T H E EXCITED SYSTEMS FORMED BY THE ABSORPTIOK OF LIGHT BY LOUIS A. TURNER
The law of Photochemistry which has been known the longest and is the best-established and the most fundamental, is that of Grotthuss and Draper, viz., that the only radiation which will produce a photochemical reaction is that which is absorbed by the reacting system. The process of absorption is, therefore, of primary importance and any generalization concerning this process should be of some importance for the photochemist. Some of the newer developments of the theories of atomic and molecular spectra and their relations to the structure of atoms and molecules are concerned with the various possible processes of the absorption of light and the properties of the rxcited systems produced by that absorption. This article will be devoted to a brief discussion of such of these results as may have some bearing on photochemical reactions. The two principal postulates of Bohr’s theory of atomic and molecular structure which has been so successful in correlating the spectroscopic phenomena are:--I) A molecular system can exist only in certain stationary states having definite energies and z ) , when the system changes from one of these stationary states of greater energy to another of lesser energy monochromatic radiation is emitted, its frequency being given by the relation hv = El - Ez.Y is the frequency, X is Planck’s constant ( = 6.5 j X IO+ erg see.), El and El are the energies of the molecule in the two states, respectively. The absorption of light is the reverse process, producing a change from a stationary state of lower energy to one of higher energy. X single atom is believed to be made up of one minute, massive, positive nucleus and numerous electrons so that the different stationary states must correspond t o different configurations of the electrons. X discussion of the quantum rules according to which these stationary states are determined is beyond the purpose of this article. Each line of an emission spectrum, therefore, is produced by one of the many possible changes of the atom from a higher to a lower stationary state. Likewise, the absorption lines correspond to changes from states of low energy t o ones of higher energy. The absorption line spectrum is, however, always much simpler than the emission line spectrum because a t ordinary temperatures the vast preponderance of the atoms exists only in the stationary state of lowest energy, the normal state, and consequently can absorb light of only those frequencies which correspond to transitions from that state to those of higher energy. The atom which has absorbed light now has a different electronic configuration and is, from one point of view, a new chemical substance, of high energy constant. If the light absorbed is in the visible region, the energy per excited atom is z or 3 volts, roughly equivalent to 50,000-7j,ooo gram calories
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per gram mol (one volt of energy is the kinetic energy of an electron which has fallen through a potential drop of one volt. One volt per atom equals 23.0 kg. cal. per gm. mol.) The atom in this excited state may do one of several things. It may simply reradiate light of the frequency of that absorbed, i t may radiate light of a lower frequency by a transition to an intermediate state, or it may give up its energy without radiating upon collision with another atom or molecule. It has been found by a variety of methods that an atom remains in one of these excited states into which it is put by absorption of radiation an average time of the order of IO-* seconds.’ If the excited atom is in a rarefied gas it will reradiate its energy before making a collision, so that such gases usually show some sort of a fluorescence spectrum. There are, however, for some atoms, a few stationary states in which the atom can remain an indefinitely long time without radiating any of its energy of excitation. This happens when there is a stationary state of greater energy than the normal one, but of such a sort that there is no possible transition from it to a lower state with the emission of radiation, or vice-versa. For instance, the excited state of a mercury atom of lowest energy which can be reached by the absorption of light is the z3P1state (zP2in the old notation) ipto which the atom is changed by absorption of light of a wavelength of 25378. U. A small fraction of a volt below this is the z3P, state from which the atom can change to various higher states by the absorption of radiation; but, once in it, can not revert to the normal state by radiating, neither can it bc brought to this state from the normal one by the absorption of radiation. I n this and other such cases, these so-called metastable states can be reached, however, by transitions from states of still higher energy. It has been shown by Dorgelo2 that in pure neon a t low temperatures atoms will remain in 16.6 volt excited stationary states for at least 1 / 1 0 of a second, as indicated by the absorption of light by atoms in these excited states. A slight trace of impurity cuts this life down to a time too small to measure. This disappearance of the metastable excited atoms and the quenching of the fluorescence of a gas with increasing pressure or admixture of other gases show that the excited atoms can lose their energy by some other method, presumably upon collision with other atoms or molecules. Such processes were called “collisions of the second kind” by Klein and Rosseland3 who predicted them by a theoretical argument. They showed that if, when two atoms collide, part of their kinetic energy can be used to raise one of the atoms to an excited stationary state (a “collision of the first kind”) the reverse process must also be a possible one. Various sorts of collisions of the second kind were experimentally investigated by Cario and Franck4 who showed that H g atoms excited by the absorption of light of a wave-length of 2537 A. U. can excite other atoms such as T1 and Na, which will emit their own spectrum, the excess energy appearing as kinetic energy. They also showed that the excited Hg atoms will produce a chemically activated form of hydrogen, presumably atomic hydrogen. All of the energy of excitation is not necessarily used up in the process occurring a t the first collision. The atom may first be put into a metastable state, giving up a small amount of energy, and then remain there
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until it finally makes a collision in a way favorable for it to give up all of its energy of excitation. Experiments of Donat6 and of Wood6 indicate that this is what happens to excited Hg atoms in mixtures with argon or nitrogen a t pressures of the order of one-tenth to one atmosphere. Processes of this kind must be involved in the various photochemical reactions' produced by illuminating mixtures of Hg vapor and other gases with 2 5 3 7 light, many of which have been studied since Cario and Franck's original experiment. This type of photochemical reactions is, of course, a very special one for i t is light of only an exceedingly narrow region of the spectrum which has any effect upon the mixture, viz., the very center of the 2537 line. Self reversal of this line removes all of the effective radiation if the mercury arc lamp used for a source is not sufficiently cooled. Stuart8 has made a study of the quenching of the resonance fluorescence of Hg vapor produced by the admixture of various other gases. Different gases give vastly different quenching effects showing that the probability of a radiationless transfer of energy a t collision depends upon the nature of the colliding molecules. It is of interest that the effectiveness of this quenching is so great for some gases that even if it is assumed that the probability of occurrence of a radiationless transition a t collision is unity, it is necessary to ascribe amuch larger effective radius to the excited Hg atom than the radius of the normal Hg atom as deduced in other ways. Similar experiments have been performed with Na vapor by Mannkopfg, who finds a different relative order of effectiveness for the different gases from that found by Stuart for Hg vapor. In many cases the absorption lines can be arranged in series converging to a limit on the side of shorter wave-lengths. Beyond this limit there is a region of continuous absorption. The successive lines of a series, by Bohr's theory, have to do with transitions from the normal state to a set of states of higher energy, one electron becoming less and less tightly bound to the nucleus. The limit corresponds to complete removal of this electron, Le., ionization. The region of continuous absorption beyond the limit corresponds to ionization of the atom and ejection of the electron with various amounts of kinetic energy, continuous because that kinetic energy can have any value. Such absorption by Na and K has been investigated by Harrison10 and the predicted photo-ionization has been studied by various workers." The continuous absorption of X-rays is a similar phenomenon. Experiments with X-rays have shown1*that the electrons have the expected velocity given by the equation + m v 2= h u - P The spectra of molecules, both emission and absorption, are interpreted in the same way as those of atoms. The differences between them are t o be attributed to the more complicated structure and resulting increase of the number of degrees of freedom of the molecules. For the molecules, as for the atoms, there are various electronic configurations but instead of each of these giving a single stationary state it is split up into a two-fold niultiplicity bccause of the various possible energies of mutual vibration of the different nuclei of the molecule and the various possible energies of rotation of the molecule as a whole. All of these motions are quantized so that for a given
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LOUIS A. TURNER
set of electron quantum numbers there are many possible vibration states aBd for each of these many rotation states. The number of stationary states of a molecule is therefore very great compared to that of an atom and the number of spectrum lines connected with transitions is correspondingly increased, giving rise to the complicated band spectra. For a complete treatment of this subject the reader is referred to the Bulletin of the National Research Council, No. 57, “Rlolecular Spectra in Gases.” This complication of the stationary states admits the possibility of transitions not possible for atoms. There are the rotation bands in the far infra-red region of the spectrum corresponding to changes of only the rotation of the molecule, and the vibration-rotation bands in the near infra-red corresponding to simultaneous changes of the vibration and rotation. The electronic bands are those which involve a change in theelectronicquantum numbers and, therefore, correspond to a single line of an atomic spectrum but because of the complication of all the various possible simultaneous changes of the vibration and rotation the single line becomes a whole system of bands. The excited molecule can, like the atom, reradiate part or all of its added energy to give a fluorescence spectruni. Such are the resonance spectra of 12, Na2, etc., studied by R. W.Wood13and others. Collisions of the second kind presumably can occur and must be of great importance in the mechanism of photochemical reaction in which the absorbing substance is molecular, the exciting light being in the spectrum region of discontinuous band absorption. There is one possible type of collision which results in the dissociation of the excited molecule itself into component parts-a sort of auto-collision of the second kind. The encrgy of excitation of many molecules is considerably greater than the energy for dissociation and it seems quite probable that upon collision this excited molecule can give up its energy by dissociating itself. There is no very direct evidence for the occurrence of this process. Kor is much known about possible, molecular, metastable, excited, electronic states. There is evidence, however, that many electronic transitions of kinds which do not take place in atoms do occur in molecules so that the probability of the existence of these metastable excited states is much less. Various band spectra have been analyzed and the electronic transitions discovered. In one case, that of the Hen bands, there has been found a sequence of transitions converging to a limit according to the same law as do the lines of a series, and apparently for the same reason. Theoretically, a t least, one might expect to be able to follow many such sequences to the limit of convergence and find a region of continuous absorption connected with ionization of the molecule. Such an absorption has not been found. There are, however, regions of continuous absorption in the spectra of molecules which seem to be connected, not with ionization, but with dissociation of the absorbing molecules. They are coiitinuous because of the continuity of the possible kinetic energies of the separated atoms. It is found that the energies of the excited states having the same electron quantum numbers are greater the greater the vibration quantum numbers, as one would expect, but that with increasing vibration quantum number the energy differ-
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ences between these states become steadily less. (It is implied that molecules having zero rotational energy are being compared). The energies of these successive states can in several cases be represented by a very simple formula involving the vibration quantum number. It indicates that the energy difference between successive vibration states becomes zero for a finite vibration quantum number and a certain value of the energy. This is thought to be the energy a t which the molecule dissociates into atoms. According to the quantum theory of the anharmonic oscillator the energy difference between successive vibration states is proportional to the frequency of vibration so that when this difference becomes zero so does the frequency, indicating that the binding force has become zero. As an example, consider the absorption spectrum of iodine. Cold iodine vapor has a discontinuous band absorption in the red to green parts of the visible spectrum whjch merges into a region of continuous absorption beginning a t about 4995 A. U. and extending into the violet. The bands have been analyzed and are apparently connected with transitions from the single normal vibration state (actually multiple because of the various rotational energies) to various vibration states of one excited electronic configuration. The frequencies of these bands are related by a simple law which indicates that the frequency difference between them becomes zero at 4995 1.U., the result of the convergence of these upper vibration levels. Dymond14 found that if iodine absorbed light of wave-length longer than this it would fluoresce but that if it absorbed light of a shorter wave-length in the region of continuous absorption there would be no fluorescence. In the first case the molecules were simply excited and could reradiate their energy but in the second case they were apparently actually dissociated. Absorption of light of a wave-length of 4995 .iU. . will, therefore, produce dissociation of the molecule into two separate atoms having zero kinetic energy. The energy is 2.469 volts (volts X X in A. U. = I2345), whereas the experimental value for the heat of dissociation of Iz is only 1.5 volts. The difference of 1.0volts must be an energy of electronic excitation of at least one of the two atoms. Such an electronic energy would be expected since this optical dissociation is continuously connected with the band absorption which does involve an electronic change. On the other hand, when dissociation occurs the electronic energy must be that of one of the excited states of the atom. The spectrum of the iodine atom has not been analyzed, but, theoretically, there should be a low state near the normal one, the two forming a doublet P state. A recurring doublet difference between the frequencies of some of the strong lines of I in the Schumann region has been found.I5 It presumably gives the energy of this next to the lowest state, the value being 0.937 volts. Subtracting this from the 2.469 volts energy for optical dissociation gives 1 . 5 3 2 volts as the heat of dissociation of iodine. This value is equivalent to 3 5 . 2 kg. cal. per mol. which is in satisfactory agreement with the direct experimental value of 34.5 kg. cal. per mol. Granting the theoretical interpretation of the spectra, the optical value is the more accurate. E\-uhnI6has made
LOUIS A. TURNER
ST2
a similar study of Brz and C1, and finds the same sort of relationships. The results are summarized in Table I.
TABLE I A Of
convergence
1 4995 Br 5107 C1 478s
hvo 2 ,469V. 2.415
2.577
2T2
-29PI
D (BpectroscoDic) Volts kg cal
0.937 0.454 0.109
1.532
35.2
1.961 2.468
45 ’ 2 56.9
D (thermal)
34.5 46.2 57
One would expect that every set of vibration levels would converge in this way, the different sets being connected with different electronic states of the molecule and of the separated atoms. For substances of which the band spectra have been sufficiently analyzed and for which the various atomic states are known, it should be possible to get several independent determinations of this energy of dissociation. This has been done for one substance, hydrogen. Witmer,” from the set of vibration states of which the normal state is the lowest found a heat of dissociation of 4.34 0.01volts. Dieke and Hopfield18 found in the far ultra-violet region of the spectrum a set of absorption bands and a region of coFtinuous absorption as in iodine, continuous absorption beginning a t 849.4 A. U. This limit gives 14.53volts for the energy of dissociation of the Hz molecule into one norfnal and one excited H atom. Assuming the energy of excitation of the H atom to be that of the state next above the normal, 10.15volts, a value of 4.38 volts is obtained for the energy of dissociation. This agrees well enough with Witmer’s value of 4.34 volts which involved a considerable extrapolation. 4.38 volts is equivalent to 100,900kg. cal. per mol., in satisfactory agreement with the best direct experimental values. These ideas have been extended and applied to various other molecules by Birge and Sponer.lg The whole matter is discussed a t length in Professor Birge’s chapter in the report on molecular spectra in gases, referred to above. Although i t should be possible to apply these calculations in all cases, given a sufficiently complete analysis of a band spectrum, it does not necessarily follow that in all cases it is possible that normal molecules can be made t o dissociate by the absorption of radiation, as the halogen molecules apparently actually do. The occurrence of such a dissociation means that there is a great probability of a large change of the vibration quantum number accompanying the electronic change. FranckZ0has pointed out that there is a connection between the change of the moment of inertia of the molecule in a transition and the magnitude of the most probable change of the vibration quantum number. The moments of inertia can be calculated from the energy differences between successive rotation states. I n the spectra of substances like iodine, the moment of inertia of which is increased with the change to the higher electronic state, large changes of the vibration quantum number are the most probable, whereas in the spectrum of nitrogen of which the moment of inertia changes by a small amount, the most probable changes of the vi-
*
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bration quantum number are the small ones. The increase of the moment of inertia means a corresponding increase of the separation between the nuclei in their position for equilibrium. It seems as if the electron configuration were changed from the normal one to the higher one instantaneously, leaving the nuclei practically the same distance apart. If this distance is then much less than the equilibrium distance for this excited state the molecule finds itself highly compressed and, being free to vibrate, does so with large amplitude. It may be that the energy of compression is greater than the energy necessary for complete separation of atoms when the nuclei are a t rest in the equilibrium position. I n this case the compressed molecule will expand, the nuclei passing through the equilibrium position with sufficient energy to separate completely with some kinetic energy left over. Whether this be the explanation or not, there is, nevertheless, the connection between a high probability of large change of the vibration quantum number and large change of the moment of inertia. The various other possible cases are discussed by Franck. KuhnI6 points out that Iz,Brp and Clz have, in the order given, a progressively greater weakening of the binding upon absorption as measured by the energy difference between successive vibration levels. The maximum adsorption by Ip occurs just a t the edge of the continuous region, that for Brp further into the continuous region, and that for Clz well into it. There is, then, this sort of independent evidence for the primary optical dissociation of these halogen molecules by the absorption of light, which has often been postulated in the explanation of various photochemical reactions. There is another type of process which may be of importance in photochemical reactions. It seems probable that in some cases a molecule in a quantized state may, instead of undergoing a transition to a lower state of high vibrational energy, change to a state where the atoms are completely separated, the remaining energy being radiated. A continuous emission spectrum would result in cases where this sort of process could occur. Rlackett and Franckp1have advanced this as the best explanation for a certain continuous emission spectrum of H t which their experiments show to be the result of primary processes, Le., independent of collisions with other molecules. Born and FrancktZhave suggested the converse process to explain certain continuous absorption spectra such as the absorption by Hg vapor a t high pressure on the long wave-length side of the 2 5 3 7 line. Two atoms colliding with large kinetic energy form a temporary “quasi-molecule” which can absorb light to produce a definite quantized excited molecule, part of the energy being the kinetic energy of the colliding atoms, the rest being made up by the radiation. Such absorption may be of importance in photochemical reactions between gases a t ordinary pressures. The effectiveness of these atoms resulting from the dissociation of the molecule must depend to a certain extent upon the fact that in some cases they do not readily recombine to form molecules. This is in accord with Bohr’s Correspondence Principle, in the case of highly symmetrical molecules such as IPor Hz.Such highly symmetrical molecules when vibrating in the normal electronic state presumably have no vibrating electric moment. Classically,
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LOUIS A. TURNER
they would neither emit nor absorb radiation so that the corresponding quantum radiation, the vibration-rotation bands, are missing. Such molecules can not be dissociated by absorption of radiation unless an electronic transition occurs so that the two atoms will not recombine with emission of radiation if both are in the normal state. Thus they do not combine except when there is some other body to take up the extra energy, as in a three body collision, or a t the surface of a solid. Practically all of the important theoretical and experimental work on band spectra has been done with diatomic molecules. Even they are sometimes rather hopelessly complicated so that it is not surprising that not much progress has been made in the study of spectra of still more complex molecules. There is no reason to doubt, however, that these more complicated molecules will behave in an analogous way. I n view of these various possible effects of the absorption of light it is no great wonder that Einstein’s photochemical law is not accurately fulfilled by many reactions. Undoubtedly the primary process does follow the law, there being one excited system produced for each quantum absorbed, but even granting that none of the absorbed energy is re-emitted as fluorescent light, the subsequent course of the reaction will depend entirely upon the chemical properties of that excited system which may combine to give a small number of resultant molecules, or initiate a chain reaction, or act as a catalyst. The light merely serves to introduce an impurity, often of high energy content, into the system and the subsequent course of the reaction may be of almost any of the known types. The number of resultant molecules produced per quantum of light absorbed is, of course, an indication of the nature of the reaction subsequent to the absorption. Since this article was written there have appeared numerous papers dealing with matters related to those discussed here. That Il’aI molecules are dissociated by the absorption of light of wave-length less than 2 4 5 d into normal I atoms and excited Na atoms, which then emit the P lines, has been shown by the experiments of Terenin,z3 of K0ndratjew,~4and of Hogness and F r a n ~ k . 2Franck, ~ Kuhn and RollefsonZ6and Franck and KuhnZ7have studied the absorption spectra of various alkali and silver halides. They discuss the theory of the optical dissociation of such heteropolar molecules and of the hydrogen halides, the absorption by which had been previously investigated by Tinge and Gerke,28and Bonhoeffer and Steiner.29 That exceedingly dry chlorine has the same absorption spectrum as moist chlorine has been found by K i s t i a k ~ w s k y ,and ~ ~ by Kornfeld and Steiner,31 thus showing that the great influence of H20 vapor upon the photochemical combination of HZand Clz is one upon the reactions following the primaly absorption. The a u t h o P has recently found that iodine vapor illuminated by strong light from a carbon arc absorbs the light of the 1830.4line of the iodine atom more strongly than when not so illuminated. This light should be absorbed by normal iodine atoms, so the experiment is taken to indicate the presence of the iodine atoms resulting from the optical dissociation.
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51s
References lZIany of the topics here considered are discussed in greater detail in the book of J. Franck and P. Jordan, “hnregung von Quantensprungen durch Stosse,” Julius Springer, Berlin, 1926. Many page references are given to this book, which is designated F. and *J. I F . and J . , p. 199. H. B. Dorgelo: Physica, 5, 429; 2. Physik, 34, 766 (1925);F. and J., p. 235. Kleinand S.Rosseland: 2. Physik. 4, 46 (1921);F. and J., p. 2 1 1 . ‘ ( 2 Sarlo: 2. Physik, 10, 185; G. Carlo and J. Franck: 11, 161 (1922); 17, 202 (1923); F. and J., pp. 227-232. 6 K. Donat,: 2. Physik, 29, 345 (192j). 6 R. W.Wood: Proc. Roy. Soc., 108A, 679 (1924). 7 See, for example, Taylor: J. .4m. Chem. SOC., 48, 2840 (1926). UH. Stuart: Z. Physik, 32, 262 (1925); F. and J., p. 223. DR. Mannkopf: 2. Physik, 36, 31j (1926). 10 G. R. Harrison: Phys. Rev., (2) 24, 466 (192 j 11 E. (3. Lawrence: Phil. Mag., 50,345 (1925); dohler, Foote and Chenault: Phys. Rev., ( 2 ) 27 37 (1926). 1* >i.deBroglie:Cornpt.rend., 172,274,527,746,~1J6(1921); J.Phys.Rad.,2,26j (1921). l 3 F. and J., p. 218; “Molecular Spectra In Gases, Chap. \‘I. l a E. G. Dymond: 2. Physik, 34, j 53 (192j ) . 15 L. A. Turner: Phys. Rev., (2, 27, 397 (1926). 16 H. Kuhn: Z. Physik, 39, 77 (1926). 1’E. E. Witmer: Phys. Rev., 28, 1223 (1926). LEG. H. Dieke and J. J. Hopfield: Z. Physik, 40, 299 (1926). 1 9 R. Birge and H. Sponer: Ph 8. Rev., (2) 28, 259 (1926). 2 o J. Franck: Trans. Faraday sbc., 21 (1925); F. and J., p. 252. 21 P. M. Blackett and J. Franck: Z. Physik, 34, 389 (1925); F. and J., p. 261. 22 M. Born,and J. Franck: Z. Physik, 31, 411 (1925). 23.4. Terenin: Z. Physik, 37 98 (1926). 24 V. Kondrutjew: 2: Physik; 39, i91 (1926). 25 T. R. Hoeness and J. Franck. 2. Phvsik. 44. 26 (1927). 2s J . Franc6 H. Kuhn and G. Rollefsdn: Z. Physik, 43; 155 (1927). 27 J. Franck and H. Kuhn: Z. Physik, 43, 164 (1927). 28 H. C. Tinge and R. H. Gerke: J. Am. Chem. Soc., 48, 1838 (1926). 29 K. F. Bonhoeffer and W.Steiner: Z. physik. Chem., 122, 287 (1926). 30G. B. Kistrakowsky: J. Am. Chem. Soc., 49, 219 (1927). 31 G. Kornfeld and U. Steiner: 2. Physlk, 45, 327 (1927). s2 L. A. Turner: Phys. Rev., 1928, April (Abstract). 3 0
Palmer Physical Laboratory, Princeton University, June. 1927.
