Abstract
In this article we shall speak not of the collisions of the kinetic theory of gases, but precisely of those in which the quantum energy of the colliding atoms or molecules before and after the collision proves to be different.
Full Text
COLLISIONS OF THE SECOND KIND.
D. Koster1.
In the kinetic theory of gases, molecules are regarded as perfectly elastic spheres. By making use of the laws of conservation of energy and momentum, one can explain, in the well-known way, friction, thermal conductivity, and the phenomena of diffusion, and also determine the dependence between the quantities that play a role here—such as pressure and specific heat—and the molecular constants. If we take the simplest case of a monatomic gas, then we know from the kinetic theory of gases that no further complications arise in this case, i.e. that there really is in atoms something corresponding to the notion of elastic spheres. From the quantum theory we know just what this “something” is.
In addition to the energy of translational motion, an atom can absorb “another quantum” of energy; as a result it enters a “special state”: one of the electrons moves not along the path “of rest,” but along one of the paths of higher energy, which again is determined by the quantum conditions. The smallest quantum energy that an atom can take up is much greater than the mean energy of translational motion at room temperature. Thus, generally speaking, an atom cannot absorb quantum energy, and its internal state remains unchanged—in other words, the collisions prove to be perfectly elastic. In this article we shall speak not about the collisions of the kinetic theory of gases, but precisely about those in which the quantum energy of the colliding atoms or molecules before and after the collision is not the same. We may imagine, for example, that a gas is heated: then the kinetic energy of the atoms increases and, in the end, there appears in it a noticeable number of collisions in which the energy of the translational motion of the atoms exceeds the quantum energy capable of being absorbed by the atom. Then, indeed, some of the atoms will absorb this quantum energy, and the collisions will no longer be completely elastic. Such processes undoubtedly often occur
in nature; however, they are not readily amenable to quantitative investigation. The situation is different with collisions of electrons with atoms.
Let us take a monatomic gas. Let the internal energy of the atom in its stable motion be \(u_1\), and let the energy in the next quantum motion be \(u_2\). The experiments of Franck (J. Franck) and Hertz (Hertz) showed that when, in a collision, the kinetic energy of the electron (in these collisions we may regard the atoms as immobile) is less than \(u_2-u_1\), the collision is perfectly elastic. But if the kinetic energy of the striking atom is greater than this quantity, then at least some of such collisions occur in such a way that the electron gives up the energy \(u_2-u_1\) to the atom, and the latter passes from its stable internal state into the next quantum state; the electron then flies on with the remainder of its energy.
In their article, as interesting as it is brief, Klein (Klein) and Rosseland (Rosseland) draw from thermodynamic considerations the conclusion that the reverse process is also possible and must in fact occur in nature. We begin, therefore, with an atom that is not in a state of internal equilibrium, but in a state of higher energy \(u_2\); it “collides” with an electron having, for example, a very small velocity. The atom gives up its surplus quantum energy \(u_2-u_1\) to the electron, which now flies on with a greater velocity, while the atom after the collision returns to its stable internal state. Klein and Rosseland gave collisions of this kind the name collisions of the second kind, whereas the collisions studied by Franck and Hertz received the name collisions of the first kind. Fig. 1 represents both cases schematically. The atom with the smaller quantum energy is represented by the smaller circle, the atom with the larger quantum energy by the larger circle. The smallest circle represents the electron, and the arrow gives an indication of the direction and magnitude of its velocity.
Fig. 1.
Here we shall set forth briefly the reasoning of Klein and Rosseland. For simplicity we shall suppose that we have a monatomic gas, with the atoms able to be in only two quantum states; let \(n_1\) atoms have internal energy \(u_1\), and \(n_2\) atoms internal energy \(u_2\), where \(u_2-u_1=u\) is a positive quantity. The atoms in these two states \(u_1\) and \(u_2\) are in mutual thermal equilibrium. Further, suppose there is a gas of electrons, which by itself is in equilibrium, with the distribution
this number of velocities is expressed by the function \(\mu(\varepsilon)\,d\varepsilon\), where \(\varepsilon\) is the kinetic energy of the electron. We ask what conditions must be satisfied in order that equilibrium should occur both among the atoms and among the electrons. Let us consider a definite group of electrons with kinetic energies lying between \(\varepsilon'\) and \(\varepsilon' - d\varepsilon'\). This group, per unit time, loses a part of its electrons as a result of their undergoing collisions of the first kind with atoms that are in the state \(a_1\). The simplest assumption that we may make is that the number of them is proportional to the number of electrons of our group \(\mu(\varepsilon')\,d\varepsilon'\), to the number \(n_1\) of atoms in the state \(a_1\), and, finally, to some multiplier \(S_1^2(\varepsilon')\), which determines the probability of a collision of the first kind. This multiplier \(S_1^2\) contains, first, something like the “effective cross-section” of the atom, which we can perhaps borrow from the kinetic theory of gases; secondly, a factor of probability, as is often encountered in quantum theory. The point is that, when an atom meets an electron, a collision of the first kind need not take place under all circumstances. The number of electrons leaving our group as a result of collisions of the first kind will therefore be
\[ S_1^2(\varepsilon')\,n_1\,\mu(\varepsilon')\,d\varepsilon'. \]
In exactly the same way we shall form the number of electrons leaving the same group as a result of collisions of the second kind:
\[ S_2^1(\varepsilon')\,n_2\,\mu(\varepsilon')\,d\varepsilon'. \]
In two different ways, however, our group is enriched by new electrons. First, by collisions of the first kind of electrons which, before the collision, possessed the energy \(\varepsilon' + u\). Their number is equal to
\[ S_1^2(\varepsilon' + u)\,n_1\,\mu(\varepsilon' + u)\,d\varepsilon'. \]
Secondly, by collisions of the second kind of electrons which, before the collision, had the energy \(\varepsilon' - u\); their number is
\[ S_2^1(\varepsilon' - u)\,n_2\,\mu(\varepsilon' - u)\,d\varepsilon'. \]
The condition of equilibrium is therefore
\[ S_1^2(\varepsilon')\,n_1\,\mu(\varepsilon') + S_2^1(\varepsilon')\,n_2\,\mu(\varepsilon') = S_1^2(\varepsilon' + u)\,n_1\,\mu(\varepsilon' + u) + S_2^1(\varepsilon' - u)\,n_2\,\mu(\varepsilon' - u). \tag{1} \]
It is easy to see that condition (1) will be satisfied if, for all values of \(\varepsilon\), the following dependence holds:
\[ S_2^1(\varepsilon)\,n_2\,\mu(\varepsilon) = S_1^2(\varepsilon + u)\,n_1\,\mu(\varepsilon + u). \tag{2} \]
We want to show that condition (2) is not only sufficient, but also necessary. In the case where \(\varepsilon'\) in equation (1) is less than \(u=u_2-u_1\), \(S_1^2=0\), because electrons with energy less than \(u\) cannot produce collisions of the first kind. We also have \(\mu(\varepsilon'-u)=0\) in the case \(\varepsilon'<u\), since the energy of the electrons is always positive. In this case, therefore, the equality (2) is certainly satisfied. Replacing, respectively, in (1) the argument \(\varepsilon'\) by the argument \(\varepsilon'+u\), \(\varepsilon'+2u\), etc., we successively obtain that (2) must hold also for \(\varepsilon'+u\), \(\varepsilon'+2u\), etc., i.e. that it must hold everywhere.
We may next introduce more definite assumptions concerning the velocity-distribution functions for atoms and for electrons. A natural assumption is the Maxwellian distribution for electrons:
\[ \mu(\varepsilon)=N e^{-\frac{\varepsilon}{kT}}\sqrt{\varepsilon}. \]
For the numbers of atoms \(n_1\) and \(n_2\), Klein and Rosseland (just as Einstein does in his well-known derivation of Planck’s radiation formula) assume that here there is a distribution of its own kind, the Maxwell–Boltzmann distribution:
\[ n_1=Cp_1 e^{-\frac{u_1}{kT}}, \qquad n_2=Cp_2 e^{-\frac{u_2}{kT}}, \]
where the weight functions \(p_1\) and \(p_2\) represent the a priori probability measure that the atom is respectively in the state \(u_1\) or \(u_2\). Thus equation (2) reduces to the following:
\[ S_2^1(\varepsilon)n_2\sqrt{\varepsilon} = S_1^2(\varepsilon+u)n_1\sqrt{\varepsilon+u}. \tag{3} \]
Although we know very little about the factor \(S_2^1\), which is of greatest interest to us here, we can derive from (3) one very important conclusion. The experiments of Franck and Hertz showed that, if in a collision the energy of the electrons exceeds even slightly the energy \(u\) necessary to transfer the atom from a stable internal state into a higher quantum state, then in fact a noticeable part of the collisions proceeds in such a way that the atom is transferred into the higher quantum state. And this means (see equation (3)) that the number \(S_1^2(\varepsilon+u)\) is a noticeable quantity as soon as \(\varepsilon\) exceeds 0 even slightly. Meanwhile the first term of this equation contains the factor \(\sqrt{\varepsilon}\). In order to compensate for it, the factor \(S_2^1(\varepsilon)\) must be considerable precisely for small \(\varepsilon\). This shows that the probability of a collision of the second kind is large when the velocity of the electron is small. This should not surprise us: indeed, if the impacting electron has a small velocity, it remains for a long time within the sphere of action of the atom, and it is quite plausible that precisely then the probability of energy transfer is large.
In exactly the same way, the possibility exists for impacts of the second kind also in collisions between atoms and molecules. In view of the fact that here we are dealing with more complicated conditions, it is desirable for this case to define more precisely what we mean by such an impact. When atoms and molecules collide with one another, we call an impact of the second kind, in general, such an impact in which one of the participating atoms loses quantum energy; this atom is, consequently, before the impact in a higher quantum state than after it. Franck1 was the first to generalize the considerations of Klein and Rosseland to collisions between atoms and molecules and from this drew interesting conclusions, which were then verified experimentally by him and his pupils2. We shall not give here a chronological account of every step taken along this path, but shall turn to the results obtained up to now in their logical connection with one another.
As noted above, in an impact of the second kind quantum energy is liberated. Where does it go? We must consider the following possibilities:
- The liberated energy is converted into the kinetic energy of the colliding atoms.
- The quantum energy of one of the atoms is sufficient, wholly or partly, to transfer the second atom into a higher quantum state.
- The quantum energy is converted into chemical energy.
We shall examine these three cases in succession.
I. Quantum energy is converted into the kinetic energy of the colliding atoms. This is an impact of exactly the same type as the impacts between atoms and electrons considered by Klein and Rosseland. A splendid example is given by Wood’s experiments3 on the quenching of fluorescence of the well-known mercury resonance line
2536.7 Å (i.e. the line \(1.5S—2p_2\) in the series scheme).
The phenomenon of absorption of resonance radiation in gases had been studied experimentally by Wood long before the appearance of Bohr’s theory. We now know that, for example, in the case of the 2536.7 line in mercury, the phenomenon consists in the fact that a normal mercury atom is transferred from the stable state (from the state \(1.5S\), in the terminology of spectral terms) into the state \(2p_2\). If nothing else happens to the atom (for example, a collision with another atom), then it can only return again
to the normal state when emitting the very same line. All the absorbed energy is thus diffusely radiated, and the mercury atom behaves with respect to this line—in a certain sense—as a classical resonator, upon which no other frictional forces act except the friction due to radiation. This phenomenon can be observed well only if the mercury vapor is in a well-evacuated tube and has its own pressure not exceeding a few millimeters of mercury. Wood investigated the influence of another gas (air) on the resonance radiation. It turned out that the latter, owing to the admixture of air, is greatly diminished—so greatly that even an amount of air corresponding to a pressure of \(1\) cm of mercury diminishes the strength of the radiation approximately \(5\)-fold.
This last phenomenon—the diminution of the resonance radiation of mercury owing to the admixture of foreign gases—is explained by Franck as an impact of the second kind. A mercury atom in the higher quantum state collides with an air molecule; in this process the mercury atom passes into the stable state, while the quantum energy is transformed into the kinetic energy of the colliding molecules, and in such a way that the law of conservation of momentum remains valid (the lighter molecule therefore acquires the greater energy). Cario proved more precisely, by experiment, the acceptability of this view. First, he repeated Wood’s experiments, but instead of air added one of the inert gases (\(He, Ne, Ar\)), in order to exclude as far as possible the likelihood of any intermediate chemical process. The effect proved to be the same as from the admixture of air. Then Cario tried to investigate the phenomenon, as far as possible, quantitatively as well. When a mercury atom is in the higher quantum state \(2p_2\), it can return to the normal state \(1,5S\) in two different ways: by emitting the line \(2536.7\ \mathring{A}\), and by collision with an air molecule. The relative frequency of the two processes determines the measure of the intensity of the resonance radiation. Cario approaches an estimate of this intensity by assuming that, when a mercury atom undergoes no collisions, it gives up its energy by means of radiation on average in \(10^{-8}\) seconds, and that when it undergoes a collision, the quantum energy is each time transformed into the kinetic energy of the colliding atoms. It is also necessary to make an assumption concerning the radius of the sphere of action of a mercury atom in the state \(2p_2\). Cario finds that, in order to obtain satisfactory agreement with Wood’s experiments, it is necessary to assume that in this case the radius is approximately three times larger than that obtained from kinetic theory for a mercury atom in the normal state. That this radius should be larger is, of course, in itself quite plausible, since the electron in the state \(2p_2\) moves along a more distant path.
If mercury vapor is illuminated by the mercury ultraviolet line \(1849\ \text{\AA}\), then in the resonance spectrum one obtains both this line and the line \(2536.7\ \text{\AA}\). The line 1849 is the first in the singlet system \((1.5S — 2P)\) of mercury; if, consequently, the line 2536.7 also appeared, then the atom, which first passed into the state \(2P\) as a result of absorption of 1849, must afterward in some way have passed from the state \(2P\) into the state \(2p_2\), in order then, by emitting 2536.7, to return to the normal state \(1.5S\). How does the transition from \(2P\) to \(2p_2\) take place? If this is accomplished by means of radiation processes, then it is possible only by an indirect path, since a direct transition from \(2P\) to \(2p_2\) is forbidden. This might, for example, take place by a path through the state \(2.5S\). Then one would first obtain the absorption \(2P — 2.5S\) of the infrared line \(10140\ \text{\AA}\), and then emission of the \(2p_2 — 2.5S\) green line \(4078\ \text{\AA}\). However, it is little probable that such a process took place, since such radiation is not observed. It therefore seems natural to suppose that the transition \(2P \to 2p_2\) occurs directly through a collision of a 2nd kind with another mercury atom, and that the difference of the quantum energies of these two states goes into the energy of translational motion of both colliding atoms.
The hypothesis presented here receives strong support in the experiment of Franck and Cario on an analogous phenomenon in sodium vapor. The sodium spectrum has a doublet structure. The first doublet of the principal series is formed by the well-known \(D\) lines \(5890\ \text{\AA}\) \((1.5 — 2p_1)\) and \(5895\ \text{\AA}\) \((1.5s — 2p_2)\); the second doublet consists of the lines 3302.3 \((1.5s — 3p_1)\) and 3302.9 \((1.5s — 3p_2)\). The \(D\) lines are typical resonance lines \((1.5s\) — normal state of the \(Na\) atom). If \(Na\) vapor is illuminated with the line 3302.9, then in the resonance spectrum both this line and both \(D\) lines are found. By chance there exists a bright zinc line which in wavelength coincides very exactly with the \(Na\) line 3302.9, and this greatly facilitates the experiment in the present case. By virtue of the explanation given above, we must suppose that when we illuminate \(Na\) vapor with the zinc line 3302.9, this line will be absorbed and the \(Na\) atoms will pass into the state \(3p_2\). Some of these atoms will collide with other atoms before they have time to give up their energy by radiation, and will pass, as a consequence of the impact, into the state \(2p_1\) or \(2p_2\). Then they will emit one of the \(D\) lines and again pass into the stable state. The excess of energy \((2p_1 — 3p_2\) or \(2p_2 — 3p_2)\) will pass, in the collision, into the kinetic energy of the colliding atoms. A \(Na\) atom passing in this way into the state \(2p_1\) or \(2p_2\) therefore has an exceptionally large velocity; if it now emits the \(D\) line, then, according to the Doppler principle, it will be broadened. This broadening must be established. This is what Franck and Cario did by a method as simple as it was elegant.
In Fig. 2 both quadrilaterals represent sodium resonance lamps. These are evacuated quartz tubes containing small amounts of metallic sodium. Their temperature is maintained at 200°. Lamp a is illuminated in turn either by the lines $D$ from the light source $Na$ (case I), or by the line 3302.9 of a zinc spark (case II). The arrow in Fig. 2 indicates the direction of the primary light; the primary light sources are not shown in the figure. In $C$ the resonance lines $D$ are observed in both cases. The conditions are so adjusted that, in both cases, in the absence of lamp b the intensity of the resonance lines $D$ is the same. If lamp b is now switched on, it turns out that the resonance light of lamp a in case I is absorbed more strongly by lamp b than in case II. This is precisely what was to be expected. In case II there is a broadening of the emitted lines $D$ according to the Doppler principle; only the central part of the lines is absorbed by lamp b, and more light reaches the observer at $C$ than in case I, where no broadening of the lines $D$ takes place.
Fig. 2.
Impacts of the type described above undoubtedly also occur in flames. The most natural assumption is that the chemical energy of combination is directly transformed into the quantum energy of the molecule. Let us consider, for example, a hydrogen-oxygen flame. If it were possible to assume that here we have to do only with the combination of two hydrogen atoms and one oxygen atom, the matter would be very simple. It would then be incompatible with the law of momentum if we assumed that the chemical energy of combination passes directly into the energy of translational motion. In actual fact, however, there is also the process of dissociation of the oxygen molecule. But it is difficult to understand how this dissociation process could give rise to a direct transformation of chemical energy into the energy of translational motion. It is much more probable that the molecule, immediately after its formation, is in a higher quantum state. It may then pass into its stable state either through radiation or through collision with another molecule. In the latter case the quantum energy is completely transformed into heat.
II. Quantum energy of one atom passes wholly or in part into the quantum energy of another atom. This case is represented schematically in Fig. 3. As in Fig. 1, the large circle represents an atom in a higher quantum state, the small circle an atom in a lower quantum state. The arrows represent the velocities of the atoms. If $A$ and $B$ are atoms of the same kind, then the process discussed here cannot be established experimentally. However, as follows from what comes later, such an exchange of quantum—
... of energies as a result of collisions must often occur in nature. If \(A\) and \(B\) are atoms of different kinds, then the transfer of quantum energy by means of an impact is possible in the following way. \(A\) is in a higher quantum state and can give up the quantum energy \(h\nu_A\).
Fig. 3.
\(B\) is in a stable state; the energy \(h\nu_B\) is needed in order to transfer it to the nearest higher quantum state. If now \(h\nu_B\) is less than \(h\nu_A\), then \(B\), upon collision with \(A\), can absorb the energy \(h\nu_B\), while the excess energy of atom \(A\), i.e. \(h\nu_A - h\nu_B\), will pass into the energy of translational motion. Franck and Cario investigated this type of impact experimentally. Mercury served as the first kind of atoms; thallium, silver, and cadmium as the second. A quartz tube containing a small quantity of mercury and thallium vapor was illuminated by the mercury line \(2536.7\ \mathring{A}\); in the resonance spectrum which the tube emitted, besides this mercury line there were found also certain lines of thallium. In order to make these thallium lines sufficiently strong, it was necessary to ensure that the mercury line did not exhibit broadening and reversal.
When the tube contained thallium alone, the thallium spectrum did not appear under illumination by the line \(2536.7\ \mathring{A}\). All this proves that this line must first be absorbed by a mercury atom (only the center of the line is absorbed by mercury vapor at the temperature of the experiment), after which a transfer of energy to the thallium atom takes place. The subsequent investigation of the energy relations confirmed this supposition. The thallium atom can borrow from the mercury atom only such quantum energy as is less than the quantity \(h\nu\) of the mercury line \(2536.7\ \mathring{A}\). In general, in the thallium spectrum there appeared only those lines for which the initial state is close to the stable state, i.e. the difference of the energies of the initial state and the stable one did not exceed \(h\nu\) of the line \(2536.7\).
The smaller the \(h\nu\) absorbed by \(Tl\), the greater is the quantity of quantum energy passing into translational energy. The emitted line must, therefore, exhibit a stronger Doppler effect. And indications of this were obtained in the experiments of Franck and Cario. The stable state of the \(Tl\) atom is the state \(^{2}p_2\)¹). In the spectrum of \(Tl\) excited in the indicated manner, both lines were found
\[ ^{2}p_2 - 1.5_s = 3776\ \mathring{A} \quad \text{and} \quad ^{2}p_2 - 3d_2 = 2768\ \mathring{A}. \]
¹) This is connected with the fact that the optical electron of \(Tl\) moves along the orbit \(6_2\).
Both lines are absorption lines of $Tl$. But the intensity ratio was not normal: 3776 Å was very bright, 2768 Å was weak. When a $Tl$ atom, as a result of an impact, passes into the state $1.5s$, a large excess of quantum energy is obtained; it is transformed into kinetic energy, and, in the emission of the line 3776, a strong Doppler effect is obtained; therefore this line is almost not absorbed by the other thallium atoms. In the case of the line 2768, close to the mercury line 2536.7, the excess energy is much smaller: this line is again absorbed by the remaining $Tl$ atoms, which in many cases return from the state $3d_2$ to the stable state in another way (not by means of the emission of 2768 Å). Similar results were also obtained with other combinations studied.
Attention should be drawn to one more remarkable feature: in certain cases it may happen that atom $B$ (see Fig. 3) absorbs more quantum energy than that which $A$ gives up. The missing quantity $h\nu_B-h\nu_A$ must be sought in the energy of the relative motion of the colliding atoms. That this phenomenon can occur is evident from the following: there was a mixture of mercury and cadmium vapors, which was again illuminated by the line 2536.7. The stable state of the $Cd$ atom is $1.5S$. In the photographs there appeared, among other things, the cadmium triplet $2p_2—1.5s$, although very weak. In order to transfer the $Cd$ atom from the stable state $1.5S$ to $1.5s$, an energy corresponding to 6.3 volts is needed. The mercury line 2563.7 corresponds to 4.9 volts. Consequently an energy corresponding to 1.4 volts had to be borrowed from the thermal motion. In accordance with this it was noticed that the triplet $2p_2—1.5s$ appeared (in contrast to the other $Cd$ lines) only at a vapor temperature not lower than 800°. Calculation shows that, in this case, only $3 \cdot 10^{-5}$ of the number of all collisions had energy of relative motion sufficient to supply the lacking quantum energy. Apparently this did not contradict the observed intensities.
III. Quantum energy passes into chemical energy.
The existence of such a transition was shown by Franck and Cario in one excellent experiment. It concerned the dissociation of hydrogen. The energy of dissociation of hydrogen, as determined by the thermal method, lies between 80 and 100 kilogram-calories per gram-molecule. This corresponds to the energy of an electron which has passed through a potential fall of 3.6—4 volts. If a hydrogen molecule dissociated directly as a result of the absorption of light, then, by Einstein’s relation, light of wavelength approximately 3200 Å would be sufficient. In fact, however, hydrogen is quite transparent down to approximately 1300 Å. When hydrogen is bombarded by electrons, there occurs the phen—
... only at 10 volts, approximately; the visible banded spectrum appears only when bombarded with electrons at 18 volts. This shows that in this case the molecular bonds have not yet been broken and that the hydrogen molecule can absorb an energy approximately five times greater than its dissociation energy without falling apart. Franck had the happy idea of trying whether a hydrogen molecule could not be dissociated by an impact with another atom that is in a higher quantum state. In this case, of course, it is necessary that the quantum energy thereby released be at least as great as the dissociation energy. This is the case if there are mercury atoms that have absorbed the line \(2536.7\ \mathring{\mathrm{A}}\) and are therefore in the \(2p_2\) state—a case that is easy to realize experimentally. As a reaction for monatomic hydrogen, its reducing action on copper oxide or tungsten trioxide was used. It is now easy to imagine the experimental arrangement. A small quantity of hydrogen and mercury vapor was exposed to the action of the \(2536.7\) line in a well-evacuated quartz tube. A MacLeod manometer was attached to the tube, separated from it by a device for cooling with liquid air; there was also a side tube with copper oxide and another tube with phosphorus pentoxide—for reduction. On illumination with the \(2536.7\) line it turned out that the pressure measured by means of the MacLeod manometer decreased; when the illumination was stopped, the pressure again became constant. When the cooling device was removed, the pressure at first rose, and then gradually returned to its initial state. This occurred because of the water that was formed in the reduction of the metal oxide and was at first retained in the cooler. It was released when the cooler was removed, and was then absorbed by the phosphorus pentoxide.
Control experiments showed that the phenomena described occurred only when these three conditions were fulfilled: the presence of mercury, the presence of hydrogen, and illumination with the line \(2536.7\ \mathring{\mathrm{A}}\), the last of which must show no reversal. After some time it turned out that the copper oxide had been reduced at the surface, as could be recognized from the red color.
Experiments like the one described open new prospects for chemistry. It is clear that in this way—at least in theory—the dissociation energy can be determined with exceedingly great accuracy. The great experimental difficulty, however, consists in the fact that in this way one can determine only the upper limit for the dissociation energy, and that we do not have a sufficient choice of atoms that could replace mercury in order to approach more closely the true value of this energy.
Undoubtedly, in many cases, when chemical processes take place or, at least, are accelerated as a result of illumination, we are dealing with collisions of the second kind. It is a great achievement of quantum theory that we are now learning to understand such processes as well—an achievement for which we are indebted chiefly to Franck and his collaborators.
Translated by T. A. Afanasyeva-Ehrenfest.