ENERGY LEVELS OF ATOMS AND MOLECULES AND THE CHEMICAL BOND1

J. Franck, Göttingen.

The subject “Energy levels of atoms and molecules in their relation to the chemical bond” is so extensive that, in the time allotted to me, I shall be able to consider only certain parts of it. In doing so, I shall permit myself to proceed in such a way that in the first part of my lecture I shall dwell on the experimental evidence for the quantum character of the absorption and emission of energy by atoms and molecules, in order then, in the second part, to approach the question of the chemical bond.

We shall start from the fundamental ideas of Bohr’s model of the atom, which I may assume are sufficiently well known that it will be enough merely to recall them briefly. We must not, however, lose sight of the fact—as Bohr himself especially strongly emphasizes—that any model which makes use of the laws of classical mechanics is only an approximation to reality. For rigorous calculations one must use the new quantum mechanics, developed with such remarkable success by Heisenberg, Schrödinger, Born, Dirac, Jordan, and others. However, the questions that concern us today—the exchange of energy in elementary atomic processes—can be presented most clearly with the aid of the views known, more or less earnestly, as “classical quantum theory.”

Atoms and molecules are built of nuclei and electrons. Electrons revolve around positive nuclei in quantum-selected planetary orbits. The transition between different quantum states of atoms and molecules can be caused by the absorption or emission of monochromatic light, with Bohr’s equation \(h\nu = W_A - W_E\) governing the relation between the energy in the initial and final states of the elementary process and the frequency of the absorbed or emitted radiation. Atoms and molecules can exist only in these selected quantum states. In the energetically most stable, lowest quantum state, atoms are found—at low temperature—under normal conditions. In higher quantum states atoms and molecules are unstable. The mean lifetime of these states can be approximately calculated from the classical damping of radiation. After this time, which is of the order of magnitude of \(10^{-8}\)–\(10^{-9}\) sec, atomic formations that are in higher quantum states return to lower states and, consequently, ultimately to the normal state. However, quantum transitions with emission and absorption do not occur between all possible quantum states; rather, the probability of transition is governed by the so-called selection principles, which are theoretically well founded. This entails the existence of excited states of atoms and molecules which are not unstable in the ordinary sense, but possess a certain stability. Such states are called metastable. In them atoms and molecules can exist for a longer time, of the order of magnitude of \(0.1\) sec. With the aid of these concepts it is possible, in principle, to explain the line series of atomic spectra and the band spectra of molecules. Absorption spectra are the simplest in appearance, since in this case the initial state is only the normal state of the atoms or molecules. In the absorption spectrum, therefore, there must be all permitted transitions from the ground state to higher quantum states. As an example of an atomic spectrum I shall cite the absorption series of gaseous sodium.

(Fig. 1). On the basis of this spectrum one can clearly establish the regularity of the transitions and the relative position of the energy levels of the atom. The absorption line with the greatest wavelength possesses an energy quantum just sufficient to transfer the atom from the ground state to the lowest state of excitation. For sodium this is the doublet of the \(D\)-lines. The next line gives the transition to the second state of excitation. Since the lines, as the quantum number increases, come closer and closer together, it is clear—and calculation confirms this—that the energy difference between higher quantum states becomes smaller and smaller as the quantum number increases, so that for an infinitely high quantum state energetically arbitrarily close neighboring states will also be possible quantum states.

Fig. 1.

To this continuous sequence of possible quantum states beyond the place of convergence there corresponds a continuous absorption spectrum, which in our figure is not sufficiently well visible. If, instead of spectral lines, we depict an energy diagram in which the positions of the energy levels relative to one another are shown by parallel lines, we obtain the following picture (Fig. 2): the first line represents the ground level, the second corresponds to the first state of excitation, and so on. If we create, by absorption of the \(D\)-lines, an excited atom in the first state of excitation, then we must, if the emission of light is not disturbed as a result of collisions between atoms, obtain fluorescence, namely monochromatic, so-called resonance fluorescence, in particular the reverse emission of the \(D\)-lines. The atom returns from the first state of exc-

Fig. 2.

excitation with emission of light into the ground state. If we illuminate our sodium vapor with the higher members of the absorption series, then in this case we shall obtain not only the emission of the exciting line, but also the possibility of transitions between higher levels. As a result, we shall obtain a whole series of lines, depending on the nature of the transitions between these levels. From this the Stokes law for fluorescence becomes directly comprehensible, according to which there can be no fluorescence light whose frequency would be greater than the frequency of the exciting light. So long as the experiment is performed at low temperature and there are no secondary processes supplying energy, this relation is completely fulfilled. Further, the fact that in fluorescence spectra there occur only those lines which correspond to allowed transitions between levels lying below the level initially excited by absorption is in agreement with Bohr’s theory. As one passes to ever higher series levels, the spectral emission, in accordance with the ever new possibilities of transitions, becomes richer. A sharp change occurs, however, as soon as we pass the convergence limit and apply even a very weak electric field. In this case, instead of the emission of light, ionization of the gas occurs. When illuminated by light whose wavelength is equal to the wavelength of the series limit, we create atoms in which the quantum orbit of the electron is infinitely removed from the positive remainder of the atom. In such a case the forces between the electron and the positive residual ion become infinitely small. With the aid of a very weak electric field we can cause the detached electrons and the positive ions to be separated at the oppositely charged electrodes, i.e., we obtain electrical conductivity of the gas. If we illuminate with light of a wavelength shorter than the wavelength of the convergence point, then ionization likewise occurs; the ions and electrons separate with a relative kinetic energy equal to the excess energy of the absorbed light quantum over the light quantum of the convergence point. Recombin-

conversion of ions into atoms takes place at the electrode itself.* This process apparently occurs without luminescence, and the energy released is for the most part converted into heat. Thus in the present case fluorescence is replaced by photoelectric ionization of gases. In the study of alkali-metal vapors, in accordance with the prediction of Bohr’s theory, a number of investigators found the appearance of ionization upon illumination with light of wavelength shorter than the wavelength of the convergence point. If the concentration of ions and electrons is chosen sufficiently large and no electric field is applied, then, upon recombination of the charge carriers in the gas, luminescence occurs in which all the spectral lines corresponding to transitions between the energy levels shown are found; in such a case the continuous spectra at the end of a series appear in the emission spectrum. A similar spectrum in terrestrial sources was recently discovered by Paschen.

Fig. 3.

Let us now consider, in the same cursory manner, the spectra of molecules; for simplicity we shall consider a diatomic molecule. In this case the spectrum is much more complex, as is seen from Fig. 3, which shows the band spectrum of iodine. The entire spectrum shown in this figure arises in place of a single spectral line of the atom, due to the transition of the electronic system from the lower level of excitation to the ground state. The complication is caused by the fact that in the molecule not only can the electronic system exist in quantum-selected states, but also the energy of vibration of the atoms relative to one another and the energy of rotation of the molecular nuclei about one another possess quantum states that can change upon absorption or emission of light, obeying Bohr’s frequency condition.

Let us now make, for the sake of convenience, the assumption (which does not correspond to reality) that the long-wavelength edge (“edge”) of the band—the name given to those groups of lines that are visible in the photograph—is caused by a quantum change of only one electronic system, without a simultaneous change in the energy of rotation and vibration. In that case the next edge in the absorption spectrum arises with the same change of the electronic system, upon which there is superimposed an increase of the vibrational energy by one vibrational quantum; the third edge corresponds to an increase of the vibrational energy by two quanta, and so on.

Thus the regularity of a series of edges in the present case makes it possible to establish the regularity of the system of vibrational quanta corresponding to a single electronic transition. The structure of an individual band is determined by the rotational quanta of the molecule. Rotational quanta have the smallest dimensions, in view of the relative slowness of the corresponding periods of rotation.

Fig. 4.

Already at normal temperature the molecules of a gas are found in a very large number of different rotational states. According to the selection principle, the number of rotational quanta may change, through absorption or emission of light, by $\pm 1$. The structure of an individual band in the absorption spectrum is due to the fact that molecules which are in the most diverse rotational states change their electronic state, their vibrational energy, and at the same time their rotational energy by $\pm 1$ rotational quantum. It is clear that if we wished to plot on a single diagram all the energy levels of a molecule, as we did for the atom, we would obtain an entirely unillustrative scheme. Therefore

I shall give here (Fig. 4) a simplified scheme, in which some levels of electronic energy are represented by long parallel strokes, and the systems of the corresponding quantum states of vibration by shorter strokes. The rotational levels are omitted. We see that, in accordance with the fact that the band edges in the spectrogram shown above (Fig. 3) are separated by almost equal intervals, the magnitude of the first vibrational quanta is almost constant.

Let us say a few words about the fluorescence of a diatomic molecule, corresponding to the resonance fluorescence of a monatomic gas. From our energy diagram one can clearly establish what is to be expected. If we illuminate the molecule with monochromatic light, then, depending on the choice of the wavelength of this light, we shall create some perfectly definite state of excitation of the molecule.

Fig. 5.

If we choose this latter arbitrarily, then, when the electronic shell returns to the normal state, not only the line which caused the excitation will be emitted, but also other lines corresponding to the possibilities of transition of the molecule both to the normal state without vibrations and to a large number of vibrational states of the ground state. Since the rotational energy can change only by \(\pm 1\) quantum, in this case we shall obtain a series of doublets in which the distance between the lines corresponds to a difference of \(\pm 1\) rotational quantum, while from the distance between neighboring doublets one can calculate the energy of the vibrational quanta. In Fig. 5 we see the results obtained by Wood under monochromatic illumination of iodine vapor. These results agree completely with the theoretical prediction. Thus we arrive at the following conclusion: experiments with absorption give us a system of quan-

vibrational quanta of the unexcited molecule, and fluorescence experiments—the system of vibrational quanta of the ground state. We shall often make use of these facts below.

After Planck’s hypothesis of light quanta had received numerous confirmations, and after the agreement, described above in general terms, of the spectral properties of atoms and molecules with Bohr’s theory had been established, there could no longer remain any doubt as to the discreteness of the energy levels of atoms and molecules. It is, however, very important that there exist independent methods for detecting precisely this discreteness. In order not to spend too much time, I shall cite, as examples of the latter, only some results from the study of electron collisions. In these investigations the quantum loss of energy by the incident electrons, or else the quantum acquisition of energy by the atoms and molecules subjected to the impacts, is established on the basis of the “characteristic” (the current–voltage diagram) of the electron current. In this case the electrons, generally speaking, are emitted by an incandescent wire with small velocities; by applying suitably chosen fields one can impart to the electrons any kinetic energy, after which they are given the opportunity to enter into collisions with the molecules of the gas under investigation. By studying the characteristic of the electron impacts one can determine the magnitude of the energy loss that took place in the collision, and by studying the products of the impact one can discover whether radiation is excited in the collision or whether ionization occurs. Finally, by determining \(e/m\) for the ions formed, one can establish the nature of the latter and thus, for example, find out whether dissociation of the molecules is associated with the ionization process.

After these investigations had been begun, they were developed by various investigators and by various methods. In order to show how quantum absorption of energy is reflected in the “characteristics” of electron currents, I shall present several curves. First of all we see (Fig. 6) how an appropriately chosen arrangement can make visible the excitation of the lowest quan-

of such a discontinuity of a monatomic gas. In the present case it is a question of the excitation of mercury. We see that at low voltages the curve proceeds as the ordinary current–voltage characteristic: approximately the same as the characteristic of thermoelectronic emission. At a certain critical accelerating field the electrons acquire such a store of energy that, upon collision with mercury atoms, they transfer them to the nearest higher quantum state. Here the electrons lose their energy. They can no longer reach the weakly negatively charged electrode, since the latter repels slow electrons. Therefore the current drops sharply. If the applied voltage is increased, then, with the increase in the velocities of the electrons, the current again rises until the electrons secondarily acquire sufficient energy to excite, upon collision with Hg atoms, the first quantum transition of the latter. This process is periodically repeated at points that are integral multiples of the excitation potential.

Fig. 6.

Fig. 7.

Evidence that in such cases the atoms are transferred to the first stage of excitation can be obtained spectroscopically. In those places of the tube where the electrons give up their energy to the atoms, the characteristic ...

for the given kind of atoms, resonance radiation, i.e., the so-called single-line spectrum, consisting of only one resonance line, should appear.

In Fig. 7 we see that indeed only one spectral line is emitted, although in the arc spectrum of the corresponding element, which is given below, there are many bright lines. The diagram in Fig. 8 shows how the current–voltage curves, with the corresponding experimental arrangement, make it possible to detect the appearance of higher stages of excitation. The numerous breaks on the curve, which was likewise obtained for mercury, show how, gradually, with increasing energy, ever new stages of excitation arise. This corresponds to the gradual addition of further spectral lines. Finally, let us consider one more curve, which will show us in what way ionization can be demonstrated on these curves of the dependence of current on voltage. This curve (Fig. 9) was also obtained in monatomic mercury vapor. We see that the current remains weak up to a certain critical voltage, at which ionization sets in. It gives the impression that at the ionization potential found in this way the number of newly liberated electrons is very large. In reality this is not so. The sharp break in the curve is due to

Fig. 8.

because the already very few newly formed positive ions, owing to their low velocities, disturb the space-charge cloud of the electrons.—In this way, for a large number of monatomic gases, the excitation levels and ionization potentials have been determined, and the values obtained prove to be in complete agreement with those that can be predicted on the basis of the spectrum according to Bohr. In some cases, especially when the absorption series of the type of atoms under investigation lies so far in the ultraviolet region that it can be carried out spectroscopically only very weakly, the method of electron collisions makes it possible to establish in advance the positions of the energy levels; then spectroscopic methods, of course much more precise, make it possible to confirm the result. Likewise, in the study of electron impacts, metastable states were first discovered. With a suitable arrangement of the experiment, the excitation of these states is sharply reflected in the curves of the dependence of current on voltage, despite the fact that these transitions, which under the action of light practically never occur, are also excited by electron impacts far more rarely than others.

Fig. 9.

Studies of electron collisions with molecules have naturally not been developed as far as in the case of monatomic gases. Quite apart from the technical difficulties (the appearance of decomposition products, etc.), in this case there arises a fundamental complication, which consists in the fact that, together with the transition of the electron shell of the molecule into another state, the vibrational energy, and also—though only slightly—the rotational energy, naturally changes.

We have here an analogy with those results which we saw earlier when considering band spectra. Therefore, roughly speaking, from the curves of the dependence of current on voltage one can determine only the approximate position of the region of strong absorption. Substantial results concerning ionization processes in molecules have recently been obtained by determining the \(e/m\) of the ions formed. The apparatus in these experiments is similar to that which Aston used in studying isotopes. These investigations showed that, by electron impact, a molecule cannot be ionized without a more or less considerable part of the energy being given over to increasing the vibrations of the molecule. Connected with this is the fact that, on the basis of investigations of electron impacts, one can draw certain conclusions about the work of dissociation of molecular ions and molecules.

Instead of electron impacts for exciting quantum jumps, one may, of course, make use of collisions of atomic formations with one another. The thermal glow of gases, as well as the thermal ionization of the latter, so successfully used by Saha (M. N. Saha) to explain the sinking of hot stellar atmospheres, belong precisely to this class of phenomena.

If we take terrestrial sources as an example, one may mention flame emission. If chemists are able to determine, with great sensitivity, alkali and alkaline-earth metals and analogous substances in the flame of a Bunsen burner, this is because the flame of a Bunsen burner—if solid carbon particles are absent—contains only gases in which visible spectral lines are excited with difficulty. The relative kinetic energy of the colliding atoms and molecules at the temperature of a Bunsen burner is insufficient for exciting these gases. On the contrary, the alkali and alkaline-earth metals have low-lying energy levels with transitions leading to the appearance of visible spectral lines. The best-known example of such lines is furnished by the sodium \(D\)-lines.

We now turn to a brief consideration of the question of how the excitation energy of atoms and molecules is applied. Klein and Rosseland were the first to point out that, from purely thermodynamic considerations, it follows that collision processes in which quantum jumps are excited correspond to the reverse processes, the so-called collisions of the second kind, in which excited atoms and molecules, as a result of collision, transform their excitation energy into energy of translational motion and into other degrees of freedom of thermal motion.

Fig. 10.

As an example of such collisions of the second kind one may cite the change in the fluorescence of monatomic and polyatomic molecules, which is observed when, in studying the fluorescence of gases, the pressure is taken so high that the molecules and atoms undergo collisions during the “lifetime” of the excited states. In the following diagram (Fig. 10) we see how the intensity of the fluorescence of iodine changes when foreign gases are added. When noble gases, such as helium, are admixed, the influence of these gases in collisions proves insignificant, and therefore we obtain a much weaker quenching of fluorescence;

rather than upon admixture with active gases. Instead, we see that the fluorescence spectrum itself changes (Fig. 11). Under the action of a noble gas, the excited molecule, upon collision, gives up small portions of its energy to the colliding partner, which acquires the corresponding amount of energy of translational motion. As a result of this we no longer obtain the pure systems of resonance lines that we saw earlier; rather, the excited molecule passes into all nearby neighboring states, in which the rotational energy differs by more or less small amounts. In this way there is obtained practically an entire band spectrum of emission, shown in the lower spectrogram of Fig. 11. (The upper spectrogram gives the resonance spectrum of pure iodine vapor.)

Fig. 11.

The fluorescence of iodine gave us an example of the conversion of excitation energy into heat motion. Another possible application of excitation energy consists in the fact that an excited atom, upon collision with an unexcited one, uses its energy in order to excite the latter. Let us take, as an example, mercury atoms in the lowest state of excitation and make them collide with atoms of the vapor of another metal whose excitation levels are lower than those of mercury (see Fig. 12). We shall

Fig. 12.

observe, in such a case, sensitized fluorescence, in which all the lines are emitted that correspond to transitions between all energy levels lying below the initially excited energy level of mercury. In some arbitrarily chosen case, for example, one in which excitation requires half the excitation energy of the initially excited atom, the other half must be distributed between the colliding partners as their kinetic energy. The lines due to transitions from this level must therefore be emitted by rapidly moving atoms and, consequently, must exhibit Doppler broadening. This is indeed what can be observed in reality.

A variant of sensitized fluorescence is the phenomenon which I shall allow myself to call sensitized ionization. If a strongly excited atom is given the opportunity to collide with other atoms, and if, at the same time, the excitation work of the first atom is greater than the ionization work of the second, then the latter will be ionized. This circumstance can be established especially well by means of the above-mentioned method for determining \(e/m\).

We now turn, finally, to the application of excitation energy in chemical processes. In order to connect this transition directly with what was said earlier, let us take as an example the transformation of the excitation energy of mercury, which is in the first excitation level, into the dissociation energy of molecules with which these mercury molecules collide. We shall illuminate a mixture of mercury vapor and hydrogen with the resonance line of mercury vapor. In such a case we shall obtain decomposition of the hydrogen: hydrogen atoms arise, exhibiting all those reducing, absorptive, and other effects characteristic of H-atoms. Since the resonance line of mercury is not absorbed by pure hydrogen, it is natural that, when pure hydrogen is illuminated by it, no photochemical reaction occurs. Recently, similar photochemical reactions sensitized by mercury have been studied for a large number of substances. I shall allow myself to point out that these reactions have even found technical application.

Studies of this kind make it possible to determine the upper limit of the dissociation work of the corresponding type of molecules. In our case the dissociation work of \(H_2\) must not exceed the excitation work of mercury. Cases of chemiluminescence, first studied by Haber and his collaborators, are a direct converse of the processes considered. If, for example, hydrogen atoms collide in sufficient number with atoms of a metal that have low excitation levels, then a case should arise in which, in such a triple collision between two hydrogen atoms and a metal atom, the hydrogen atoms combine into a molecule, while the liberated heat of combination is used to excite the metal atom. And indeed, such cases have been observed many times, although sometimes the process is not a simple elementary process. As an example I shall mention that Bonhoeffer obtained excitation of the resonance line of mercury by means of recombining hydrogen atoms, although the dissociation work of hydrogen is less than the energy necessary for emission of this line. Evidently, excitation here takes place in two stages, and, apparently, the formation of metastable mercury molecules plays a role; these possess lower excitation levels than the atoms. One may imagine that in a triple collision between an \(Hg_2\) molecule and two H atoms there arises a metastably excited mercury molecule, which in a second triple collision decomposes into an excited and a normal atom. I shall not, however, enter more closely into the consideration of this example.

From the field of ordinary, well-developed photochemistry, which serves as an excellent school example of the use of excitation energy for chemical processes, I shall cite only a few separate cases among those in which the primary processes can be indicated.

Einstein’s photochemical law of equivalence states that for each absorbed light quantum there initially arises one reacting molecule, provided that the quantum of radiation is greater than or equal to the thermal effect of the reaction. In doing so, we do not take into account secondary reac-

Warburg was the first to demonstrate the validity of this law in certain processes that are readily accessible to detailed analysis. At the present time, apparently, in photochemical dissociation processes it is possible, from the appearance of the absorption spectrum, to conclude in which cases Einstein’s law of equivalence in the primary process should be valid, and in which cases we—again disregarding secondary processes—should expect deviations of the yield from the theoretical value. For this purpose we shall use those results concerning the nature of band spectra which we have already partly discussed above. If we excite molecules by absorption of light, then the energy received is, generally speaking, used for the most part to excite the electronic system; a relatively smaller part goes into increasing the vibrational energy of the molecule, and a practically negligible part into increasing the rotational energy. But in order to bring about dissociation, it is precisely the vibrational or rotational energy of the molecule that must be made greater than the work of dissociation. It is therefore not surprising that a molecule can receive, without decomposing, quantities of energy as excitation energy many times greater than the work of dissociation. In the absence of perturbations, as we have seen, the absorbed energy is predominantly given back in the form of fluorescence light. If, however, a photochemical investigation is to be carried out, then already in order that the amount of substance being transformed can be followed analytically, the pressure is made so high that the excited molecules, before emission occurs, have time to undergo repeated collisions. As a result of collisions, the excitation energy is transformed into other forms, and among the many possible ways of using this energy there is also the possibility of a dissociation process occurring. It follows from this that, under the circumstances described, the primary yield of a photochemical reaction is, generally speaking, lower than that which could be expected on the basis of Einstein’s photochemical law of equivalence.

Alongside the cases just considered, there are also cases in which, as a result of the absorption of light, simultaneously with the electronic jump, such an amount of energy is transferred to the vibrations of the nuclei that the molecule dissociates. In this case the law of equivalence must be valid for the primary photochemical process. One gets the impression that in practically all cases where Warburg found confirmation of the law of equivalence, precisely analogous processes occur. To assign a photochemical reaction to one class or another, it is necessary to investigate the absorption spectrum, from which the laws governing quantum series can be found. We must therefore turn once more to the consideration of the structure of molecular spectra. In Fig. 9 we saw part of a quantum series in the molecular spectrum of iodine. In Fig. 13 a scheme is presented of the entire quantum series,

Fig. 13.

found from a series of photographs of spectra taken under different experimental conditions. For simplicity, only the quantum lines are plotted in this figure. We see that at first they proceed at nearly equal distances, then draw closer together and, in the end, tend toward the place of convergence, adjacent to which is a continuous spectrum. The interpretation of such places of convergence of bands is completely analogous to that which we gave for the places of convergence in the serial spectra of atoms. Whereas in the latter case dissociation into an electron and an ion occurs, in the former case dissociation into two atomic components occurs. Knowing the frequency of the place of convergence of the bands and using the quantum relation, one can calculate the corresponding work of dissociation, just as one can calculate the work of ionization from atomic serial spectra. However, it should be borne in mind that it is not always from the place of convergence of the bands that one can find the work of dissociation into normal atoms; in each case it must be checked into what parts the molecule breaks up. We shall clarify this for ourselves if we make use of

previously given Fig. 4. The very lowest electronic level corresponds to the system of vibrational quanta of the normal molecule. Let us first assume that this system belongs to an ordinary homeopolar molecule, such as, for example, the iodine molecule. If, while preserving the normal state of the electron shell, we continually increase the vibrational energy, then, in the end, we shall arrive at two normal atoms. The distance from the convergence point of the quanta to the initial level of the non-vibrating molecule is equal to the normal work of dissociation of the molecule. But we have no possibility of increasing the vibrational energy of a molecule by the absorption of light while at the same time keeping the electronic system unchanged; we can increase the vibrational energy by sufficiently large amounts only in the presence of a simultaneous electronic transition. If the electronic jump in our case corresponds to the smallest quantum transition, then we shall pass to the system of vibrations of the excited molecule. In the limiting case such an excited molecule breaks up not into normal atoms, since the electronic system is no longer in the normal state, but the component parts of the molecule will now be a normal and an excited atom. In such a case we shall obtain, from the convergence point of the bands, the dissociation work of the normal molecule if we subtract, from the value obtained on the basis of the \(h\nu\)-relation, the excitation energy that remains in one of the atoms.

Since the excitation levels of atoms are known in most cases, the calculation can in fact be carried out. It is possible, however, to obtain the work of dissociation of the molecule in the ground state directly, provided that from the study of fluorescence one can trace the system of vibrational quanta of the ground state up to the convergence point. Both methods are often used, and below I shall give a table containing the results obtained in this way. Unfortunately, it is not always possible to trace a series of quanta to its limit. In these cases one may proceed by finding the regularity of a series of quanta from a large number of its terms and then determining the position of the limit by extrapolation. Of course, such extrapolation

with known accuracy is possible only in the case when a sufficiently large number of quanta is accessible to observation. In some cases, in the study of emission or absorption spectra, only a small number of quanta is detected. These cases correspond to transitions in which the vibrational energy undergoes only small changes. Conversely, there are cases in which so considerable a change of vibrational energy is obtained that only continuous spectra alone are produced. In such cases excited molecules do not arise at all; instead, there is always a decomposition into components which move away from one another with an excess of kinetic energy. If one of the components is an excited atom that emits light, then the supernormal velocity can be detected by the Doppler effect.

Fig. 14.

The reason for the large differences in the structure of band spectra becomes clear from a discussion of the structure of the molecule. A molecule consists of heavy nuclei vibrating relative to one another and of light electrons. In the transition to a new quantum state, the system of light electrons may undergo changes in its spatial distribution, which take place so rapidly that the heavy nuclei do not have time to follow them. Let us suppose that the distance between the nuclei during the quantum transition practically does not change at all. If now, as a result of the transition of the electronic system into a new state, a change in the bonding forces occurs, then the nuclei will find themselves in a position that does not correspond to their new equilibrium position, as is shown schematically in Fig. 14 (where the lower part of the drawing represents the normal molecule, and the upper part—the excited-

As a result of this, the nuclei acquire a more or less considerable store of potential energy relative to their new equilibrium position, and they can convert this potential energy into vibrational energy. If the potential energy acquired in this way exceeds the work of dissociation of the molecule in the new quantum state, then the molecule decomposes. I shall now give a table of the works of dissociation found by the optical methods mentioned above. For the reasons indicated above, the resulting accuracy is different in different cases. In those cases where figures obtained by the thermodynamic method are known, they are given in the table (see p. 531).

In conclusion I shall say a few more words about how, from the character of the dissociation process taking place, one may judge the nature of the chemical bond. We shall here distinguish between ionic compounds and atomic compounds. In an ionic bond, in the ground state, positive and negative ions vibrate relative to one another, and if the vibrational energy of such a molecule is increased to a value equal to the work of dissociation, without allowing a quantum transition of the electronic system, then in the limit the molecule decomposes into ions. On the contrary, an atomic compound, when the vibration is increased, carried out, as they say, adiabatically with respect to the electronic system, decomposes in the limit into normal atoms. Whether the corresponding molecules possess an electric moment or not, or—using the usual terminology—whether they belong to polar or non-polar compounds, is immaterial from the point of view of the above division into atomic and ionic molecules. For an atomic compound, too, as a result of polarization, may possess an electric moment. The establishment of the regularity of the series of quanta by investigation of fluorescence must in this case show whether we are dealing with an atomic or with an ionic compound. In those cases where the investigation of fluorescence does not lead to the goal, one can draw a conclusion from absorption experiments. In doing so, it is only necessary to bear in mind that an atomic compound represents an excited state of an ionic one,

and, conversely, an ionic compound—the excited state of an atomic one. But in such a case it follows from the diagram in Fig. 4 that, if the ground state belongs to the ionic compound, then the point of condensation of the excited molecule may correspond to dissociation into normal atoms. Thus true ionic compounds must decompose, as a result of the absorption of light, into normal atoms, which is indeed found in all alkali-halide compounds. Conversely, the silver halide salts have proved, upon investigation—both of fluorescence and of absorption—to be atomic compounds, so long as they are investigated in the gaseous form. However, conclusions about the properties of one and the same compound in the solid state or in solution cannot be drawn directly from the nature of the bond in the gaseous state, for it may depend on the surroundings which of the terms—of the ionic or of the atomic compound—will be the most stable. Typical examples in this respect seem to me to be hydrogen chloride and hydrogen bromide: according to the investigations of Bonhoeffer and Steiner on their absorption spectra, they must undoubtedly be assigned to the atomic compounds, whereas in aqueous solution they are very strong acids. Time does not permit me to substantiate the conclusion that, in different states of excitation, the work of dissociation of a molecule may be completely different. In the case of the noble gases we have hitherto had no possibility at all of detecting a compound in the ground state, whereas in the excited state such a compound is realized, as can readily be inferred from the spectrum. I think, however, that the possibility of such cases is perfectly understandable if one proceeds from the generally accepted view that the character and strength of a possible compound are determined wholly by the electron shell, since the latter is completely different in different states of excitation. Hence there follows directly the difference in the behavior of molecules and atoms in different states of excitation.

1. Lecture delivered at a meeting of the German Physical Society on December 10, 1927; published in Ber. d. Deutsch. Chem. Ges., 1928, No. 3, p. 445. ↩