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NEW DATA ON QUANTUM ENERGY EXCHANGE IN COLLISIONS OF ATOMS AND MOLECULES¹
J. Franck.
According to Bohr’s atomic theory, atoms and molecules possess discrete stationary energy states determined by quantum relations. In these states electrons may revolve in so-called quantum orbits around the positive nucleus without emitting electromagnetic waves of a frequency corresponding to the frequency of their revolution, contrary to the requirements of classical theory. In the same way, positively and negatively charged ions may rotate about their common center of gravity or oscillate with respect to one another without emitting the corresponding infrared waves. Radiation—and, moreover, monochromatic radiation—arises only when an atom or molecule passes from one stationary quantum state to another. The frequencies of the monochromatic light emitted in this process are calculated from the difference of the energies in the two quantum states between which the transition takes place, according to the frequency equation:
\[ w_a - w_e = h\nu, \]
where \(w_a\) is the energy of the initial state, and \(w_e\) is the energy of the final state reached after the elementary act of emission has occurred. The state determined by the smallest quantum number for the given system, i.e. possessing the least energy, is called the normal, or unexcited, state. In this state we usually find atoms and molecules at low temperatures. Higher, or excited, states may be obtained by supplying, for example, light waves that are absorbed by the normal atom or molecule in accordance with the above-mentioned frequency rule. Excited states are unstable. After a short interval of time has elapsed, the system returns, either directly or through intermediate stages, to the normal state. Every spectral line has a certain
¹ Translated from the author’s manuscript.
element corresponds, in this case, to a transition between two quantum states of the system. In the case of atoms, in the optical spectral region, which is readily accessible to observation, one may confine oneself to considering only transitions of the most weakly bound electrons from one quantum orbit to another (of course, such quantum transitions affect the orbits of the remaining electrons). The supply of energy required to reach higher quantum states is not, however, limited to the process of quantum absorption of light indicated above; energy may also be supplied to atoms and molecules by collision with other atoms and molecules, or also with electrons; this energy is likewise received in whole quanta. Let us first consider the simplest case of collisions between atoms. The application of the kinetic theory of gases in this case has shown that these collisions can be described on the basis of the laws of collision of ideally elastic spheres. According to the principles of atomic theory, this possibility is justified only by the fact that the energy of translational motion in collisions of atoms at normal temperature is small in comparison with the energy required to transfer an atom from its normal state into one of the higher quantum states. The mean kinetic energy of atoms at room temperature is approximately \(5.3 \cdot 10^{-14}\) ergs. Meanwhile, for the transition from the normal state to the nearest higher quantum state in a cesium atom, which is distinguished by an extremely small excitation energy, \(Q = 2.2 \cdot 10^{-12}\) ergs is required. But even this energy is already large in comparison with the mean energy of translational motion of molecules at room temperature. The velocities of motion of molecules are distributed according to Maxwell’s law, and therefore even at room temperature there must exist some atoms with exceptionally large energy of translational motion, greater than \(Q\). The number \(n\) of atoms whose energy exceeds the excitation energy \(Q\) is related to the total number of atoms as follows: \(\dfrac{n}{n_0} = e^{-\frac{Q}{kT}}\), whence it follows that this fraction may be neglected,1 since \(\dfrac{Q}{kT}\) in our case is equal to 41.
The mean kinetic energy of atoms increases in proportion to the absolute temperature; therefore at high temperatures, for
of atoms possessing, upon collision, an energy sufficient to bring about a quantum transition in one of the colliding atoms will be appreciable. In this case we are no longer entitled to assume elastic collisions. To prove that in such collisions the energy of the translational motion of the two colliding atoms is used for the excitation of a quantum transition is possible only indirectly, though with great certainty. The task of this article is to set forth this question and the problems connected with it, since they have found an experimental solution.
Much more directly than in the case of collisions of atoms, the transfer of the energy of translational motion into the quantum energy of excitation can be demonstrated in considering collisions of electrons with atoms. Numerous experiments have indeed shown that in the case of such collisions one can directly confirm the fundamental principles of Bohr’s atomic theory1. Electrons collide with atoms in monatomic gases quite elastically, in the sense of the kinetic theory of gases, so long as the kinetic energy of the electrons is less than the energy required for the excitation of the first quantum transition. As soon as this degree of energy is attained, a noticeable fraction of all collisions is accompanied by a transfer of the energy of translational motion into quantum energy. It can be shown that the electrons lose precisely that fraction of their energy of motion which is used as quantum energy. If, during these experiments, spectroscopic photographs are taken, one can see that precisely those spectral lines arise which, according to the frequency condition, must appear in transitions from the calculated states of excitation to states of lower energy or to the normal states. Such a confirmation of the fundamental concepts of Bohr’s atomic theory is easier to carry out by means of experiments with electron impacts than in the corresponding experiments with atomic impacts, since, owing to the electric charge of the electrons, the latter can be given, by applying electric fields, a precisely known and, at will, variable energy, which the electrons transfer to atoms in collisions. Likewise, the loss of velocity of the electrons can be accurately established by investigating what potential difference of a retarding electric field the electrons can overcome before and after collisions. For uncharged atoms these means are inapplicable. We shall therefore first consider whether observations of collisions of atoms at high temperatures2 provide a basis for the assumption of relations of the same kind as in the case of electronic collisions. If
NEW DATA ON THE QUANTUM EXCHANGE OF ENERGY
and in this case a finite fraction of the colliding atoms, possessing the necessary relative energy, converts the energy of its translational motion into quantum energy, then this must be reflected in the corresponding spectral radiation of the gas under these conditions. In doing so, one should expect that, with a gradual increase in the temperature of any gas, there should first appear that line which corresponds to the transition from the first excited state to the normal state. If different gases are compared, then the gas with the smallest excitation energy should emit light at the lowest temperature. If the temperature is raised further, then, corresponding to the increase of the relative energy, which rises with temperature, ever higher energy levels will be reached, as a result of which further spectral lines will appear. The application of Bohr’s theory to spectroscopic data, especially to the regularities that make it possible to arrange the spectral lines of an element in series of related lines, makes it possible, when the serial scheme is known for a given kind of atom, to calculate exactly, from the frequency condition, the energy corresponding to the excitation of each spectral line. In general, the most easily excited spectral lines lie in the region of the short waves of the visible spectrum, or in the ultraviolet part; lines of the yellow or red part of the spectrum correspond to transitions between higher energy levels. Therefore they should be more difficult to excite than the principal lines. In the alkali metals the line of least excitation energy, being the member with the greatest wavelength in the absorption series, always lies in the visible spectral region. Temperature excitation in the alkali metals should therefore be manifested, at relatively low temperatures, by the appearance of the lines just mentioned. This is indeed confirmed by old spectroscopic data. If alkali metals, or their salts that decompose rapidly at the flame temperature, are introduced into a flame, then, as is known, the doublet of the sodium \(D\)-lines or the red line of rubidium appears already in a flame of such low temperature as an alcohol flame, whereas the other lines arise only in a flame of higher temperature. If one systematically compares the spectral lines of various alkali and alkaline-earth metals that arise in a flame of one and the same temperature, then one can see that, at a given temperature, the more lines appear, the lower the excitation levels of the corresponding metals. Let us take, for example, an ordinary Bunsen flame and consider the spectral radiation of a definite region of the flame when various salts are introduced (for this purpose a place with a temperature of about \(1530^\circ\) C was chosen). For lithium, only one line will be observed; for sodium, two; for potassium, three; for rubidium, four; for cesium, six spectral lines, i.e. we see the more spectral lines, the less
the excitation energy of the corresponding kind of atoms. The elements of the series of alkaline-earth metals, Hg, Cd, Zn, behave in an entirely analogous way. Passing from an ordinary Bunsen burner to an air blast flame with a temperature of about \(1900^\circ C\), and then to an oxygen blast flame with a temperature of about \(2100^\circ C\), we find the appearance of further spectral lines, as was to be expected in accordance with the considerations set forth above. Evidence for the transformation of the energy of translational motion into quantum energy may be provided not only by the spectral radiation of the flame, but also by its conductivity upon the introduction of salts. Namely, if one supplies to the atom such an energy as is sufficient to remove the electron in the atom from its principal orbit to an orbit with an infinitely large quantum number, then this will correspond, in other words, to such a removal of the electron from the positive atomic residue that the forces between the electron and the ion become imperceptible and the atom will be ionized. The energy necessary for ionization is therefore computed from the limiting frequency of the absorption series \(\nu_\infty\), multiplied by Planck’s element of action \(h\). This energy, for most elements, is less than twice the energy needed for the excitation of the first quantum transition. If the temperature is so high that the indicated transitions occur very often, then the energy in collisions will in some cases be sufficient for ionization. Although such collisions will occur more rarely, this ionization can nevertheless be conveniently detected. Our means in this respect are considerably more sensitive than the methods of spectroscopic investigation, since one has to observe currents that are easily measured with a galvanometer. Even in an ordinary Bunsen flame the conductivity increases very strongly upon the introduction of a salt. At a given temperature and an equal quantity of evaporated metal, the increase of conductivity in the series of alkali metals is again greatest for cesium, which has the smallest ionization energy, and least for lithium. Making use of plausible assumptions concerning the number of ionizing impacts, Noyes and Wilson1 have recently been able to explain well even the absolute magnitude of the conductivity of a flame upon the introduction of various salts. Thus, undoubtedly, we are dealing here with temperature ionization.
The circumstance also agrees very well with this: that at high temperatures one can also, in the ions thus obtained, excite spectral luminescence in turn. Of course, in this case the elements of different groups of the periodic system behave differently. The alkaline-earth metals have weakly bound valence electrons2. If, by means of temperature ionization, we remove
if one electron is taken from these atoms, an alkaline-earth ion with one valence electron is obtained, similar to the alkali atoms. The alkaline-earth ion, consequently, should be easily excitable. Indeed, even at the temperature of a soldering flame one can detect the lines of the ionic spectrum (often called the spark spectrum) of the alkaline-earth metals. Conversely, the ionic spectra of the alkali metals do not appear in the flame. This was to be expected, since when the weakly bound valence electron is split off by the thermal ionization of an alkali atom, there remains an alkali ion, similar to the noble gases and difficult to excite. Saha1 used these considerations concerning the thermal glow of gases, which follow from Bohr’s atomic theory, for astronomical problems. In this way he succeeded in bringing a large number of astrophysical observations into one general picture and in explaining many apparent contradictions. Thus, for example, the presence of lines of heavy calcium in such layers of the solar atmosphere that are higher than the layers where the lines of the lightest element—hydrogen—are observed had been incomprehensible. This paradox, however, is explained simply by the different excitation energies of both kinds of atoms. For the excitation of spectral lines in the visible part of the spectrum in hydrogen, a considerably greater energy is required than for calcium. In the upper layers of the atmosphere, where the temperature is lower than in the lower layers, the energy of collisions is still sufficient for the excitation of calcium, but insufficient for the excitation of the spectrum of hydrogen, although at this height hydrogen is present in a considerably larger percentage. In the case of easily ionized elements the corresponding substance may likewise fail to be detected spectroscopically in the heated atmosphere of a star because, at the temperature of the atmosphere, the atoms of the element are completely ionized. Thus, for example, the spectra of cesium and rubidium are not detected on the Sun. According to Saha’s theory, these spectra should be sought in places of the lowest temperature on the Sun, for example in certain parts of sunspots; indeed, there they have been found.
Experiments on the thermal glow of gases in an electric furnace, carried out by King2 for a number of substances, give purer results than the flame experiments briefly described above, and than astronomical data. They confirm the results found in flames with different temperatures. On the basis of these spectroscopic observations one may conclude that, just as in collisions of electrons with atoms, so also in collisions of atoms with one another, the energy of translational motion is transformed into quantum energy only if the relative energy in the impact has a magnitude sufficient for the excitation of quantum transitions.
For the case of collisions of atoms and electrons, Klein and Rosseland1 obtained certain thermodynamic conclusions which can be applied in exactly the same way also to the case of collisions of atoms with one another. Suppose that we have a gas heated so strongly that inelastic impacts frequently occur between the atoms, accompanied by the transformation of the energy of translational motion into quantum energy; in such a case there should occur a decrease in the number of atoms with high velocities.
The Maxwellian distribution of velocities required by thermodynamics for thermal equilibrium could be realized only if the energy of translational motion, lost in part or in whole by certain atoms, were restored to them. In the case of thermodynamic equilibrium, to each elementary process occurring \(n\) times per second in a definite direction there must correspond an elementary process in the reverse direction, occurring just as often. To simplify the problem, let us imagine a gas consisting of atoms possessing only two quantum states, normal and excited; the energy of translational motion of the fast atoms in \(n\) collisions is expended in the transition to the higher quantum state. The reverse process must consist in the excited atoms colliding \(n\) times per second with slow atoms and thereby transforming their quantum energy, without radiation, into the energy of translational motion of both colliding atoms. At the suggestion of Klein and Rosseland, impacts which bring an atom into the excited state are called impacts of the first kind, while impacts accompanied by transitions to a lower quantum state without radiation are called impacts of the second kind. The frequency of impacts of the first and second kind in thermodynamic equilibrium must therefore be the same. One may ask in what way thermal radiation is then brought about at all, if every excited atom again gives up its excitation energy without radiation in collisions. The answer, of course, is that only a certain percentage of the excited atoms undergo transitions without radiation, and these will be such atoms as, before the expiration of their lifetime in the excited state, i.e. before a spontaneous transition with radiation, collide with a slow atom. The remaining atoms radiate freely; however, the light emitted in thermal equilibrium is absorbed by other atoms, so that instead of one excited atom emitting its energy, another excited atom appears, again capable of an impact of the second kind. Thus we are dealing with a chain of equilibria between radiation and absorption, on the one hand, and impacts of the first and second kind—
NEW DATA ON QUANTUM EXCHANGE OF ENERGY
with another, and the radiating and non-radiating transitions are also in temperature equilibrium with one another.
We could conclude on the basis of temperature broadening that, out of all collisions of atoms whose relative energy is sufficiently great, some finite fraction leads to the excitation of quantum transitions. It follows from this that, when slow atoms collide with excited ones, the probability of transitions without radiation must be very large. The number of collisions of slow atoms is small in comparison with the number of collisions of fast atoms, since the mean number of collisions is proportional to the relative velocity of the atoms. If, therefore, for fast atoms only a small percentage leads to collisions of the first kind, then, for equilibrium to be possible, it is necessary that a large percentage of collisions of slow atoms lead to collisions of the second kind. It is therefore not difficult to carry out an experimental proof of such collisions of the second kind. Let us illuminate a certain gas, under low pressure, with light¹) whose frequency corresponds to the first member of the absorption series of the given gas: upon absorption of light of such a frequency, some of the atoms of the gas pass into the nearest higher quantum state. In this process it is observed, in agreement with Bohr’s theory, that the gas emits the energy received in all directions in the form of fluorescence radiation of the same wavelength. This phenomenon, discovered long before Bohr’s atomic theory by Wood first in mercury, and then by Dunoyer, Wood, and Stretton in vapors of the alkali metals, is called resonance radiation, since, in the sense of the classical theory, the frequency of the incident light is in resonance with the atom’s own vibration. It turned out that at low pressures the absorbed light is completely re-emitted, i.e., no absorption with heating of the gas takes place. If another neutral gas, for example a noble gas, is mixed into the gas at low pressure, then it is observed that, as the pressure of this added gas increases, the brightness of the resonance fluorescence continually decreases; Bohr had already expressed the supposition that this quenching of fluorescence and the simultaneous heating of the gas are caused by collisions of the second kind. The higher the pressure of the admixed gas, the shorter will be the interval of time between two collisions of atoms, and the smaller will be the probability that an excited atom will have time, before the collision, to emit again the quantum of energy it has received. In this way one can compare the mean time between two collisions, known from the kinetic theory of gases, with the mean time for an atom to remain in the excited state: making plausible assumptions about the cross-sectional area of the excited atom and assuming, preliminarily, the probability of collisions of the second kind with slow
¹) J. Franck, Z. f. Physik, 9, 259, 1922; G. Cario, Th. 10, 185, 1922, and the corresponding dissertation; G. Cario and J. Franck, Th. 11, 161, 1922.
atoms in this cold gas is equal to unity (which, according to what was said above, is not far from the truth), we obtain for the duration of the excited state a value from \(10^{-8}\) to \(10^{-9}\) seconds. This agrees with the consequences following from Bohr’s correspondence principle, and with W. Wien’s direct measurements,\(^1\) who was able to determine the damping of the glow of canal rays flying into a vacuum. On the basis of this rough estimate one can as yet extract nothing for testing the dependence, following from the correspondence principle, of the duration of stay in the excited state on the frequency of the light emitted in the act of radiation. According to what was said above, it must be assumed that the excitation energy in a collision of the second kind is transformed, in an elementary act, into the energy of translational motion of both colliding atoms. In this case unusually fast atoms should arise. For example, the excitation of the resonance fluorescence of mercury corresponds to an energy \(7.8 \cdot 10^{-12}\) ergs. The average kinetic energy of an atom at room temperature is \(5.5 \cdot 10^{-14}\) ergs. If, as the atoms colliding with the excited mercury atoms, one chooses argon atoms, whose atomic weight is 5 times smaller than that of mercury, then in a collision of the second kind, by the law of conservation of momentum, the mercury atom excited by resonance light must acquire a kinetic energy of \(1.3 \cdot 10^{-12}\) ergs, and the argon atom an energy of \(6.5 \cdot 10^{-12}\) ergs. The excess velocity of such unusually fast atoms will be expended only in further co-collisions. The question arises whether it is possible to prove experimentally that in collisions of the second kind the total excitation energy is indeed transformed in an elementary act into other forms of energy (in the case considered—into the energy of translational motion). There are several ways to do this. The simplest method consists in carrying out the following experiment. In a cold gas, when it is illuminated, excited atoms are obtained, as set forth above. To this gas (which we shall denote by the letter \(A\)) are mixed such atoms as possess lower excitation levels than the light quantum \(h\nu\) absorbed by the atoms of the first kind. If the excited \(A\)-atoms collide with \(B\)-atoms, then the excitation energy may be partly expended in transferring the \(B\)-atoms into a higher quantum state, and only the remaining energy will manifest itself as the energy of translational motion of both atoms. For clarity we shall ascribe special properties to the gases \(A\) and \(B\). Let the absorption line of gas \(A\) be the line with frequency \(\nu\); let the corresponding absorption line of gas \(B\) be \(\nu'\), with \(\nu' = \tfrac{3}{4}\nu\). In Fig. 1 (p. 72), schematically, in the usual manner, the excitation energies of these lines \(h\nu\) and \(h\nu'\) are represented as straight lines related as \(1 : \tfrac{3}{4}\). If this mixture is illuminated with light of frequency \(\nu\) and such a pressure is chosen that the excited \(A\)-atoms collide with \(B\)-atoms, then,
\(^1\) W. Wien, Ann. d. Phys. 60, 594, 1919; 66, 229, 1921.
besides the resonance fluorescence of gas \(A\) with frequency \(\nu\), weakened owing to collisions, there must also arise fluorescence light of gas \(B\) with frequency \(\nu'\). The difference of energy \(\frac{h\nu}{4}\), according to the theorem of conservation of momentum, will be distributed between the two atoms \(A\) and \(B\) in such a way that the \(B\)-atom will acquire kinetic energy of magnitude
\[ \frac{h\nu}{4}\cdot \frac{1}{1+\frac{m'}{m}}, \]
where \(m\) and \(m'\) denote respectively the masses of the \(A\)- and \(B\)-atoms. Thus we shall obtain \(B\)-atoms whose kinetic energy will be large in comparison with the kinetic energy of other atoms, provided only that \(h\nu\) is large in comparison with the mean energy of thermal motion. In this case, however, the light of frequency \(\nu'\), emitted by such a rapidly moving atom \(B\), can be determined by a stationary observer from the Doppler effect. Instead of the frequency \(\nu'\) of an atom at rest, the stationary observer will see the frequency \(\nu''\), connected with \(\nu'\) by the following equation:
\[ \nu''=\nu'\left(1+\frac{v}{c}\cos\varphi\right) \]
In this equation \(v\) is the velocity of the atom, \(c\) the velocity of light, and \(\varphi\) the angle formed by the directions of motion of the atom and of observation. In practical cases \(v\) is always so small in comparison with the velocity of light that the change of frequency, or the broadening of the line caused by this change, cannot be detected directly spectroscopically. However, the Doppler effect can be noticed from the fact that the line of the atoms of gas \(B\), broadened in this way, will absorb light more weakly than in the case of direct excitation of the resonance fluorescence of gas \(B\) when it is illuminated by light of frequency \(\nu'\).
Fig. 1.
This effect was in fact observed, although, of course, for practical reasons the experiment had to be carried out somewhat differently from the thought scheme described above. The experiment was performed in the following way. Sodium vapor was illuminated by the second member of the absorption series, i.e. by light whose quantum \(h\nu\) is sufficient for strong excitation of the sodium atom. Strutt1 found that under these conditions, in the fluorescence light, in addition to the exciting line, there appears the first member of the absorption series of sodium, i.e. the \(D\)-doublet. According to atomic theory, this result is explained by the fact that the transitions accompanied by radiation occur between the quantum state reached upon absorption of light and the state in which the atom is capable of emitting the \(D\)-lines as resonance fluorescence. However, alongside transitions accompanied by radiation, transitions without
radiation under the influence of collisions of the second kind. If the number of transitions without radiation is increased by adding, for example, argon to a pressure of two millimeters, then we obtain rapidly moving atoms which, fluorescing, can emit the \(D\)-lines. The difference in energy of the quantum states between which the transition without radiation occurs is distributed among the sodium and argon atoms. Indeed, it turns out that the fluorescence light of the \(D\)-lines produced in this way is absorbed by sodium vapor at the same temperature much more weakly than the resonance fluorescence produced when the same gas mixture is illuminated by the light of the \(D\)-lines.
A series of experiments entirely analogous to the thought experiment set forth above proves that, in a gaseous mixture of components \(A\) and \(B\), when illuminated by light absorbed by \(A\), all spectral lines appear in the form of sensitized fluorescence for which the excitation energy is less than the quantum \(h\nu\) of the light absorbed by gas \(A\). Such experiments were carried out with mixtures of mercury and thallium, mercury and lead, mercury and bismuth, mercury and silver, and mercury and cadmium. When illuminated by the light of the mercury absorption line \(253.67\,\mu\mu\), at comparatively low temperatures there appear only those lines of the admixed metal vapors whose excitation energy is less than \(h\nu\), corresponding to the line \(253.67\). If, however, the temperature of the mixture was chosen sufficiently high that the relative energy in collision constituted an appreciable fraction of the excitation energy \(h\nu\), then higher spectral lines also appeared. Thus, for example, it was found that, in collisions of excited mercury atoms with cadmium atoms, the quantum energy of the mercury atoms combined with the energy of translational motion in the collision in such a way that a higher quantum state of cadmium could be reached. This case is the exact reverse of the case described in the thought experiment above. There the quantum \(h\nu\) of the incident light absorbed by the gaseous atoms \(A\) was greater than the \(h\nu'\) of the light emitted by the atoms \(B\). The difference in energy was then converted into energy of translational motion. In the present case, however, \(h\nu'\) is greater than \(h\nu\), and the energy difference \(h\nu' - h\nu\), necessary for emission, is borrowed from the energy of translational motion. This process may best be characterized as follows: before the collision both atoms were in definite quantum states; after the collision they are again in definite quantum states; only during the collision has a quantum transition occurred. Exactly which transitions can occur depends only on the total energy present in the collision, quite independently of whether this energy is present in the form of quantum energy or of energy of translational motion. The energy of translational motion can assume arbitrary values; therefore it serves as a reservoir or source for those energy values which prove to be superfluous or which are lacking in the attainment of a definite quantum state.
NEW DATA ON THE QUANTUM EXCHANGE OF ENERGY
Relations arising in collisions of atoms and molecules, or of molecules with one another, are in principle similar to those that occur in collisions between atoms. They are, however, considerably more complex, since, in addition to quantum transitions of electrons from one orbit to another, one must take into account quantum changes in the energy of the vibrations of atoms relative to one another and in the energy of rotation of the atoms. This complication is manifested, as is well known, in the emission and absorption spectra of molecules, in the so-called band spectra, which consist of a much larger number of lines than atomic spectra—the so-called line spectra. According to Bohr’s atomic theory, band spectra arise when quantum changes of rotational and vibrational energy are superposed\(^1\) on quantum transitions of electrons. Correspondingly, the fluorescence spectra of polyatomic molecules under monochromatic excitation are more complex than the spectra of atoms. If illumination is by light that causes, in a given molecule, the smallest quantum transition of an electron and simultaneously changes the energy of vibration and rotation of the atoms, then the fluorescence light will consist of the exciting line and, in addition, at a constant distance from one another (on the frequency scale), there will be a large number of doublets. Most of these doublets have wavelengths longer than that of the exciting light; some, however, will have shorter wavelengths. Such a picture is especially distinct in the fluorescence spectrum of iodine when excited by the green mercury line. This spectrum, called by Wood a resonance spectrum, is explained as follows. According to Bohr’s correspondence principle, the vibrational energy of an anharmonic oscillator, as which we must imagine the molecule, can change upon absorption and emission by a large number of quanta, whereas the rotational energy of the molecule can decrease or increase only by one quantum of energy. In the transitions under consideration there is added to this still a change in the angular momentum of the electron. If, upon absorption of light, a definite excited state of the molecule is reached, then the emission of the absorbed energy occurs with a simultaneous increase or decrease of the rotational energy by one quantum: thus every line is split into a doublet with a separation of the components (in frequencies) of \(2\nu_r\), where \(h\nu_r\) equals the energy of one quantum of rotation. These quanta are very small; therefore the components of the doublet are situated very close to one another. In addition to this fine structure of the lines, the fluorescence spectrum is conditioned by the superposition of vibrational quanta on the quantum transition of the electron. Complete emission of the absorbed energy consists in the emission of light of the frequency of the exciting light, i.e., in the direct reversal of the process of excitation. If the excited molecule, upon returning
\(^1\) Literature concerning band spectra may be found in the book by A. Sommerfeld, Atombau und Spektrallinien.
of the electronic configuration into the normal state retains part of the absorbed energy in the form of vibrational quanta as internal energy, then lines arise whose vibration numbers are smaller than the frequency of the exciting light; they differ from the latter by an integral multiple of some constant quantity, i.e., they give a series of lines situated at equal intervals. If, upon emission, the molecule gives up that reserve of internal energy which it possessed before the absorption process, in the form of vibrational quanta, then there again arise, at equal intervals, lines with a wavelength shorter than the wavelength of the exciting light.
If one assumes that collisions occur before emission, then the excited molecule will have the possibility of giving up any values of rotational and vibrational energy, since no selection principle (Auswahlprinzip) of transitions extends to collisions; in this case the molecule may also lose its excitation energy in an impact of the second kind. As a result there will be obtained, on the one hand, a general weakening of the emitted light, owing to the transition of part of the energy into the energy of translational motion of atoms and molecules; on the other hand, many new states of excitation will arise, more or less close to the initial state, and instead of a series of equidistant lines there will be obtained an entire banded spectrum with innumerable, closely spaced lines, the intensity maximum of which will be shifted toward long waves in comparison with the unperturbed fluorescence spectrum. This typical picture of molecular fluorescence has thus far been obtained only in the case of the well-studied fluorescence of iodine.
Conversely, the energy of excited atoms can be made to pass over to molecules. Experiments analogous to those described above, in which, upon illumination by light absorbed by atoms, sensitized fluorescence of molecules would be observed, have not yet been carried out. It is very difficult to accomplish them, since molecules not possessing excitation energy in most cases react strongly chemically, or dissociate readily. However, the transfer of quantum energy from atoms to molecules can be proved precisely by the presence of dissociation processes caused in these molecules. Instead of sensitized fluorescence, one therefore has to observe a sensitized photochemical reaction. A simple example of such a reaction may be the following process: a mixture of mercury vapor and hydrogen is illuminated by the light of the line \(253.67\ \mu\mu\), absorbed by mercury. The quantum \(h\nu\) of this line, when calculated per 1 gram-molecule of absorbing molecules, corresponds to the communication of 112 large calories of heat. The heat of dissociation of hydrogen, on the basis of physicochemical and physical results, lies between 70–90 large calories. A mercury atom, excited upon illumination by light of the indicated wavelength, therefore contains,
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sufficient energy to bring about the dissociation of the hydrogen molecule upon collision with it. Indeed, it has been possible to show that, under the given conditions in a mixture of mercury vapor and hydrogen, the latter dissociates. At the same time the usual properties of atomic hydrogen are observed: it is occluded by the walls of the vessel and reduces oxides which, at the temperature of the experiment, are not reduced by molecular hydrogen. We believe that the example cited differs from other sensitized photochemical reactions described in the literature by its particular simplicity, since here there are undoubtedly no intermediate reactions, and the process consists in the transition of quantum absorbed energy into chemical energy upon collision.
In principle there is no great difference between an ordinary photochemical reaction and a sensitized one. According to Einstein’s fundamental photochemical law, a photochemical reaction can occur if the incident light is absorbed and its quantum $h\nu$ is greater than the amount of heat required for the molecular chemical process. The primary process in this case is the formation of an excited molecule. It is extremely improbable that such an excited molecule could transform its excitation energy arbitrarily into chemical energy. A necessary consequence of this would be the conversion of all the absorbed energy into energy of motion of the atoms. In the act of absorption, however, as set forth above, in most cases the chief energy is spent on the transition of an electron of the molecule to a higher quantum orbit, and only a small part of the energy is expressed in quanta of vibration of the atoms relative to one another; the energy of rotational quanta may practically be entirely neglected. Consequently, one should expect that, upon absorption of light, the molecule can be supplied with energy many times greater than that thermally necessary for its dissociation, and yet the molecule will not decompose. The transformation of the absorbed energy into chemical energy will occur only in the event that the excited molecule, before emission, is perturbed by collision with other atoms and molecules. In this case it experiences, to some degree, a collision of the second kind1 within itself, in which the quantum energy of the electron is distributed over the degrees of freedom of atomic vibrations and rotations, and the molecule decomposes just as in thermal collisions. Hence it follows that photochemical decomposition must occur with a very small efficiency coefficient, unless the quantum $h\nu$ of the incident light is equal to or only slightly greater than the heat required for the chemical process, since part of the energy must be imparted to atoms and molecules causing collisions of the second kind. The photochemical law of equivalence, according to which for each absorbed quantum there arises one reacting
(in the present case, the dissociating) molecule, should hold exactly only in the case when the absorbed quantum is considerably greater than the amount of heat necessary for the decomposition of the molecule. We shall not dwell here on the extent to which this is confirmed on the basis of photochemical investigations. We shall set forth, however, facts showing that molecules, upon absorption of light, and also under electron impacts, may, without decomposing, acquire values of energy considerably greater than are needed for their dissociation. An example of this is the fluorescence of iodine mentioned above upon excitation by the green line of mercury. In this case the absorbed quantum is considerably greater than the heat of dissociation of iodine, calculated per molecule. Nevertheless molecular fluorescence occurs, i.e. the molecules do not decompose upon absorption, but emit the absorbed energy, provided only that in the excited state they do not undergo perturbations. Only an increase of pressure or an admixture of foreign gases entails a weakening of the fluorescence and, as mentioned above, a partial transfer of energy to the perturbing atoms. The fraction of energy transferred in such collisions to the perturbing atoms, and the fraction of energy expended on dissociation of the molecule, apparently depend to a considerable extent on the atomic weight and the chemical nature of the colliding atoms and molecules; however, so far nothing more definite can be said in this respect. The pressures at which photochemical reactions are usually investigated are so great that emission of the absorbed energy in the form of fluorescence cannot be of significance here.
The corresponding relations take still sharper form for hydrogen molecules. The work of dissociation of hydrogen has a value, as has already been said¹), between 70 and 90 kg-calories. The corresponding quantum should correspond to wavelengths from 311 μμ to 400 μμ. In this spectral region hydrogen is completely transparent, and likewise electrons possessing the corresponding kinetic energy, equivalent to 3–4 volts, cannot decompose hydrogen. The greatest wavelength which hydrogen absorbs under normal conditions lies at about 120 μμ. From there a banded absorption spectrum extends to very short waves. It is difficult to work with light of such short wavelengths, and therefore there are no experiments concerning the excitation of fluorescence in hydrogen; experiments have, however, been carried out on collisions of electrons with hydrogen molecules, the kinetic energy of the electrons, equivalent to 10–20 volts, corresponding to the indicated short waves. Under these conditions, if the gas is pure and the pressure low, hydrogen emits its many-line molecular spectrum. It remains, therefore, in molecular form, although the absorbed energy exceeds the work of dissociation by 6–7 times. This also explains—
¹) G. v. Knorring. Zeitschr. f. Phys., 14, 19, 1923. (Hetting. Dissertation.)
it is found that in discharge tubes in pure dry hydrogen at low pressure there arises practically only a many-line spectrum; the atomic spectrum of hydrogen itself, e.g. the Balmer series, is detected only weakly and quite indistinctly, as will be discussed further on1. Strongly excited hydrogen molecules do not dissociate, if there are no perturbations, but emit the absorbed energy in the form of a band spectrum. If the pressure is increased, or, still better, if a neutral gas, e.g. helium, is admixed to the hydrogen in large quantity, then the many-line spectrum is almost completely extinguished, and a line spectrum appears instead. Under these conditions the excited molecules are already perturbed and do not emit, but dissociate into normal or excited atoms, provided only that the absorbed energy is equal to or greater than the sum of the work of dissociation of the molecule and the work of excitation of the atom. The energy absorbed by molecules corresponds to the quantum levels of the molecule; therefore values of the energy will hardly be found for which the quantum energy present in the molecule will be exactly equal to the indicated sum. As a result, excited atoms with large velocities will again arise, which can be detected by the Doppler effect. In this way the above-mentioned indistinctness of the atomic spectrum is explained. In the case observed by Merton, there was evidently no Stark effect, the presence of which might have entailed a broadening of the lines, since upon the addition of helium (40 mm) the line spectrum became brighter and sharper. The addition of helium cannot diminish the Stark effect, but it can fully explain the disappearance of the Doppler effect, provided only that the helium pressure is sufficiently high. Of the excited atoms formed in the dissociation of excited molecules at high pressures, only atoms with small velocities will radiate; the rest, before radiating, will undergo a larger number of collisions, thereby returning without radiation to their normal state. The energy levels of the molecule are situated very close to one another; therefore a sufficient number of excited molecules will be found whose energy is very close to the sum of the dissociation energy plus the excitation energy of the atom. Such molecules will give slowly moving atoms.
On the basis of the interpretation set forth, it is clear that an excited molecule possessing an energy greater than the sum of the work of dissociation plus the work of ionization of the atom can, under a perturbation caused by collisions, dissociate into an atom, an ion, and an electron. It would take us too far afield to set forth all the grounds indicating that this process is the lowest stage of ionization of hydrogen. If, however, we accept this opinion, then from the fact that the indicated stage of ionization is attained in the collision of mo-
Ya. Frank
hydrogen molecule with electrons of kinetic energy equivalent to 16.5 volts, one may conclude that the work of dissociation of the hydrogen molecule, expressed in volts, is equal to \(16.5 - 13.6 = 2.9\) volts, where 13.6 volts is the work of ionization of the hydrogen atom, calculated exactly from the boundary of the Lyman series. 2.9 volts correspond to a dissociation work of 68 large calories per gram-molecule of hydrogen decomposed. There is no satisfactory agreement between this value and the value determined by physicochemical methods. This discrepancy can be explained either by the inaccuracy of the indicated methods, or by the fact that the degree of ionization at 16.5 volts must be interpreted differently. For interpretation one may make, for example, the unlikely assumption that the hydrogen molecule breaks up into the constituent parts \(H_+\) and \(H_-\). If the corresponding simple energy calculation is carried out, then indeed a degree of ionization smaller by \(1\frac{1}{2}\) volts is obtained, since in the formation of a negative hydrogen ion from an atom and an electron approximately this amount of energy is liberated.
In conclusion let us consider a case in which chemical energy is used to excite quantum transitions. Haber and Just, as early as 1911,¹ showed that in chemical processes taking place at the boundary of the surface of alkali metals with phosphorus, halogens, etc., electrons are liberated; they indicated, moreover, that in this case the heat of reaction falling to the reacting pair of molecules is greater than the work of detaching an electron from the surface of the alkali metals. Haber and Zisch² have recently again undertaken an investigation of this question and have shown that, when gaseous streams of chlorine and sodium flow simultaneously, chemiluminescence arises, in which, for example, the \(D\)-line is observed. The interpretation of this chemiluminescence, likewise proposed by the authors, is completely analogous to the explanation of the processes considered above. Upon collision of chlorine and sodium, molecules are formed containing the entire heat of reaction in the form of energy of vibration and rotation.
They must, as Herzfeld pointed out on another occasion, undoubtedly dissociate, unless in collisions with other atoms or molecules part of their kinetic energy is taken away from them. Such unusual molecules with high energy, upon collision with sodium atoms, can transfer them into higher excited states and thus cause radiation, for example of the \(D\)-lines, although the mean temperature of the gas is not so high that such radiation could be thermal luminescence. Another excellent example of this is provided by the experiments of Kautsky and Zocher³ on the chemiluminescence of oxidosilicon. These authors proved that it is not the reacting—
¹ Haber u. Just. Ann. d. Phys. 36, 308, 1911.
² Haber u. Zisch. Zeitschrft. f. Physik 9, 267, 1922.
³ Kautsky u. Zocher. Zeitschrft. f. Phys. 9, 267, 1922.
the molecule, but the energy released in recombination excites the still undecomposed oxydiacetylene and causes it to luminesce. This substance glows in exactly the same way, regardless of whether the energy is supplied in the form of light or in the form of cathode rays. The examples of chemiluminescence described in the literature can evidently, to a greater or lesser extent, be interpreted in the same way. They are, however, not so easy to analyze.
From the thermodynamic point of view, photochemistry is a process inverse to chemiluminescence. In the former case, under illumination, we create excited molecules which, upon collision, convert the absorbed quantum energy into chemical energy; in the case of chemiluminescence, the chemical energy of the newly formed molecules passes into quantum energy, which is partly emitted. Both of these processes must occur with equal frequency at thermal equilibrium. The weakness of chemiluminescent glow is explained by the low probability of emission without perturbations at high pressures. The various theories found in the literature concerning the connection between chemical reactions and radiation (e.g., the theories of Perrin and Lewis) take no account at all of the influence of collisions. The calculation is carried out as though chemical dissociation were a quantum transition occurring upon absorption of light, while the formation of a molecule were a process accompanied by the emission of light. Such a view, according to what has been said above, is incorrect.
All the data set forth may be expressed in the following proposition. Atoms and molecules are, both before and after collision, in definite quantum states. During the collision itself, the entire available store of energy may be used to excite quantum transitions, independently of the form in which this store is present in the colliding systems.
Translated by S. Vavilov.