Abstract
The article is a revised version of a report delivered at the 3rd Congress of the Association of Physicists in Nizhny Novgorod in September 1922.
Full Text
ACTIONS OF LIGHT AND THE THEORY OF QUANTA1
S. I. Vavilov.
§ 1. The propagation of light in matter is accompanied, generally speaking, by changes both in the light and in the matter. The division of the phenomena of the optics of a material medium into actions of light, on the one hand, and actions of matter on light, on the other, is essentially artificial; both groups of processes are in fact inseparably connected with one another, and therefore it is more correct to speak in general of the interactions of light and matter. However, the present state of theoretical optics is such that the two related groups of phenomena are considered from entirely different points of view. For understanding the actions of matter on light, i.e. the phenomena of reflection, dispersion, scattering of light, double refraction, rotation of the plane of polarization, etc., the physicist remains—or rather is compelled to remain—on the classical ground of Fresnel–Maxwell optics. On the other hand, the understanding of the phenomena of the action of light on matter is accessible to the same physicist only with the aid of the theory of quanta, which contradicts the principles of classical optics. The photoelectric effect, the chemical actions of light, the complex phenomena of secondary luminescence (fluorescence, phosphorescence), etc., are very simply connected with and described by the fundamental postulates of the theory of quanta. It is, of course, premature to speak of complete agreement between the extraordinarily complex manifestations of the actions of light and the theory of quanta. One may assert, however, that guiding lines have emerged which make it possible to carry out at least a rational systematization of the facts. In classical optics the actions of light remained in a chaotic, unsystematized form, frightening by their complexity and confusion.
The contradictions between the classical theory and the theory of quanta inevitably entail internal misunderstandings within each of them. In what follows, alongside an exposition of the extraordinarily fruitful results of the theory of quanta in the field of the actions of light, we shall have to touch upon a number of contradictions which place the theory in a difficult position.
§ 2. The fundamental possibility of a qualitative understanding of the actions of light exists also in the classical theory. One may even, somewhat exaggerating the state of affairs, say that only the classical theory permits one to “understand” the actions of light; the quantum theory, in its present state, gives rather only a quantitative “description” of phenomena.
The initial idea of the classical optics of a material medium is the idea of resonance. Interactions of light and matter are possible only by virtue of the resonance of the molecular vibrators of matter to light oscillations. Already Newton1, trying to understand the thermal actions of light, posed to the future investigator the following question: “Do not bodies and light act mutually upon one another: bodies—emitting light in all directions, reflecting, refracting, and bending it, while light—heating bodies and imparting to their parts an oscillatory motion, in which heat consists?” The same supposition was expressed by Bouguer2: “It is difficult to imagine,” he writes, “that a part of the light rays should not lose a share of its force in exciting a peculiar motion in the small molecules composing the body. This motion, or oscillation, must correspond to the loss of some quantity of motion in the incident light.” The brilliant use of resonance for explaining the dispersion of light in matter in Sellmeier’s theory and the scattering of light in Lord Rayleigh’s theory gave this idea such support that it firmly withstands, even to our day, the turbulent onslaught of new facts.
The basic experimental law of the interactions of light and matter is the independence of the corresponding coefficients determining the phenomenon from the energy of the incident light.
The coefficients of reflection, refraction, and absorption of light do not depend on the brightness of the incident light over an enormous interval of variation of the energy. In exactly the same way, the magnitude of light pressure, the strength of the photoelectric saturation current, and the brightness of secondary radiation are strictly proportional to the energy of the incident light, i.e. the corresponding coefficients remain constant. From the standpoint of the classical theory of resonance, such a result is equivalent to saying that the displacements caused by external forces in the molecular resonator must be such that the forces are expressed linearly and homogeneously in terms of the displacements and their time derivatives. The equations of the classical theory are constructed (in the majority of cases) under the assumption of the simplest case of the condition just stated. The bonds of the parts of the ether and of the molecule are assumed to be ideally elastic, i.e. obeying Hooke’s law. On this basis, the equation of motion of a molecular resonator situated outside the action of external forces is expressed as follows:
\[ m\frac{d^{2}x}{dt^{2}}=-ax \ldots\ldots\ldots\ldots\ldots\ldots (1) \]
where \(m\) is the mass of the moving part of the resonator, \(x\) is the displacement, and \(a\) is a constant determining the magnitude of the elastic force. Such a vibrator is used in Sellmeier’s theory. It is easy to see, however, that a resonator of type (1) is still unable to explain, even qualitatively, the various interactions of light and matter. In the region of complete coincidence of the periods of oscillation of the light and the vibrator (1), the dispersion and absorption do not have infinitely large values—experiment shows that they are finite. Hence it becomes necessary to endow the vibrator with damping, assuming, for example, the possibility of radiation of the accumulated energy. Introducing into equation (1) a term corresponding to damping, we arrive at the fundamental equation of Planck’s theory, which makes it possible to obtain the law of light scattering exactly confirmed by experiment. But even such an addition to the theory still cannot explain the disintegration of the resonator with which one evidently has to deal in the photoelectric effect and in the chemical actions of light. Disintegration corresponds to the “elastic limit”—the resonator cannot be ideally elastic. It is possible in principle, however, to reconcile the elastic properties of the resonator, which, as we have seen, follow from the independence of the coefficients of interaction between light and matter from the brightness, with the apparently “nonelastic” properties resulting from the presence of the photoelectric effect and the chemical actions of light. In a real body, owing to thermal molecular motions, elementary resonators will, in encounters and collisions, enter the force fields of other resonators, and law (1) will be violated. Sellmeier’s elastic resonator can, thanks to molecular collisions, lose its elastic properties for a short time. During these short intervals there may occur a transfer of internal energy from one resonator to another, disintegration of resonators, and so on. From this point of view, equation (1) can be applied to a resonator during its “free path.” Thus, taking into account the presence of thermal disordered motions of resonators, we obtain the possibility of interpreting the various actions of light also in the classical theory. It should be noted, however, that attempts at a mathematical treatment of such a view are few, and in this respect the accounts with the classical theory are not yet settled. Lorentz1 used this path in his theory of absorption. He succeeded in showing that the existence of thermal motion in a gas is mathematically completely equivalent to the fact that in equation (1) there appears a term corresponding to damping: \(g \cdot \dfrac{dx}{dt}\), where \(g\) has the following value:
\[ g=\frac{2\nu_0^2}{\tau}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots (2) \]
where \(\nu_0\) is the frequency of the resonator’s natural oscillations, \(\tau\) is the time of free path. The application of Lorentz’s theory to the experimental absorption curves, however, did not confirm it. The discrepancy between theory and experiment exists both with respect to the form of the absorption curves and with respect to their dimensions. It must be noted, however, that the question cannot be considered completely settled, since there are not sufficient grounds for equating \(\tau\) in formula (2) with the time of free path following from the kinetic theory of gases. The time during which the optically active parts of a molecule remain without disturbances from other molecules may, generally speaking, also differ from the time of free path.
With respect to the other groups of phenomena of the action of light, the above-described classical scheme of resonators in disordered motion has not been systematically carried through. Work in this direction has been delayed by the fact that there exist many facts contradicting the classical scheme. We shall point out several such facts.
The primary stage of the action of light must, evidently, consist in the absorption of light by a resonator. In the classical theory, the magnitude of absorption and dispersion stands in a simple relation to the number of resonators contained in a unit volume of the substance. Applying the equations of the theory to experimental data, we can calculate the number of resonators simultaneously absorbing and dispersing light. The most substantial success of the classical theory consisted in the fact that, for many of the simplest cases (rarefied gases, dilute dye solutions), the number of absorbing resonators \(n\) proved to coincide with the number of molecules of the substance present, \(N\). At this point the theory received excellent confirmation. The situation is exactly the same in Rayleigh’s theory of the scattering of light by gas molecules. All this leads to the following conclusion: in resonant phenomena of dispersion and absorption, all the available molecules of the substance simultaneously take part to an equal extent.
If this is so, then the fundamental propositions of the classical theory entail a number of consequences for the various actions of light. Let us dwell on some of them.
The primary stage of the action of light is the absorption of light by the molecules of the substance. In this respect all molecules, as experiment shows, are equal in rights. On the other hand, as we have already seen, a condition for the action of light is, in addition, the collision of the given molecule with others. Collisions will occur for different molecules that have absorbed light, obviously, not simultaneously. Moreover, different collisions, generally speaking, will not be equivalent. A collision that will lead to the expected result, for example to a photoelectric effect or to photochemical decomposition, can occur only: 1) with a definite orientation of the colliding molecules, 2) with a definite kinetic energy of the moving particles, and finally 3) with a definite internal—
of the energy of the molecule absorbing the light. It is not difficult to see that the first two factors must depend on the temperature of the medium, for both the rate of change of the orientation of the molecules and their average kinetic energy increase with increasing temperature. Experience shows, however, that in those cases of the action of light where the process is not complicated by entirely secondary phenomena, the rate of the process does not depend on temperature. The strength of the photoelectric current, for example, does not depend on temperature; the rate of the simplest photochemical processes likewise is practically independent of temperature. The slowness of such irreversible actions of light, such as the photoelectric effect and photochemical reactions, on the one hand, and their independence of temperature, on the other, stand, from the point of view of the classical theory, in sharp contradiction.
Let us point out one more case of the helplessness of the classical theory in the face of an experimental fact. The maximum of the energy-distribution curve of secondary radiation (fluorescence) is shifted somewhat toward longer wavelengths relative to the maximum of the absorption curve (Stokes’ law). Stokes’ law, in itself, presents a considerable difficulty for the classical, resonance theory. The attempts at explanation proposed up to now are unsatisfactory. However, independently of this, here we encounter yet another difficulty. In the classical theory, radiation must necessarily correspond also to absorption in the same interval of wavelengths (Kirchhoff’s law). Therefore the fluorescence of a medium should be accompanied by additional absorption. The search for such “absorption of fluorescence” continued for a very long time, until the decisive experiment carried out by Wood in 19081 gave a definitive negative answer. Fluorescence radiation is not connected with absorption; in other words, the number of absorbing centers in this region must be negligibly small. Meanwhile, according to resonance theory, we would have to expect that all molecules take part in the additional absorption.
Any chapter of the doctrine of the actions of light can furnish an abundant class of facts still unresolved in the classical theory.
There are no grounds for the categorical conclusion that it is impossible to give a theory of the actions of light consistent with classical principles; one may say in advance, however, that this path is a very difficult one, inevitably connected, as is clear from the preceding, with the application of the methods of statistical physics.
§ 3. The situation is entirely different in the theory of quanta. In the classical theory the principles themselves are clear; difficulties arise in the applications. In the theory of quanta the principles, in their modern formulation, are extraordinarily enigmatic; their application is strikingly simple, and the results agree no less strikingly with experiment.
THE ACTION OF LIGHT AND THE THEORY OF QUANTA
Quantum theory up to the present (it has existed for about 20 years) does not have a clear, generally accepted formulation. One has to speak of different variants of the theory. The only general proposition present in all variants of the theory is this: the internal energy of an elementary formation (atoms, molecules) can be transmitted to the external medium (the ether, other molecules) only in quanta:
\[ \varepsilon = nh\nu \ldots\ldots\ldots\ldots\ldots\ldots (3) \]
where \(n\) is an integer \(0, 1, 2, 3,\ldots\), \(h\) is a universal constant of nature, approximately equal to \(6.54\cdot 10^{-27}\), and \(\nu\) is a certain frequency of oscillations determined for the given system. Until the internal energy has the magnitude (3), it cannot be transmitted to the external medium. Thus, for example, the possibility of radiation by an atom or molecule over considerable intervals of time, in contradiction to the principles of classical electrodynamics, is excluded. Formula (3), despite its simplicity, conceals the possibility of several variants of the theory. In applying it to different groups of facts, one has so far had to change these variants. To understand the laws of line spectra it is necessary, for example, to assume that \(n\) in (3) is equal to 1. For the derivation of the formula for black radiation, on the contrary, one has to assign to \(n\) arbitrary integral values. True, the probability that \(n\) has values \(>1\) is extremely small for [[unclear: several words obscured by blot]] parts of the spectrum; nevertheless the case \(n>1\) is of great [[unclear: word obscured by blot]] significance.
[[unclear: beginning of paragraph obscured by blot]] contradiction exists, however, with respect to the meaning of \(\nu\) in formula (3). If the giving up of energy to the external medium consists in the emission of monochromatic light of frequency of oscillations \(\nu\), then the meaning of \(\nu\) is half clarified. What remains unclear is only why \(\nu\) has this value and not some other—new hypotheses are needed for this. In the original variant of Planck’s theory of black radiation, \(\nu\) coincides with the frequency of oscillation of an elementary harmonic oscillator \(\omega\). Thus, in order to explain the continuous spectrum of black radiation, one has to assume the existence in the body of oscillators with all possible frequencies of oscillation \(\omega\). In Bohr’s theory of line spectra, the simple connection between the frequency of intra-atomic motions \(\omega\) and the frequency of the emitted light \(\nu\) is, generally speaking, lost:
\[ \nu \ne \omega \ldots\ldots\ldots\ldots\ldots\ldots (4) \]
An atom or molecule can have a whole series of discrete values of \(\omega\), connected with the so-called1 “stationary states” of the system.
If the system passes from a state characterized by energy \(E_m\) into a state with energy \(E_n\), then light of frequency
\[ \frac{E_m-E_n}{h}=\nu \ . . . . . . . . . . . . (5) \]
is emitted or absorbed (according to the sign).
For the simplest system of the hydrogen atom, consisting of an immobile nucleus and an electron moving around it, the frequency of revolution of the electron in the various states is expressed as follows:
\[ \omega_n=\frac{4\pi^2 e^4 m}{n^3 h^3}\ . . . . . . . . . . . . (6) \]
where \(e\) and \(m\) are the charge and mass of the electron. When the atom passes from some \(n\)-th state into the \(n-1\)-state, light of frequency \(\nu\) is emitted, determined on the basis of (5) by the following relation:
\[ \nu=\frac{2\pi^2 e^4 m}{n^2 h^3}\left\{\frac{2n-1}{(n-1)^2}\right\}\ . . . . . . . . . . . (7) \]
From comparison of (6) and (7) it follows that \(\nu\) is not equal to \(\omega_n\). Only for values of \(n\) that are extremely large, when in expression (7) it is permissible to replace
\[ \frac{2n}{(n-1)^2} \sim \frac{2}{n}, \]
do expressions (6) and (7) practically coincide.
Still more complicated is the question of the relation between the frequency of the absorbed light \(\nu'\), the frequency of the emitted light \(\nu\), and the frequency of the periodic motion of the atomic or molecular system \(\omega\). This problem has fundamental significance for judging the actions of light from the point of view of the quantum theory, since, obviously, the initial stage of such an action must consist in the absorption of light. Planck’s original theory and Bohr’s theory solve the problem in an entirely formal and essentially extraordinarily puzzling way. The energy states of the system can change only by jumps; only the energy states \(E_1, E_2,\ldots\) are conceivable—intermediate states are excluded. Thus the absorption of the energy of external radiation can again occur only in whole quanta. This point of the theory is perhaps its most vulnerable one. Up to now one had to point only to the violation of the principles of classical electrodynamics; but in the point concerning the quantum absorption of light we encounter the organic impossibility of imagining a process of this kind without abandoning the law of conservation of energy.
In Planck’s first theory the question posed above is resolved formally by the equality:
\[ \nu=\nu'=\omega, \]
but this equality is, in essence, a new and hardly intelligible hypothesis. In Bohr’s theory:
\[ \left. \begin{array}{c} \nu \ne \omega\\ \nu' \ge \nu\\ \nu' \ne \omega \end{array} \right\} \ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots (8) \]
The possibility of using the idea of resonance for the interaction of light and matter is thus completely excluded. The phenomena of dispersion, the scattering of light, etc., as it were do not exist for quantum theory; at any rate, the theory in its present state closes its eyes to them.
Stark, Einstein, and other physicists attempted to cut the Gordian knot of the problem of quantum absorption by the hypothesis of “light quanta.” From this point of view, a quantum of energy emitted by a certain system exists and propagates in space discretely, and therefore it is absorbed as a whole. The light quantum is still defined by the value (3), while the relation between \(\nu'\) and \(\omega\) in this theory is entirely unclear. On the other hand, it is obvious that
\[ \nu \le \nu' \ldots\ldots\ldots\ldots\ldots\ldots (9) \]
All the variants of quantum theory set forth above appeared and exist only by virtue of brilliant quantitative confirmation in experiment. But we have seen above that the resonance theory is also excellently confirmed by experiment in the domain of such phenomena as dispersion and the scattering of light, which are inaccessible to the quantum theories described above.
The only attempt to throw a bridge across this strange abyss was made by Planck. He showed that, for explaining the regularities of black radiation, only the postulate (3) of the quantum emission of energy is sufficient, while the absorption of energy may occur continuously, in accordance with the principles of classical theory. Thus many results of the resonance theory (for example, dispersion) turn out not to contradict quantum theory. Later Planck proved that the theory of discontinuous band spectra, the so-called rotational spectra, can also be obtained under the assumption of continuous absorption of light1.
Bohr, in his latest works, establishes an indubitable correspondence between the principles of classical theory and the consequences of quantum theory. However, this correspondence is in essence only a formal statement of an experimental fact—an equality is established between quantities that are not theoretically connected. We are dealing with yet another new postulate, and the theory assumes an extremely confused appearance.
In the end, in order to understand the action of light, the modern physicist has either to pass over in complete silence the primary stage of the process—the absorption of light1—and begin directly with the second stage, the results of absorption, or else, when considering absorption, to look at it “classically,” and subsequently to pass over to the point of view, for example, of Bohr’s theory. The two eyes of modern theoretical optics—the “classical principles” and the quantum theory—unfortunately very often look in different directions; the object is “doubled,” and no single fused image is obtained. Only in Planck’s second theory does this doubling disappear, and therefore, willy-nilly, in interpreting the action of light one often has to make use of Planck’s conceptions, despite the fact that applying them to the theory of line spectra will apparently present considerable difficulties. We do not, however, know of any definite attempts in this direction.
§ 4. The photoelectric effect. When light is absorbed, electrons may be emitted from a substance. Experiment can determine the number of electrons emitted per unit of absorbed light energy, \(N\) (the strength of the saturation photoelectric current), and the value of the initial energy with which the electrons leave the substance, \(\dfrac{mv^2}{2}\). The fundamental postulate of the quantum theory (3) immediately makes it possible to indicate upper bounds both for \(N\) and for the initial energy, quite independently of the experimental conditions. We assume that from an atom or other elementary system, under the influence of light, only one electron can be emitted at a time. There are fairly weighty experimental observations in favor of such an assumption regarding the “elementary photo-effect.”2 If the frequency of the active light is \(\nu\), and the amount of absorbed energy is \(E\), then on the basis of (3) the maximum possible value for the number of emitted electrons is as follows:
\[ N \leq \frac{E}{h\nu}\ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ (10) \]
\(N\) may be less than \(\dfrac{E}{h\nu}\), since the photoelectric effect is not obligatory for all molecules passing through the quantum state. The quantum state is a condition necessary for the emission of an electron, but not sufficient, and in this sense the quantum theory can predict nothing.
As regards the initial energy of the emitted electron, the quantum theory is likewise able, generally speaking, to indicate only an upper bound. On the basis of (3)
\[ \frac{mv^2}{2} \leq h\nu\ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ (11) \]
The initial energy, as determined experimentally, may be considerably less than the quantum \(h\nu\) for several reasons. First of all, the frequency \(\nu\), which determines the absorbed quantum \(h\nu\), is, generally speaking, greater than the frequency \(\nu'\) of the emitted (or, in general, transmitted) quantum \(h\nu'\). Further, in order to extract an electron from the system, a certain work \(w_1\) must be expended. In the solid and liquid phase of a substance, the electron under experimental conditions must, in addition, perform work against surface forces \(w_2\). As a result, even in the case where the absorbed quantum coincides with the given-off quantum, being determined by the frequency \(\nu\), we obtain the following value for the initial energy:
\[ \frac{mv^2}{2}=h\nu-w_1-w_2 \ldots \ldots \ldots \ldots \ldots (12) \]
If \(h\nu < w_1+w_2\), then, obviously, the electron is not at all able to emerge at the surface of the substance. Choosing such a frequency of the incident light \(\nu_0\) that
\[ h\nu_0=w_1+w_2, \]
we may rewrite equality (12) in the following form:
\[ \frac{mv^2}{2}=h\nu-h\nu_0 \ldots \ldots \ldots \ldots \ldots (13) \]
Practically, therefore, the photoelectric effect can begin only for light with an oscillation frequency not less than \(\nu_0\).
It is apparently necessary to distinguish two types of photoelectric effect. In one case, the electrons fly out of atomic systems and, consequently, the work \(w_1\) in formula (12), expended in overcoming intra-atomic bonds, may be considerable. On the other hand, the ejection of free electrons from metals is possible. These electrons may also be “semi-free,” i.e. partly bound to the surrounding atoms, but in any case the bond will be considerably smaller than within atomic systems.
These considerations are confirmed by the remarkable works of Millikan1, on the one hand, and of de Broglie2 and Whiddington3—on the other.
In the first series of works Millikan proved the validity of the general relation (12) for clean surfaces of \(Na\), \(K\), and \(Li\). The relation is fulfilled so exactly that it provides a new method for determining the constant \(h\). Millikan’s results were also confirmed for a number of other metals. Later Millikan succeeded in proving that, for the metals he studied, the work \(w_1\) is practically equal to zero. This remar—
definitive conclusion can be explained only on the assumption that the electrons ejected in the normal photoelectric effect are free, or very weakly bound.
The above-mentioned works of de Broglie and Whiddington concern the photoelectric effect occurring in metals under the action of X-rays.
When a metallic plate was illuminated with monochromatic X-radiation, obtained, for example, from a tungsten anticathode, electrons appeared with various initial velocities. In a magnetic field the beam of electrons was spread out into a “spectrum” depending on the magnitude of the velocity. This magnetic spectrum gave an image on a photographic plate; each line of the spectrum corresponds to a group of electrons with the same velocity. De Broglie and Whiddington obtained rather distinct “line spectra,” characteristic for each illuminated metal and for the frequency of the X-rays. The results of these investigators showed with sufficient accuracy that in this case the electrons are of intra-atomic origin. According to Bohr’s theory, the \(n\) electrons corresponding to an atom with atomic number \(n\) are arranged around the atomic nucleus in orbits characterized above all by the work required to remove an electron from the given orbit to infinity. These orbits, in relation to X-ray spectra, are usually denoted by the letters \(K, L, M, N\), and so on. The lines of the magnetic spectra obtained by de Broglie and Whiddington correspond to initial energies of the following magnitudes:
\[ h\nu - w_k \]
\[ h\nu - w_L \]
\[ h\nu - w_M \]
As a result, Bohr’s theory of atomic structure and law (12) are once again confirmed. This law was derived in 1905 by Einstein on the basis of the most extreme modification of quantum theory—the hypothesis of light atoms, of which we spoke above.
Up to now, the strict validity of equation (12) is regarded by many as the strongest argument in favor of light quanta. The initial velocity of the emitted electrons is wholly independent of the intensity of the incident light, being determined only by the frequency of its oscillations; on the other hand, the emission of electrons occurs instantaneously—there is no measurable time of accumulation of light energy in the substance. These two facts are undoubtedly extremely difficult for the classical theory, but it can hardly be asserted that they cannot in principle find an explanation, at least in Planck’s compromise theory. The independence of the initial velocity of the electrons from the intensity follows not from special assumptions of one or another version of quantum theory, but from the fundamental postulate (3), common to all versions.
The instantaneous occurrence of the photoelectric effect, in the case of illumination of surfaces of large dimensions, can be explained in Planck’s theory in the following way. Even before illumination, the elementary systems of matter (atoms, molecules, quasi-free electrons) possess a certain internal energy, generally speaking less than one quantum; this energy is distributed statistically: in some systems it may differ from a whole quantum by an infinitely small amount, in others it is infinitely small, etc. Thus, with a large number of such systems the photoelectric effect can begin instantaneously. In particles of exceedingly small dimensions a delay is often observed1, measured in some cases in whole minutes. This delay is apparently of secondary origin—it decreases when the density of the surrounding gas is reduced; but whether it disappears completely is an unresolved question. Even the smallest particles of metals obtained by sputtering in an arc contain so large a number of atoms that there is no basis for expecting an improbable delay.
Postulate (3) flawlessly explains the phenomena connected with the initial energy of photoelectrons. As regards the strength of the saturation photoelectric current, i.e. the number of emitted electrons, postulate (3) determines only the upper bound (10). In fact this bound is never attained—the number of emitted electrons is a very complex function of various factors; it is necessary to distinguish the normal and the anomalous (selective) photoeffect, etc. These facts require new hypotheses, without, however, contradicting the fundamental postulate.
§ 5. Photochemical processes. Every molecular chemical transformation requires a certain minimal work, expended in overcoming intramolecular bonds (dissociation) or in creating new bonds (combination); in the latter case there may also be a release of energy freed in the new configuration. Let us first consider reactions of the purely dissociative type, proceeding, for example, according to the scheme:
\[ AB \to A + B \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ (14) \]
Let the minimal energy necessary for decomposition be \(Q\). This energy can in many cases be determined. Let the same reaction take place under the influence of light absorbed by the molecule \(AB\) with frequency \(\nu\).
Postulate (3) forbids the transfer of the internal energy of the system outward until it has reached the magnitude \(h\nu\). Hence we immediately obtain an upper bound for the number of molecules \(N\) that can
decompose over some interval of time. If the energy absorbed during this time is \(E\), then on the basis of (3) we again arrive at the familiar formula:
\[ N \le \frac{E}{h\nu} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (15) \]
Not all molecules \(AB\) passing through the quantum state are obliged to decompose; the necessary and sufficient conditions for decomposition are not fully known to us. One of the necessary conditions, following from the law of conservation of energy, is evidently the following:
\[ h\nu \ge Q \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (16) \]
Thus one may in advance exclude those light rays which, being absorbed by the substance, cannot act photochemically—they cannot cause the decomposition of the molecule. The situation is not so hopeless with rays that are not absorbed by the molecule \(AB\), but have such a frequency \(\nu\) as satisfies condition (16). Let us imagine that, besides the molecules \(AB\), in the given volume there also exist molecules \(C\), which absorb light of frequency \(\nu\), but do not decompose in doing so. Let us further suppose that the molecules \(C\) are incapable of combining either with the molecules \(AB\) or with the decomposition products \(A\) and \(B\). In such a mixed medium reaction (14) is already possible, and here is why.
The molecule \(C\), on the basis of postulate (3), can transmit its energy to the external medium only in whole quanta \(h\nu\). This transfer may take place, generally speaking, in various ways—in the form of radiation, in the form of the energy of a photo-electron, and, finally, upon collision with another molecule, transfer of the internal energy \(h\nu\) is possible in such a way that it is liberated in the form of kinetic energy of the struck molecule or of its parts. This last case is of interest to us here. The quantum of energy \(h\nu\) cannot be accumulated by the molecule \(AB\) in the form of radiation, but it can be transferred to it by the molecule \(C\) upon collision; condition (16) will be fulfilled, and the molecule \(AB\) may fall apart. The molecule \(C\) thus plays the role of an intermediary in transmitting light energy of frequency \(\nu\) to the molecule \(AB\). These simple considerations were developed in recent times by Franck1.
Franck2, together with his collaborator Cario, gave a brilliant example of a photochemical reaction of this type. Until now it had not been possible to decompose the hydrogen molecule \(H_2\) into atoms by photochemical means. The reaction proceeds, however, upon heating. From thermochemical data it follows that for the decomposition of the hydrogen molecule at least \(6.1 \cdot 10^{-12}\)
... ergs per molecule. From condition (16) we find that the smallest frequency of light oscillations at which dissociation of \(H_2\) is possible is
\[ \nu=\frac{6.1\cdot 10^{-12}}{6.54\cdot 10^{-27}}=9.3\cdot 10^{14}, \]
which corresponds to light with wavelength \(320\,\mu\mu\). From the dispersion of molecular hydrogen one may conclude that the absorption of light by hydrogen occurs near \(120\,\mu\mu\). Normal light sources do not give radiation of sufficient energy in this region of the spectrum; therefore the decomposition of hydrogen cannot be effected directly photochemically. One can, however, make use of an intermediary, as Cario and Franck did. Mercury vapor vigorously absorbs light of wavelength \(253.67\,\mu\mu\), which corresponds to a quantum \(h\nu\) considerably larger than the minimum energy \(6.1\cdot 10^{-12}\) ergs required for the destruction of \(H_2\). On the other hand, at normal temperature mercury vapor does not react with hydrogen. By mixing mercury vapor with hydrogen, we thus obtain a mixture of molecules of type \(AB\), subject to decomposition (hydrogen), and intermediary molecules \(C\) (mercury), which absorb light but do not decompose. Illuminating with the light of a mercury lamp a mixture of hydrogen with mercury vapor contained in a quartz vessel, Cario and Franck readily detected dissociation of molecular hydrogen.
In this reaction of Cario and Franck we have the simplest and most instructive case of photochemical reactions proceeding in the presence of a sensitizer. The role of dyes as sensitizers-intermediaries for photographic plates is well known. The role of chlorophyll in plants in the assimilation of the carbon dioxide of the air under the action of sunlight is likewise reduced to a sensitizing action, as the investigations of Bayley and his collaborators convince us especially firmly.
Everything said above applies to simple (irreversible) decomposition reactions of type (14). We have already said that in this case too equation (15) indicates only the upper limit for the number of decomposing molecules. Generally speaking, not all molecules that have absorbed a quantum necessarily decompose: they may transmit the quantum to the external medium and to others, in a less decisive way (radiation, photoeffect, etc.). All the more remarkable is it that almost all the studied reactions of type (14), as experiment shows, correspond to the limiting case of equality in condition (15). Very few such reactions are known; they were studied chiefly by Warburg and, recently, have been investigated in Nernst’s laboratory. The study of such reactions is especially difficult because process (14) is usually accompanied by side reactions of a purely chemical type, for example:
\[ AB+B=A+2B \]
\[ AB+A=B+2A \]
and so on. Accounting for such reactions is not always possible. Overcoming these difficulties is the next task of photochemistry.
The question is still more complicated with respect to synthetic photochemical reactions. There are many processes of this type; it is precisely they that play a large role both in the life of nature and in technology. But even the simplest reaction of photosynthesis—the formation of hydrogen chloride in light, carefully studied since the time of the classical investigation of Bunsen and Roscoe—is still unclear. Nernst1, on the basis of thermochemical data, assumes, for example, that the initial reaction is still the decomposition reaction:
\[ Cl_2 \longrightarrow Cl + Cl. \]
This reaction obeys condition (15), as was also recently discovered in Nernst’s laboratory2. But the main photochemical process is followed by a chain of purely chemical processes:
\[ \begin{aligned} Cl + H_2 &= HCl + H\\ H + Cl &= HCl\\ H + Cl_2 &= HCl + Cl\\ Cl + Cl &= Cl_2\\ H + H &= H_2 \end{aligned} \]
The decomposition of one molecule of \(Cl_2\) thus entails the formation of molecules of hydrogen chloride, until the last two processes in the chain of reactions given have occurred. Thus the decomposition of one chlorine molecule is followed by the formation of an enormous number of hydrogen chloride molecules: millions of \(HCl\) molecules are formed per quantum of light energy. This conclusion is confirmed by experiment. In the end, condition (15) seems to be violated, but, as is clear from the preceding, this violation is only apparent and is explained by secondary processes.
Nernst’s view takes as the basis of the process of \(HCl\) photosynthesis the photochemical formation of chlorine ions. This conclusion, however, is contradicted by the absence of noticeable ionization in a mixture of chlorine and hydrogen under illumination, as Le Blanc and Volmer3 showed. The tendency to interpret synthetic photochemical reactions by the primary formation of ions is very widespread and finds confirmation in the parallelism, observed in some cases, between the photochemical and photoelectric processes. But such parallelism is by no means general; moreover, it is not difficult to show that the primary formation of ions entails, generally speaking, the necessi-
...possibility of some continuation of the process even after the illumination has ceased, which contradicts experience. Thus there are no sufficient grounds for assuming the necessary causal connection between the photoelectric effect and complex photochemical processes; the parallelism observed in experiment may be explained otherwise.
On the basis of the general postulate (3), we may, without making additional hypotheses, suppose that for a photochemical reaction of any type the corresponding absorbing molecule must at the given moment pass through a critical state characterized by internal energy \(h\nu\). But for synthetic reactions one more essential supplement is needed. Let us consider the following gaseous reaction:
\[ A + B \to AB \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (16) \]
Let \(A\) be the component absorbing light. For photosynthesis (16) to be possible, it is evidently necessary that the molecule \(A\), while passing through the quantum state, be in contact with \(B\); otherwise the reaction is impossible. If the quantum state of \(A\) lasts only an instant, and if, on the other hand, the duration of the encounter of \(A\) and \(B\) is also instantaneous, then reaction (16) is practically impossible,—the probability that the moment of encounter of the molecules and the moment of transition through the quantum state coincide will be infinitely small. There are two ways out of this difficulty. It may be assumed that the time during which the molecules \(A\) and \(B\) remain within their spheres of action is finite. Such a view is quite consistent with our notions of the molecular force field and even finds some quantitative confirmation, at least as to order of magnitude. The other possibility is connected with the assumption of the duration of the critical state. Possessing the internal critical energy \(h\nu\), the elementary system, from this point of view, gives up this energy not at once, but after a certain interval of time (Verweilezeit). In Bohr’s theory, for example, an electron, having received the energy \(h\nu\) and having moved to an outer orbit, does not return immediately, but remains for some time on the outer orbit: the causes of its return must be external causes (for example, molecular impacts), and, consequently, the time of such an unstable critical state of the system will be a variable quantity, depending on chance. There is reason to suppose that the average value of this interval of time under some conditions is of the order of \(10^{-8}\) sec.\(^{1}\) The hypothesis of the prolonged existence of the critical state of an atom is very plausible in Bohr’s theory and, in general, in all variants of quantum theory that assume discontinuous, quantum absorption. If a system receives energy at once as a whole quantum, then it is very
\(^{1}\) O. Stern and M. Volmer. Phys. Zeitschr. 20, 183. 1919.
naturally to think that this quantum also remains in the system until such time as one or another external cause brings about its release; it is far more difficult to imagine the transfer of a quantum by virtue of unknown internal causes. In Planck’s theory (continuous absorption), at least as applied to black radiation, the critical state cannot be long-lasting; if at the moment when the energy of the system reaches the value \(h\nu\) the system does not transfer energy to the external medium, absorption continues uninterrupted as before up to the second critical state \(2h\nu\), and so on.
Closely connected with the question of the duration of the quantum state is the problem of the duration of the emission of the quantum \(h\nu\) into the external medium (in the particular case, the duration of emission). One may assert, of course, that the release cannot be instantaneous, but, on the other hand, no variant of quantum theory is capable of determining the duration of the release. Attempts to determine this quantity in the case of emission are inevitably connected with the application of the correspondence principle, i.e., with the results of classical theory1. Meanwhile, the question of the duration of release acquires no small importance in all problems analogous to the problem of photosynthesis (16). If the process of the molecule \(A\) releasing a quantum has begun before its encounter with the molecule \(B\), then this molecule is already deprived of the possibility of receiving a whole quantum from \(A\). For the transfer of an entire quantum it is necessary that the time spent by \(A\) in the sphere of action of \(B\) be greater than the duration of emission.
All these questions are only being outlined and, apparently, are far from resolution. In particular, the problem of photosynthesis is still obscure in many respects. One may assert only that postulate (3) is a very reliable guide in the tangled labyrinth of photochemical processes; in the simplest cases experience confirms it directly; in complicated cases postulate (3), together with thermodynamic relations, makes it possible to make sense of a large number of possible complicating side processes.
Postulate (3), as has already been said, lies at the foundation of all variants of quantum theory. Defenders of the theory of discontinuous quantum absorption try to see in photochemical processes as well an argument in favor of their theory. The basis of the argument is the same as in the photoelectric effect: 1) the duration of the photochemical process—not all molecules, for example, decompose at once; 2) the reaction begins immediately after the start of illumination; the so-called “photochemical induction,” observed in some cases, is explained by secondary chemical processes. The hypothesis of discontinuous absorption explains these facts very simply—by the probability of collision of the quantum \(h\nu\) and the corresponding molecule; not all molecules will meet the quantum,
and those that are encountered immediately decay. Such views were first expressed by Einstein in 1905, but from time to time they are revived even now. Recently Silberstein1 has used them for the interpretation of processes in the photographic plate, and one has, nolens-volens, to operate with such risky concepts as the “cross section” of a quantum. The hypothesis of “light quanta” had great heuristic significance, allowing Einstein to derive, in an extremely simple way, the laws of the photoelectric effect and of photochemical processes, which we have already used; but in any utilization of “light quanta” for one or another conclusion one should not forget the glaring contradiction of this concept with the fundamental facts of optics. The significance of light quanta is the same as that of the heat, electric, magnetic, and other fluids, which in their time served honorably for heuristic purposes but are essentially incorrect. On the other hand, Planck’s theory (continuous absorption) fully admits an interpretation both of the instantaneous onset of photochemical processes and of their duration. Before the molecule is illuminated, the medium already possesses internal energy, having in different molecules all possible values from 0 to \(h\nu\). The absorbed light gradually supplements this energy up to a whole quantum, and in this way different molecules will pass through the critical state at different times.
§ 6. Secondary radiation. The internal contradictions of modern optics appear very sharply in the domain of phenomena of secondary radiation. Experiment shows that the passage of light through matter is always accompanied by the matter’s own luminescence. With respect to the frequency of the incident light’s oscillations, this luminescence can be divided into two classes: opalescence and fluorescence. This division can, to be sure, be carried out only in terms of the classical theory. Opalescence is the result of forced oscillations of the particles of the medium, far from the region of resonance; fluorescence (in the broad sense of the word) corresponds to resonance of the light oscillations with the natural oscillations of the molecular system.
In the domain of phenomena of scattered light (opalescence) everything is satisfactory from the point of view of the classical theory. Experimental investigations of recent years by Cabannes2 and Strutt3 (Lord Rayleigh, Jr.) have at last provided the long-awaited laboratory proof of the scattering of light by molecules of a pure gas. The energy of the scattered light and its dependence on wavelength proved to be in complete agreement with Rayleigh’s classical theory. The state of polarization of light scattered by a gas is also well accounted for by this theory, if the incomplete isotropy of the corresponding molecular systems is taken into account. From the scattering data the number of scattering cen-
tors; the number of molecules scattering light in a gram-molecule, determined from this, agrees very closely (to within a few percent) with Avogadro’s number. The determination of the magnitude of the scattering of sunlight in the Earth’s atmosphere leads to the same results. Rayleigh’s formula can be derived from the general classical theory of dispersion1, and from this point of view the experimental investigations of recent times in the field of light scattering may be regarded as a brilliant success of the classical theory, which may fittingly be set against the successes of quantum theory in various fields.
Rayleigh’s theory, however, is applicable only to regions comparatively far from resonance. As soon as the absorption region begins, the classical laws prove powerless; the secondary radiation acquires the complex features of fluorescence, and quantum theory comes into force. Outside the resonance region the phenomena are determined mainly by the character of the incident light—by its frequency, energy, and polarization; there is no need whatever for “quantization” of the light energy. This circumstance, in our opinion, is one of the strongest arguments against any attempts to atomize light. The quantum \(h\nu\) and the constant \(h\) determine the properties of matter, not of light2.
What are the features of fluorescence light, and what properties may be expected on the basis of quantum theory? It is convenient to divide the question into three parts: 1) the energy of fluorescence, 2) the frequency of the oscillations, and 3) the state of polarization. Postulate (3) at once answers the first part. A fluorescing molecule can give energy to the external medium only in the form of an integral quantum \(h\nu\). Hence, as we have already said above, there follows a simple explanation of the absence of absorption of fluorescence. The number of molecules simultaneously emitting an entire quantum is negligible in comparison with the total number of molecules capable of simultaneously absorbing light. Such is the sole, quite general consequence that follows without any additional assumptions, which we can draw concerning fluorescence on the basis of postulate (3) alone. This postulate cannot, however, settle the question of the energy of fluorescence definitively. The transfer of a quantum \(h\nu\) to the external medium does not yet imply, generally speaking, that this energy will appear wholly in the form of fluorescence. It is possible to suppose that part of the quantum will be expended otherwise, for example in imparting some velocity to an electron, etc. From this point of view, the energy of the elementary act of fluorescence is
\[ \varepsilon \leq h\nu \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (17) \]
The absence of absorption of fluorescence and inequality (17) are all that can be extracted from postulate (3) for the field of fluorescence. The question
...the frequency and polarization of the radiation is not solved without additional assumptions.
Einstein in 1905 put forward the following new hypothesis, following directly from the theory of light quanta: the emitted energy is always equal to \(h\nu\), where \(\nu\) is the frequency of the radiation. This hypothesis, which is sometimes confused with Planck’s postulate (3), is entirely new; it concerns exclusively radiation. It is most convenient to formulate it in the following form:
\[ \nu=\frac{\varepsilon}{h}\ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ (18) \]
where \(\nu\) is the frequency of the emitted light, and \(\varepsilon\) is the change in the energy of the system during radiation. Let us apply the frequency condition (18) to inequality (17). Denote the difference
\[ h\nu-\varepsilon=p\ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ (19) \]
According to Einstein’s hypothesis, \(\varepsilon\)—the energy of the elementary act of fluorescence—is equal to \(h\nu'\), where \(\nu'\) is the frequency of the fluorescence light. Substituting the value of \(\varepsilon\) into (19), we find
\[ \nu'=\nu-\frac{p}{h}\ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ . \ (20) \]
\(p\) corresponds to the work expended in separating the quantum \(h\nu\), in addition to radiation—for example, in imparting some velocity to an electron. Equation (20) gives an explanation of the basic, general phenomenon of fluorescence—the Stokes law. Experiment shows that the region of maximum fluorescence radiation is always shifted toward longer waves relative to the spectral region of maximum absorption. The Stokes law is a stumbling block for the classical, resonant theory; on the other hand, it follows directly from Einstein’s hypothesis (18). Einstein explains the phenomenon of fluorescence as follows: in a molecule of a fluorescing substance, upon absorption of the quantum \(h\nu\), a photoelectric effect occurs; an electron is released with kinetic energy \(h\nu-p\), while the work \(p\) is expended in overcoming internal bonds. This electron subsequently becomes bound again with the same or another molecule, whereupon its energy is released in the form of radiation of frequency \(\nu'\), determined by condition (20). The quantity \(p\) may be variable—it depends on the entire history of the electron’s journey, from the moment of ejection to its return; in exceptional cases \(p\) may even become positive: upon encounters with other molecules the electron may acquire additional energy, and \(\nu'\) will become greater than \(\nu\). Thus one explains the possibility of a broadened fluorescence band and, at the same time, the possibility of the appearance of so-called “anti-Stokes” frequencies in the spectrum, greater than the frequency of the exciting light. Einstein’s view of the mechanism of fluorescence is not essentially new.
As early as the beginning of the nineties of the last century, Wiedemann and Schmidt considered fluorescence as a glow accompanying the restoration of a molecule. From this point of view, in a fluorescent substance a process of the following kind takes place:
\[ \begin{aligned} AB + \text{absorbed energy} &\longrightarrow A + B \\ A + B &\longrightarrow AB + \text{radiation} \end{aligned} \qquad \} \ . . . . . . \ (21) \]
\(AB\) is a molecule of the substance; \(A\) and \(B\) are products of decomposition (according to Einstein, Stark, and others, an ion and an electron). We shall see below that the phenomenon of polarization of fluorescence apparently refutes scheme (21).
In Bohr’s theory, Einstein’s hypothesis (18) is used; therefore it is clear that Stokes’ law is also satisfied. The mechanism of fluorescence in this theory does not differ in any way from the mechanism adopted for every kind of radiation. As a result of the absorption, in one way or another, of a quantum of energy \(h\nu\), an atomic or molecular system passes from one stationary state to another. From this state, under the influence of various causes, the system may return either to its initial state or to one of the intermediate, “allowed” states. Return to a state characterized by a lower energy is accompanied by radiation, the frequency of which is determined by Einstein’s condition (18). Different molecules will, generally speaking, undergo different transitions. Hence the possibility of the emission of an entire line resonance spectrum when the system is excited by monochromatic light. The intensities of the lines are determined by the probabilities of the corresponding transitions; the probability itself may be found from the correspondence principle. Thus Bohr’s theory of fluorescence in fact coincides with the general theory of spectra. The successes of the latter, one may say, are transferred in advance to the former as well, as is confirmed by numerous experiments.
Bohr’s theory is essentially different from scheme (21): there is no longer any question of a process of dissociation—only of internal changes of the system. The scheme of Bohr’s theory may be represented approximately as follows:
\[ \begin{aligned} A + \text{absorbed energy} &\longrightarrow B \\ B &\longrightarrow C_i + \text{radiation} \end{aligned} \qquad \} \ . . . . . . . . . \ (22) \]
where \(A\), \(B\), and \(C_i\) correspond to the various stationary states of the system, the index \(i\) indicating the possibility of several stationary states.
Summing up, one may say that Einstein’s supplementary frequency condition (18) formally resolves the question of the frequency of the oscillations of fluorescence light in the quantum theory. Classical theory is powerless in this respect.
A substantial argument against the resonance theory of fluorescence was considered, for more than 50 years, to be the absence of polarization of fluorescence, in contrast to the polarization of scattered light. It is not difficult to show, however, that the absence of polarization is a necessary but insufficient sign for concluding that fluorescence is non-resonant in nature. Earlier experimental data referred almost exclusively to aqueous solutions of fluorescent dyes. Repeated observations could not detect polarization of fluorescence under excitation by either natural or polarized light. However, in 1909 Wood succeeded in proving quite irreproachably the presence of partial polarization (17–30%) of the fluorescence of iodine, sodium, and potassium vapors. The same results were obtained by Dunoyer, who extended them to lithium vapors. At low temperatures (low vapor density) the polarization in Dunoyer’s experiments reached 30–40%. At the end of 1922 Wood1 succeeded in establishing (qualitatively) the strong polarization of the ultraviolet resonant radiation of mercury. In 1920 Weigert2 found that some dyes in aqueous solutions (erythrosin, Bengal rose) also give strongly polarized fluorescence, and pointed out in this connection that an increase in the viscosity of the solvent promotes an increase in the degree of polarization. Later Schmidt3 showed that fluorescein in a glycerin solution gives strongly polarized fluorescence. Quite numerous experiments in this direction have been carried out by the author of the present review and by W. L. Lewschin4. It was found that all dyes (26 dyes were investigated) can be made to give polarized or unpolarized fluorescence light by changing the viscosity of the solvent. In aqueous and alcoholic solutions, strongly polarized light is given only by weakly fluorescent dyes; the fluorescence of aqueous solutions of typical brightly fluorescent dyes is practically unpolarized. For all dyes there exists a definite limit of partial polarization, which cannot be exceeded under any experimental conditions. For almost all dyes this limit is about 35%. The polarization of fluorescence proves to be a very complex function of various physicochemical factors. The study of this field has only just begun, and for the time being possible
S. I. VAVILOV
only general qualitative conclusions. The possibility of interpreting fluorescence as luminescence accompanying the process of recombination of parts of a molecule (21) is excluded. In this representation, between the absorption of the exciting light and the fluorescence there is inserted the intermediate link of dissociation of the molecule, and any possibility is lost of connecting the polarization of the primary light and the fluorescence.
If one disregards the relation between the frequencies of the primary and secondary radiation (Stokes’ law), then the polarization phenomena set forth can be quite fully interpreted on the basis of the resonant classical conception, as was first pointed out by Wood. If the fluorescing molecules are optically perfectly isotropic, then the secondary radiation should be completely polarized, both when excited by natural light and by polarized light, on the same basis as in the scattering of light by isotropic Rayleigh molecules. Something different will occur if the molecules are anisotropic. In the case of stationary anisotropic molecules arranged chaotically in a given medium, the fraction of polarized light can be calculated on the basis of the results obtained for the scattering of light by Rayleigh1. Depending on the degree of anisotropy of the molecules, the degree of polarization of fluorescence under excitation by polarized light will vary from 50 to 100%. Molecular motion cannot influence the scattering of light with respect to polarization, since we are dealing with forced vibrations, which immediately cease when the illumination ends; therefore Rayleigh’s formula, derived for stationary molecules, acquires general significance. Fluorescence corresponds to natural vibrations possessing a definite duration; Rayleigh’s formulas are applicable in this case only when the emission time is shorter than the time of the undisturbed state of the fluorescing molecule. If thermal rotation of the molecules is taken into account, it can be derived2 that the degree of polarization for a completely anisotropic molecule (linear dipole) decreases from 50% (stationary dipoles) to 14.3%. In the case where the perturbations become sufficiently strong and frequent (for example, in a mobile liquid of low viscosity), the polarization may disappear completely. Consequently, the degree of polarization of fluorescence in the classical resonant theory may have any values from 0 to 100%, depending on the molecular state of the medium (temperature, pressure, viscosity, etc.), the degree of anisotropy of the molecule, and the duration of emission. The theory of quanta, without additional assumptions, can clarify nothing with regard to the polarization of secondary radiation. Postulates (3) and (18) contain only assumptions concerning the energy
[[unclear: beginning of line obscured]] radiation frequency. A formal solution of the problem in this case can be obtained only by the methods of the “correspondence principle,” i.e., in the final analysis, by again resorting to the classical interpretation. It may be added that the primary role in interpreting experimental observations on the polarization of fluorescence, from the point of view of quantum theory, will have to be assigned to the time of residence of the molecule in the critical quantum state, of which we have already spoken above.
In the end one may say that the polarization of fluorescence, unlike other aspects of this phenomenon, finds a satisfactory explanation in the classical resonance theory and provides no new arguments in favor of the quantum theory.
§ 7. We have briefly reviewed the most characteristic features of the three principal groups of actions of light. Quantum theory has almost everywhere proved to be a miraculous panacea resolving all possible difficulties. It is precisely the study of the actions of light that gives the firmest support to the general postulates of the theory (3) and (18). The content of postulate (3), however, is considerably broader than the domain of optics. The energy imparted to an elementary system may be of any form; if it is assimilated by the system and has the magnitude \(h\nu\), we obtain the same results as under the action of light. The kinetic energy of electrons or molecules imparted to a system may lead to ionization (analogous to the photoelectric effect), to chemical processes (an analogue of photochemical reactions), to luminescence, cathodoluminescence, thermoluminescence, etc. (an analogue of fluorescence). The possibility of realizing all these processes is still determined by postulate (3). The character of the luminescence of all possible types of luminescence follows from Einstein’s hypothesis (18). We have no possibility of setting forth here the long chain of experimental and theoretical works in this field, accompanied by the invariable success of the quantum theory.
A seemingly combined action of different agents is also possible. If for the ionization of a molecule an energy \(h\nu\) is required, then it may receive it partly through absorption of light of frequency \(\nu'\), imparting a quantum \(h\nu'\), and partly at the expense of the kinetic energy of an electron (or ion) in a discharge tube, with energy \(h\nu''\). Ionization is possible if
\[ h\nu' + h\nu'' = h\nu . \]
Franck and Westphal\(^{1}\), and later Smyth and Compton\(^{2}\), succeeded in showing, for example, that the ionization potential of iodine vapor, equal under normal conditions to 9.4 volts, in the case of fluorescence of the vapor is lowered to 6.8 volts. The difference \(9.4 - 6.8 = 2.6\) volts agrees rather precisely with the quantum of light energy absorbed in
\(^{1}\) J. Franck u. Westphal. Verh. d. D. Phys. G. 14, p. 159, 1912.
\(^{2}\) H. D. Smyth and K. T. Compton. Phys. Rev. 16, 501, 1920.
fluorescence. The combined action of this kind is possible, however, by no means always; apparently, the necessary condition for it is the transfer, by each agent separately, of the molecule from one stationary state to another. If, under the influence of light, the molecule passes from the stationary state \(a\) into the state \(b\), then by the energy of the electron the molecule is transferred from \(b\) to \(c\). In other words, we are not dealing with a purely combined action, but with the action of each agent in stages. To carry out the transition from the state \(a\) to \(b\) by the energy of light smaller than a quantum, plus the supplementary quantum of the electron’s energy, is apparently impossible. This fact is well explained by the hypothesis of light atoms, confirming once again its heuristic value.
§ 8. The tactics of the modern physicist with respect to that duality of viewpoints which has been sufficiently outlined above are aptly expressed by Warburg: “We leave some forces for the siege of the fortress in the rear, while continuing the advance along the whole front with the main forces.” In this fortress, which has not surrendered but is under siege, there nest many important problems, and one of the chief ones is the question of absorption, of the primary stage in the action of light. The main forces advancing along the front simply keep silent about absorption; the besiegers storm it as best they can. We are already acquainted with some attempts to take the citadel—the hypothesis of light atoms is among them. Other extreme means are also proposed. Let us mention some of them. According to Webster1, for example: “We may encounter phenomena where it is disadvantageous to insist on the law of conservation of energy in its categorical form. It seems to me that in the present problem this is precisely the case. What is important is the explanation of the phenomena, not postulates. Instead of assuming an accumulation of energy in an atom which later radiates, let us simply suppose that the energy is destroyed, and that after some time an electron begins to move in the atom, emitting oscillations of large amplitude until a whole quantum, or a photo-electron with the energy of a quantum, is released. From this point of view the law of conservation of energy is a statistical effect.” In this way Webster attempts to reconcile dispersion with the theory of quanta.
The rejection of the law of conservation of energy is necessary for applying the fundamental postulate of Bohr’s theory on the existence of stationary states in the molecule to the fact of continuous absorption of light. This is now recognized by many theoreticians, beginning with Bohr himself. Tetrodе2, using the mathematical apparatus of the general theory of relativity and the Einsteinian picture of a four-dimensional world of variable curvature, attempts to consider absorption as
something predetermined, specified by the given world. We encounter a kind of “determinism”: “In the classical theory, radiation occurs ‘at random’; light is absorbed wherever it happens to be. In Tetrode’s theory, radiation at one point of the world and absorption at another are processes that condition one another. With every emission it is predetermined when, where, and how absorption will occur. The Sun would not emit if it existed in isolation in the universe and no other bodies absorbed its radiation. From this point of view there is no fundamental difference between thermal radiation and thermal conduction. Given completely general fundamental equations, absorption may even precede radiation.” Light emitted in the form of a quantum is likewise absorbed as an entire quantum, although at an intermediate stage it may spread out spatially, as interference phenomena show.
Attempts of this kind, in our opinion, testify more to the difficulty of the problem than to its solution. The accumulation of new difficulties rarely resolves the old ones.
The most acceptable approach to solving the problem of absorption remains, as before, Planck’s theory, which combines the principal results of the classical theory with the basic postulates of quantum theory. Let us recall once more that this theory explains the laws of discontinuous black radiation, discontinuous rotational spectra, and does not fundamentally contradict the basic facts in the domain of the actions of light. There are not sufficient grounds to suppose that attempts to extend Planck’s theory to other areas of the optics of material media will prove fruitless.