A paper published by Einstein in 1912 [34] is usually taken as the source of the
“second law of photochemistry.” In the opening paragraph, he states:
In the following the Wien irradiation law and the photochemical equivalence law will be derived through an essentially thermodynamic way. As for the latter law, I mean the statement that for the destruction of one equivalent through a photochemical process the irradiation energyNhvis required, whereNis the number of molecules in a gram-molecule, hthe known constant in the Planck irradiation energy formula andvthe frequency of the active radiation. Such law appears to be essentially a consequence of the assumption that the number of molecules destroyed per unit of time is proportional to the density of the active radiation. It should be stressed, however, that the thermodynamic dependence and the irradiation law do not allow substituting this hypothesis by a preferred one, as it will be mentioned at the end of the paper.
This paper prompted a note by Stark [35], who remarked that in a paper of his in 1908 [36], he had stated that “the direct chemical effect of light consists in the separation of valence electrons from their bonds” and had arrived to the following statement: “the amount of substance primarily reacting upon light absorption is proportional to the intensity of the active light, since both the reacting amount of RC(=O)R' R-R' + CO
R. R'. CO
R-COOH + R'H hn
H2O Scheme 2.2 The
photochemical cleavage of a C–(C¼O) bond
22 2 The Framework of Photochemistry: The Laws
substance and the number of absorbed photons are proportional to the number of valence electrons that absorb an amount of light of a certain frequency that is equal or larger than the bond energy. Specifying this statement for the amount of gram- moles (Nmolecules) for the case that the workV¼hvis afforded upon absorption of a quantum of lighthvper molecule leads to the sentence: the primary reacted gram-mol corresponds to the amount of lightNhv.”
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 already in his first paper on quantum hypothesis for the case of the dissociation of a photosensitive molecule into ions” [37].
Actually, this appears to be the case. In the first one of his 1905 papers (the
“miracle” year during which he revolutionized physics), he found an expression for the volume dependence of the entropy of monochromatic radiation and, by com- paring it with the Boltzmann’s principle, arrived to the conclusion that a “mono- chromatic radiation of low density behaves—as long as Wien’s radiation formula is valid—in a thermodynamic sense, as if it consisted of mutually independent energy quanta of magnitudeRβv/N” (the dual matter-wave nature). He observes that it is then “plausible to investigate whether the laws on creation and transformation of light are also such as if light consisted of such energy quanta.” Considering photoluminescence, where “monochromatic light is changed to light of a different frequency,” he assumed on this basis that “both the original and the changed light consisted of energy quanta of magnitude (R/N)βv, where vis the corresponding frequency.” He then added: “we must then interpret the transformation process as follows. Each initial energy quantum of frequencyv1is absorbed and is—at least when the distribution density of the initial energy quanta is sufficiently low—by itself responsible for the creation of a light quantum of frequencyv2. . .as well as energy of other kinds, e.g. heat. It is immaterial through what intermediate pro- cesses the final result is brought about. Unless we can consider the photoluminescing substance as a continuous source of energy, the energy of a final light quantum can, according to the energy conservation law, not be larger than that of an initial light quantum; we must thus have the condition:
R=N
ð Þβv2ðR=NÞβv1
or
2.4 Relation with Light Quanta 23
v2v1
This is the well-known Stokes’rule. We must emphasize that according to our ideas the intensity of light produced must—other things being equal—be propor- tional to the incident light intensity for weak illumination, as every initial quantum will cause one elementary process of the kind indicated above, independent of the action of the other incident energy quanta. Especially, there will be no lower limit for the intensity of the incident light below which the light would be unable to produce photoluminescence” [38].
It should also be noticed that, apart from the above thermodynamic demonstra- tion, Einstein also offered a deduction of the law. In this case, he considered the Bohr states between which a molecule passed by absorption or emission of a quantum. He considered two such states, Zm and Zn, of energy Em>En, with EmEn¼hv in equilibrium at a temperature T where the radiation density ρ corresponding to the frequencyvis very low. Under these conditions practically all of the molecules would be in the lower quantum stateEn. If, besides reverting to Enby emission of a photon, a molecule in the higher stateEmcould also, and far more rapidly, undergo a unimolecular reaction to give productW(Zm!W), then at a temperature higher thanT, one molecule will be promoted to theEmstate per photon absorbed, and almost all of them will react to giveW. This results into the deduction of the practical validity of the law.
In this case, Einstein explicitly distinguished primary and secondary photochem- ical processes [39], a point that was obvious for him but unfortunately not for many chemistry practitioners. This point was even more clearly stated by Stern and Volmer, who evidenced that the Einstein law could not be applied to the chemical products without consideration of the overall process. In fact, a satisfactory ratio- nalization was offered on this basis for some reactions, e.g., assuming that the cleavage
H-Br!HþBr
was the only primary process in the photodecomposition of HBr, and adding to it the possible secondary processes
HþH!H2
BrþBr!Br2
HþHBr!H2þBr BrþHBr!HþBr2
led to the prediction that one molecule of hydrogen and one molecule of bromine were formed and two molecules of HBr were destroyed for every quantum absorbed, as indeed found experimentally.
24 2 The Framework of Photochemistry: The Laws
Likewise, the occurring after the primary act:
Cl2!2Cl
of a chain process upon irradiation of a mixture of chlorine and hydrogen:
ClþH2!HClþH and
HþCl2!HClþCl
well explained that in this case many thousands of molecules were decomposed for every quantum absorbed.
Furthermore, the occurrence of a reaction could not be correlated with the energy involved in the primary process, e.g., iodine absorbed quanta higher in energy than the I–I bond but cleaved with efficiency much less than unitary and part of the radiation absorbed was given back as fluorescence.
All of these observations were best accommodated by having an electronically 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].