law is, strictly speaking, valid only for impenetrable spheres at infinitely low volume fractions of the solute (equivalent to concentration at very low values). However, it can be extended to particles of other shapes, defining the particle radius then as the radius of a hydrody-namically equivalent sphere. In this case Vjj is defined as the molar volume of impenetrable spheres which would have the same frictional properties or enhance viscosity to the same degree as the actual polymer in solution. 

In order for a photochemical reaction to occur the radiation must be absorbed, and with the advent of the quantum theory it became possible to understand the relationship between the amount of radiation absorbed and the extent of the chemical change that occurs. It was first realized by A. Einstein (1879-1955) that electromagnetic radiation can be regarded as a beam of particles, which G. N. Lewis (1875-1940) later called photons each of these particles has an energy equal to /iv, where v is the frequency of the radiation and h is the Planck constant. In 1911 J. Stark (1874-1957) and independently in 1912 Einstein proposed that one photon of radiation is absorbed by one molecule. This relationship, usually referred to as Einstein s Law of Photochemical Equivalence, applies satisfactorily to electromagnetic radiation of ordinary intensities but fails for lasers of very high intensity. The lifetime of a moleeule that has absorbed a photon is usually less than about 10 sec, and with ordinary radiation it is unlikely for a molecule that has absorbed one photon to absorb another before it has become deactivated. In these circumstances there is therefore a one-to-one relationship between the number of photons absorbed and the number of excited molecules produced. Because of the high intensity of lasers, however, a molecule sometimes absorbs two or more photons, and one then speaks of multiphoton excitation. 

The ability to use high-potential fields (100-900 V/cm) provides faster migration and flow rates, leading to rapid, highly efficient separations. Using Einstein s law of diffusion, the statistical equivalence of variance, and number of theoretical plates, the maximum separation efficiency (N) is given by Eq. (32) (N = -l- jUeo)U/2D), where D is the... 

The photochemical reaction of a material starts with photon absorption. In other words, only the photons absorbed by the molecule can bring about photochemical reactions. This is the first law of photochemistry, also called the Grotthuss-Draper law. The second law of photochemistry is one molecule is activated when one photon is absorbed. This is called the Stark-Einstein photochemical equivalence law. Generally, a particular group in an irradiated molecule absorbs a photon with an appropriate wavelength. When photoabsorption occurs, the molecule in the ground state is... 

Plotnikov later took pain in demonstrating [19] that taking the Grotthuss-Draper law in a quantitative sense, that is, that not only light has to be adsorbed, but that the effect is proportional to the radiation absorbed, could replace the Stark-Einstein law, but he obviously missed the point. The equivalence law states much more precisely that absorption of one quantum of light causes one photochemical act. Whether this applies in every single case or, more correctly, which is the mean probability that this statement applies to one type of acts or to another one, and under which conditions it can be affirmed that this applies to a chemical reaction, is another question (see below). That the effect is proportional to the absorbed flux— provided that the terms are properly defined—is obvious. 

Stark thus claimed that he had correlated the number of reacted molecules and the amount of light absorbed through the Plank constant h some years in advance to Einstein and that this was one of the cases where the same conclusion had been arrived at through different paths. Einstein answered to Stark about the priority issue that himself did not comply with it, since this would be of interest for practically nobody, and he had rather intended to show that it could be arrived at the equivalence law through a purely thermodynamic procedure, avoiding to invoke the quantum hypothesis. He added that there was no need to discuss priority, since the equivalence law was a fully obvious consequence of the quantum hypothesis and indeed he had formulated the law aheady in his first paper on quantum hypothesis for the case of the dissociation of a photosensitive molecule into ions [37]. 

The importance of the issue is attested by the decision by the Faraday Society of convening an international meeting in 1925 in Oxford. This was attended by more than 30 scientists and was subdivided in two sections, the first one devoted to the validity and experimental support of the equivalence law and the latter one to mechanistic photochemistry. In introducing the first section, A J Allmand evidenced [48] that this simple and attractive relation, put forward with the authority of Einstein, has proved a great stimulus to research in a somewhat neglected field of chemistry, and a field, moreover, in which an impasse seemed to have been reached in respect of such matters as the primary mechanism of... 

Allmand AJ (1926) Einstein s law of photochemical equivalence. Introductory address to part... 

The second principle of photochemistry is called the photochemical equivalence law, or the Stark-Einstein law, which states the absorption of light occurs in the quantum unit of photon or one molecule absorbs one photon, and one or less molecule can be photolyzed accordingly. ... 

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