Ionization Potentials and Excitation Potentials of Gases and Vapors.

N. N. Semenov.

§ 1. Brief description of the methods of investigation.

Modern physics differs greatly from the physics of the nineteenth century. This difference consists chiefly in the different objects of investigation. Earlier physics was concerned with the investigation of macroscopic phenomena, i.e., phenomena occurring in visible bodies composed of a large number of elements—atoms. Modern physics investigates chiefly the very elements themselves—phenomena occurring in molecules, atoms, and the like, i.e., microscopic phenomena. In accordance with this new task, experimenters have developed new methods. There are very few ways of penetrating inside the atom, but these few have yielded a large amount of information. Among such methods, one of the foremost places is occupied by the method of bombarding atoms with electrons of various velocities. Atoms consist of electrons held together by electrical forces. An electron that bombards an atom and penetrates more or less deeply (depending on its velocity) into the atom is an intra-atomic probe, by means of which one can investigate the intra-atomic forces and the stability of the orbits of electrons situated at various depths within the atom. Direct experiments have shown that electrons with velocities less than \(3 \cdot 10^{8}\) cm per second (the so-called slow electrons) do not penetrate into atoms at all. This means that they can interact only with the outer atomic electrons.

And since our task is precisely the investigation of the outer electrons, this means that we must study phenomena occurring when atoms are bombarded by slow electrons with velocities less than \(3 \cdot 10^{8}\) cm per second. In this case we shall be certain that the phenomena observed by us are indeed caused only by the outer electrons.

Before proceeding to set forth the methods of investigation of the phenomena that interest us, we shall indicate the usual method of obtaining a beam of electrons of a given velocity. Free electrons are usually obtained,

one of two methods. First, from a metal surface heated to yellow heat (usually a platinum or tungsten wire heated by a current); second, from a metal plate (best of all zinc) illuminated by ultraviolet light (usually from a voltaic or mercury arc). On leaving the metal these electrons have negligible velocities. To give them the proper velocity, the following simple method is always used. The emitter is surrounded by a grid, and a potential difference \(V\) is applied between the grid and the emitter in such a way that the emitter serves as the cathode and the grid as the anode. Then the electric field will accelerate the negatively charged electrons. Each electron has charge \(e = 4.774 \cdot 10^{-10}\) absolute electrostatic units; on the path from the emitter to the grid it acquires energy equal to the product of the charge by the potential difference, i.e. \(eV\). This energy will evidently pass into the kinetic energy of the electron, equal to one half the product of the electron mass by the square of its velocity. Thus, the velocity of the electron at the grid itself is determined by the equality

\[ \frac{mv^2}{2} = eV \tag{1} \]

where \(m\) is the mass and \(v\) the velocity of the electron. In this formula all quantities must be expressed in absolute units. In practice, \(V\) is usually measured in volts. Therefore, if \(V\) is expressed in volts, the velocity is determined by the equation \(\frac{mv^2}{2} = \frac{eV}{300}\), whence \(v = \sqrt{\frac{2e}{m}\,\frac{V}{300}}\).

Since the charge and mass are the same for all electrons, the velocity \(v\) is entirely determined by the applied potential \(V\). Having flown through the mesh of the grid into the space where the phenomena under study take place, all electrons possess one velocity, determined by the formula given above and set by us as desired by applying one or another potential between the emitter and the grid. This method of specifying the velocity of electrons is so customary that in all articles electron velocities are usually expressed not in centimeters per second, but conventionally in volts. By formula (1) it is always easy to pass from this conventional designation of velocity to its absolute value. In particular, the above-mentioned velocity \(3 \cdot 10^8\) cm per second corresponds, in conventional units, to 30 volts of velocity. In exactly the same way, the velocity and kinetic energy of an electron are usually expressed not in ergs, but conventionally in volts. The magnitude in ergs is readily found from the conventional units in volts from the equation \(\frac{mv^2}{2} = \frac{eV}{300}\). Thus, conventionally, energy and velocity are expressed by the same number.

If it is desired to obtain electrons not only of a specified velocity but also of direction, then instead of the grid a diaphragm is placed, one or several in succession, in order to select a narrow beam of electrons.

In the space beyond the grid or beyond the diaphragm, the electrons collide with the atoms of one or another rarefied gas or vapor, i.e., more precisely, they interact with the outer electrons of these atoms. This circumstance is reflected in the electrons of the beam in two ways: first, the direction of their motion changes; second, their velocity changes. The velocity changes because they can spend part of their energy on the displacements and disturbances of the atom’s outer electrons. By studying the scattering and loss of velocity of the electrons in the beam, we can draw certain conclusions about the disturbances that may occur in the atom, and thus investigate the behavior of the outer atomic electrons.

A second, more direct way of investigating intra-atomic phenomena that occur when electrons of a definite velocity strike an atom consists in observing these processes themselves. These processes may be of two kinds.

1) If a free electron, upon striking an atom, transfers to an outer electron of the atom energy sufficient for the latter to be able to fly out of the atom, overcoming the attraction of the remaining positively charged part of the atom, then ionization will occur: the initially neutral atom will be split into two charged parts: a free electron and an ion—a positively charged part, an atom without one electron. As we shall see below, the presence of such ions can be detected. The minimum energy of the electron beam at which the appearance of ions begins is, obviously, equal to the energy necessary for ionization, i.e., for the removal of an outer electron from the atom.

2) If the energy of the primary electron is insufficient for ionization of the atom, then the energy which it transfers to the atomic electron will pass into the energy of some motion, for example, the vibrational motion of the atomic electron. In all kinds of intra-atomic disturbances of electrons they emit light. Thus we must expect the appearance of luminescence of atoms when they are struck by the electrons of the beam.

The emitted light can be investigated optically with the aid of a spectroscope, or (in the case when the light is ultraviolet) by the photoelectric effect which it produces on electrodes.

From 1913 to 1923 about a hundred works accumulated devoted to the investigation of the phenomena discussed in this article. In detail the methods of individual authors differ, but in the main almost all of them can be assigned to one of four types, of which two relate to observation of atoms, and two to observation of the primary electrons after they have collided with atoms. Below we give, in the most schematic outline, the four indicated methods.

Method I. In its original form this method was proposed by Lenard and applied for investigations chiefly by Franck and Hertz. In Fig. 1 the internal parts of the apparatus are shown schematically: \(A\)—electron emitter, \(B\)—grid, \(C\)—solid electrode.

All these electrodes are sealed into a glass vessel containing a gas or vapor at a pressure of about 0.01 mm of mercury, so that the electrons on the path from \(A\) to \(B\) almost do not collide with atoms, while on the path from \(B\) to \(C\) they collide on average once.

Fig. 1.

Between \(A\) and \(B\) there is applied a potential difference \(V_1\) volts accelerating the electrons; between \(B\) and \(C\), a retarding potential difference \(V_2\), greater than \(V_1\). Then the electrons, having passed through the mesh of the grid \(B\) with a store of velocity \(V_1\) volts, lose it under the action of the retarding field in the space \(BC\). And since \(V_2 > V_1\), none of the electrons will reach \(C\), and they will all be turned back toward the grid. If the electrons have a velocity sufficient for ionization of atoms, then, colliding in the space \(BC\) with atoms, they will cause there the appearance of new electrons and positive ions. As for the electrons, they will go under the action of the field toward the grid, while the ions, possessing a positive charge, will be directed toward the electrode \(C\) and will create a current between \(B\) and \(C\). By placing a galvanometer or electrometer in this circuit, one can measure this current as a function of the speed of the primary electrons, i.e., of \(V_1\). The curves obtained have the form shown in Fig. 2. The current appears at a certain definite speed of the primary electrons \(V_1 = V_0\) volts. This shows that ionization occurs at an energy of the bombarding electrons

\[ \frac{V_0 e}{300} \]

ergs. This minimum energy is evidently equal to the work of ionization of the atom.

Fig. 2.

Soon, however, it was found that such an interpretation of the quantity \(V_0\) is incorrect, and that in fact \(V_0\) is the minimum energy which must be imparted to an atom for it to begin emitting light. This light, being ultraviolet, causes emission of electrons from electrode \(C\), as a result of which a current is also created between \(B\) and \(C\). To distinguish the ionization potential from the excitation potential, Gaucher so modified the original apparatus: he placed in front of \(C\) one more grid \(B'\). In the space \(BB'\) he appli-

the same potential difference \(V_2\) as in the first experiment, between \(B\) and \(C\); between \(B'\) and \(C\) he produced the field in two ways, namely:

1) Between \(B'\) and \(C\) he applied no potential difference (then his experiment coincided with the one described above), and

2) Between \(B'\) and \(C\) he applied a potential difference \(V_3 < V_2\), retarding for positive ions. It is easy to see that, since \(V_3\) is less than \(V_2\), the positive ions, despite this retarding field, will nevertheless reach the electrode \(C\): the energy \(V_2 e\) accumulated by them in the space \(BB'\) is greater than \(V_3 e\)—the energy that they will lose in the space \(B'C\). But the photoelectrons will not be able to fly off from the electrode \(C\), since the electric field \(V_3\) will prevent them.

Acting by the first method, we obtain curve I in Fig. 3; by the second—curve II of the same figure. Obviously, \(V_R\) corresponds to the luminous potential, \(V_J\)—to the ionization potential.

Thus it was possible to separate the phenomenon of luminosity from ionization, and this method is suitable both for investigating the ionization energy, which in volts we shall henceforth denote by \(V_J\), and for the energy of luminosity, which we shall denote by \(V_R\).

On curve I one may observe a bend at the point \(a\), which corresponds precisely to the ionization potential obtained from curve II. The reason for such a sharp increase of current is clear: beginning with these velocities, ionization appears, and the initial photoelectric current is strengthened by the ionization current. Thus, already from the first curve one can find both thresholds, \(V_R\) and \(V_J\). Curve II is needed only in order to make certain to what these potentials correspond: to luminosity or to ionization. In a more detailed experimental study of the interval \(c—a\) of curve I, one sometimes obtains on it one or two additional bends, corresponding to electron velocities \(V'_R\) and \(V''_R\) volts. This indicates that at these critical velocities the bombarding electrons produce new types of excitation of the atomic electrons, which begin to emit light that is more strongly acting in the photoelectric sense, i.e. light of a shorter wavelength.

Fig. 3.

In exactly the same way, in the part \(a—b\) of curve I, one sometimes observes one more bend, corresponding to the second ionization potential. However, as we shall see below, this occurs only in those cases in which

the gas is inhomogeneous and consists of two kinds of molecules possessing, of course, different ionization potentials.

Thus, from the data obtained by this method it follows that the electrons of the beam, at an energy less than \(V_R\) volts, do not produce luminescence at all and, consequently, do not excite atomic electrons. Beginning with an energy of \(V_R\) volts, they produce a definite type of perturbation of the atomic electron, expressed in the emission of atomic light. At an energy \(V'_R\) the primary electrons begin to produce a new type of perturbation, expressed in the emission of atomic light of shorter wavelength. Finally, beginning with velocities equal to \(V_J\), the intra-atomic electron, under the action of the free electron, leaves the atom—the phenomenon of ionization occurs.

For each kind of atom and molecule the quantities \(V_R\), \(V'_R\), and \(V_J\) have their own definite value.

For mercury, for example, by this method the values \(V_R = 4.9\) volts, \(V'_R = 6.7\) volts, \(V_J = 10.4\) volts have been found.

Method II. This method was first applied by Franck and Hertz; the principal results were obtained by Mac-Lennan. The arrangement is the same as that shown in Fig. 1. Only the electrodes are located in a quartz vessel. This is done so that the ultraviolet light emitted by atoms when they are bombarded by electrons of a specified velocity can be observed with the aid of a quartz spectrograph.

Investigations by the second method reduce to a spectroscopic investigation of the light emitted by atoms when they are bombarded by electrons of various velocities. It turned out that all metal vapors behave as follows: at velocities less than the radiation potential \(V_R\), found by the preceding method, the atoms, in accordance with the data set forth above, emit no light at all. Beginning with velocities of the bombarding electrons equal to \(V_R\), light appears consisting of strictly monochromatic oscillations. In the spectrum only one line was observed. We shall henceforth denote the corresponding wavelength by \(\lambda_r\). Finally, at velocities equal to \(V_J\), the entire line spectrum of the given vapor appears.

As for the wavelength \(\lambda_r\), it always coincides with one of the principal lines of the absorption spectrum of the given vapor. For mercury \(\lambda_r = 2536\) Å (angstrom \(= 10^{-8}\) cm.). Its appearance occurs at \(V = 4.9\) volts, which coincides with the value \(V_R\) found by Method I. The circumstance that by this method no lines corresponding to the second radiation potentials were observed, nor the analogous lines in certain gases, such as helium, argon, etc., as we shall see below, is explained by the excessively short wavelength of this radiation, for which quartz already ceases to be transparent.

Method III was applied chiefly by Franck and Akeson and consisted in measuring those losses of energy which electrons bombarding an atom undergo upon collision with it.

The apparatus is shown in Fig. 4. \(A\) is the emitter, \(B\) is the diaphragm for selecting a narrow beam of electrons, \(C\) is the grid, \(D\) is the solid electrode. Between \(A\) and \(B\) a potential difference \(V_1\) volts is applied, so that the electrons fly through the aperture in \(B\) into the space \(BC\) with a velocity \(V_1\) volts. In the space \(BC\) there is no field (\(B\) and \(C\) are at the same potential). Here the electrons collide with molecules of the gas or vapor, the density of which is chosen so that along the path \(BC\) an electron, on average, encounters not more than one atom. The electrons then pass through the meshes of the grid into the space \(CD\) and strike the electrode \(D\). The number of electrons reaching \(D\) is measured by the strength of the current between \(D\) and \(A\).

Fig. 4.

Electrons enter the space \(DC\) with different velocities, since in collisions with molecules in \(BC\) they lose one or another part of their energy. The velocities of these electrons in this space are measured in the following way.

Between \(C\) and \(D\) a field is created which retards the electrons flying through the meshes of grid \(C\). If this field is created by a potential difference \(V_2\) between \(C\) and \(D\), then it is evident that all electrons passing through grid \(C\) with velocities greater than \(V_2\) volts overcome the retarding field and reach electrode \(D\). Those of them which, upon entering the space \(CD\), have velocities less than \(V_2\) volts will not be able to reach electrode \(D\) and will turn back toward the grid. Measuring the strength of the current between \(D\) and \(A\) as a function of the retarding field \(V_2\) between \(D\) and \(C\), for a given field \(V_1\) between \(A\) and \(B\), one obtains curves

Fig. 5.

of the type shown in Fig. 5. Here the curve drawn through the crosses corresponds to mercury vapor; the curve drawn through the circles—to a vacuum (the mercury vapor was frozen out by cooling); the initial velocity \(V_1 = 10\) volts. Along the abscissa axis are plotted the retarding potentials \(V_2\), and along the ordinate axis—the corresponding currents between \(D\) and \(A\), i.e., quantities proportional to the number of electrons reaching the electrode \(D\). The ordinates of any point of the curve, for example \(a\), give the number of electrons reaching \(D\) in the retarding field \(V_a\), i.e., the number of electrons that have velocities greater than or equal to \(V_a\) volts. In the same way, the ordinate of point \(b\) is the number of electrons having velocities greater than or equal to \(V_b\) volts. Consequently, the number of electrons whose velocities lie in the interval between \(V_a\) and \(V_b\) will be proportional to \(i_a - i_b\). Obviously, to every difference \(\Delta V_R\) along the abscissa axis there corresponds a difference of the ordinates of the curve \(\Delta i_R\). This \(\Delta i_R\) is proportional to the number of electrons whose velocities lie in the interval \(\Delta V_R\). It is easy in this way to construct graphically a curve of the dependence of \(\Delta i\) on \(V\). And since \(\Delta i_R\) is proportional to the number of electrons possessing velocities \(V_R\), this curve indicates what fraction of the electrons has one or another velocity. Thus, from the curve for mercury vapor in Fig. 5 we obtain the curve of Fig. 6.

Fig. 6.

This curve shows that almost all electrons, after passing through the vapor layer, have velocities either somewhat less than 5 volts or about 10 volts.

And since the initial velocities of the electrons are \(V_1 = 10\) volts, it is obvious that the losses of energy undergone by the electrons in collisions can be only quite definite quantities, namely either \(10 - 5 = 5\) volts, or \(0\).

A more detailed study of the velocity distribution gives, in addition to the two maxima, a whole series of others, which point to possible portions of energy transfer to atoms. These portions, obviously, are obtained from the differences between the initial energy of the electrons \(V_1\) and the energy corresponding to the electrons situated at one or another maximum on a curve similar to Fig. 5. These differences are always constant, independent of the value of the initial velocities of the electrons \(V_1\), determined by the potential difference between \(A\) and \(B\).

Thus, the transfer of energy by the primary flying electron to the intra-atomic electron occurs only in definite portions. It turned out that, for each substance, these portions are exactly equal to the excitation potentials and the ionizing potential of that substance, found by methods I and II. In particular, for mercury these portions were equal to 5 volts, 6.7 and 10.5 volts, which agrees with the values \(V_R\), \(V'_R\), and \(V_I\). In addition, however, several further critical values \(V''_R\), \(V'''_R\) were discovered, corresponding to the remaining excitation potentials, which had not been found by methods I and II.

In studies of the velocity distribution at a potential \(V_1\), smaller than the first excitation potential \(V_R\) (for mercury less than 5 volts), it was found that electrons lose no energy at all in collision, being reflected from atoms like elastic bodies. Thus \(V_R\) is the smallest portion of energy that a free electron can transfer to an atom.

Method IV. This method, first applied in 1914, is based on the fact that primary electrons, up to velocities equal to the excitation potential of a noble gas or metallic vapor, are elastically reflected (without loss of velocity) from molecules. At velocities equal to \(V_R\), however, they lose all their velocity.

The experiments were carried out in a cylindrical condenser. Along its axis there was stretched a platinum filament, heated by a current and emitting electrons. Around it, at a distance of 1–2 cm, there is a mesh cylinder; around this cylinder, at a distance of 2–3 mm, there is a second solid cylinder. Between the filament and the mesh an accelerating field \(V_1\) is applied for the electrons; between the mesh and the solid cylinder a retarding field \(V_2\) is applied for the electrons. The potential \(V_2\) must be chosen smaller than the sought potential \(V_R\). The condenser is filled with gas or vapor at a comparatively high pressure, of the order of 0.1–1 mm of mercury. At such pressures the primary electrons undergo many collisions with molecules on the way from the filament to the mesh. The measurements consist in measuring, with a galvanometer, the number of electrons reaching the solid cylinder as a function of the magnitude of \(V_1\).

Let \(V_1 < V_R\). At the indicated pressures the electrons undergo many collisions with molecules on the way to the mesh. However, owing to the fact that at velocities smaller than \(V_R\) the electron is reflected from the molecules completely elastically (without loss of energy), the velocity of the electron will be determined by the potential of that place in the condenser where the electron is at the given moment; when it reaches the mesh, its velocity in volts will be \(= V_1\). Through the cells of the mesh it enters the second part of the condenser between the mesh and the cylinder, where a retarding field \(V_2\) is applied for the electrons. If \(V_2 > V_1\), there will be no current—the electrons will all return to the mesh. If \(V_1 = V_2\), then part of the electrons will reach the cylinder and create a current. This will continue as long as \(V_1 < V_R\); when \(V_1 = V_R\), then at the very cells of the mesh the primary electrons will transfer all

energy to an electron of the molecule at the nearest collision; this energy will go into the emission of light. Thus the primary electrons lose all their velocity at the meshes of the grid and therefore cannot overcome the field \(V_2\). The current between the cylinder and the filament will again cease.

For \(V_1 > V_R\), the loss of velocity by the electrons will occur inside the cylinder at the place where \(V = V_R\). At the meshes of the grid the electrons will evidently have velocity \(V_1 - V_R\); when this quantity is equal to \(V_2\), the current will again flow. It disappears when \(V_1\) is equal to \(2V_R\), and so on. As a result, one obtains a curve for the dependence of the current \(i\) between the cylinder and the filament of the type shown in the figure. This curve refers to mercury vapor. The first maximum is obtained at \(V_1 \lesssim 5\) (Fig. 7), the second at \(V_1 \lesssim 10\), the third at \(V_2 \lesssim 15\). The distances between the maxima are evidently equal to the sought excitation potential, in the present case 4.9 volts, which agrees with the values obtained by methods I, II, and III.

Fig. 7.

§ 2. Results of measurements for metal vapors.

Studies of ionization and radiation potentials have been carried out for most vapors of metals of the first and second groups (alkali and alkaline-earth). The vapors of these metals are monatomic.

The results of these investigations may be summarized as follows:

1) An electron possessing an energy less than \(V_R\) volts is elastically reflected by the atom (without loss of energy), i.e. it does not enter at all into an exchange of energy with the intra-atomic electron.

2) An electron possessing an energy equal to \(V_R\) volts transfers it entirely, upon collision, to the intra-atomic electron, the atom then emitting monochromatic radiation, whose wavelength we shall denote by \(\lambda_R\), and whose frequency by \(\nu_R\).

3) For each vapor there are also observed, besides \(V_R\), several more thresholds \(V'_R, V''_R\), etc., which determine portions of energy that the electron can transfer to the atom. At an electron energy \(V'_R\)

an atom emits radiation in which, besides the frequency \(\nu_r\), there occurs a frequency \(\nu'_r\), greater than \(\nu_r\).

4) An electron possessing an energy equal to \(V_J\) volts ionizes the atom upon collision.

5) The frequencies \(\nu_r, \nu'_r\), etc., coincide with the lines of the absorption series of the given vapor, and between the frequencies \(\nu_r, \nu'_r\) of these lines and the potentials \(V_R, V'_R\) there holds the relation

\[ h\nu_r=\frac{eV_R}{300}, \quad h\nu'_r=\frac{eV'_R}{300} \]

and so on, where \(h\) is Planck’s constant.

6) Between the ionizing potential and the limit of the optical series, whose first terms are \(\nu_2\) and \(\nu'_2\), there exists the relation

\[ h\nu_\vartheta=\frac{V_\vartheta e}{300}, \]

where \(\nu_\vartheta\) is the frequency of the shortest line (the limit) of the absorption series. Upon ionization of the atom, emission of the entire line spectrum of the given vapor is always observed.

In Table I are given the results of measurements for various vapors; in addition to the observed values, we also give the \(\nu_r, \nu'_r, \nu_\vartheta\) calculated from the relation

\[ h\nu_r=\frac{eV_R}{300}, \quad h\nu'_r=\frac{eV'_R}{300}, \quad h\nu_\vartheta=\frac{eV_\vartheta}{300}, \]

where \(\nu_r, \nu'_r\), and \(\nu_\vartheta\) are the frequencies of the first, second, and last line of the absorption series or, what is the same thing, the directly observed frequencies of spectra emitted by atoms when bombarded by electrons with energies \(V_R, V'_R, V_J\) volts. As is seen, the calculated and observed values agree quite well. In one of the columns are given the wavelengths corresponding to the frequencies \(\nu_r, \nu'_r\), and \(\nu_\vartheta\), and in those cases where the corresponding \(\nu\) is underlined, the radiation was in fact observed upon bombardment by electrons, beginning with velocities \(V_R\) or \(V'_R\); in the other cases the numbers are taken directly from optical data on the wavelengths of the first, second, and last member of the absorption series of the given vapor.

Attention should be drawn to the fact that an electron can transfer energy to an intra-atomic electron only in strictly definite portions. This experimental fact stands in direct contradiction with the usual conceptions of mechanics and electrodynamics and, evidently, is connected with laws of a special kind governing intra-atomic motions.

It has turned out that all six of the indicated results can be derived from Bohr’s theory of the atom and constitute a clear experimental confirmation of this theory.

§ 3. Explanation of the stated facts from Bohr’s atomic theory.

We cannot in the present article set forth the foundations of Bohr’s theory. For acquaintance with it one should turn to special articles, of which there are a sufficient number in the Russian literature1. We be-

TABLE I.

| Metal | \multicolumn{3}{c}{\(V_R\)} | \multicolumn{3}{c}{\(V_J\)} |
|---|---:|---:|---:|---:|---:|---:|
| | Observed | Calculated | \(\lambda_R\) | Observed | Calculated | Series limit \(1{,}5S\), \(\lambda_J\) |
| Na | 2,13 | 2,092
2,094 | 5895,94¹
5889,97¹ | 5,13 | 5,11 | 2412,13 |
| K | 1,55 | 1,602
1,609 | 7699,01¹
7664,01¹ | 4,1 | 4,32 | 2856,7 |
| Rb | 1,6 | 1,55
1,58 | 7947,6¹
7810,3¹ | 4,1 | 4,55 | 2968,4 |
| Cs | 1,48 | 1,38
1,45 | 8943,5¹
8521,1¹ | 3,9 | 3,87 | 3184,3 |
| Mg | 2,65
4,42 | 2,7
4,33 | 4572,65²
2853,06³ | 7,75 | 7,61 | 1621,7 |
| Ca | 1,90
2,65 | 1,88
2,92 | 6574,59²
4227,9¹ | 6,01 | 6,09 | 2027,56 |
| Zn | 4,18
5,65 | 4,01
5,77 | 3076,88²
2139,33¹ | 9,5 | 9,35 | 1319,98 |
| Cd | 3,95
5,35 | 3,78
5,39 | 3076,88²
2268,79¹ | 9,0 | 8,95 | 1378,69 |
| Hg | 4,9
6,7 | 4,86
6,67 | 2537,4²
1849,6¹ | 10,38 | 10,39 | 1187,96 |

¹ Serial terms \(1{,}5S - 2P\).
² “ ” \(1{,}5S - 2p_2\).
³ “ ” \(1{,}5S - mp\).

We shall recall only some of its results, necessary for explaining the facts set forth.

From the point of view of mechanics, obviously, at the corresponding velocities all sorts of orbits of the outer electrons are possible, provided only that the velocity is such that the centrifugal force balances the attraction of the electron into the atom. According to Bohr’s theory, not all of these orbits are possible, but only quite definite ones, for which the angular momentum is equal to an integral multiple of \(\dfrac{h}{2\pi}\), i.e. \(n\dfrac{h}{2\pi}\), where \(n\) is an integer; \(n\) is the number of the orbit: on the first, nearest one, \(n=1\), on the second \(n=2\), etc.

Only in these selected orbits can the electron revolve. This is Bohr’s first assertion. Revolving in each such orbit, the electron possesses a perfectly definite energy—the sum of its potential and kinetic energies. This energy depends on the number of the orbit \(n\) and decreases as \(n\) decreases. In the orbit with \(n=1\) the potential energy of the electron is the smallest, and since all processes tend to proceed in the direction of decreasing potential energy, it is natural that this very orbit is the most stable, and at every convenient opportunity the electrons will tend to pass into this normal orbit. Thus, in the normal state of the atom, the electrons revolve in the nearest normal orbit.

In view of the assertions stated, it is not difficult to show that the fact that a primary electron can transmit its energy to an atom only in quite definite portions is in full agreement with them. Indeed, according to the assertion of Bohr’s theory, an electron can revolve only in quite definite orbits. The energy of an electron in the orbit \(n\) is denoted by \(W_n\), and for any atom of a given substance this is a completely definite quantity (which can even be calculated numerically from Bohr’s theory). Let us consider what will happen as a result of the collision of an electron possessing energy \(W_0\) with an atomic electron situated in the normal orbit and therefore possessing energy \(W_1\). The external electron obviously cannot receive energy from the atomic electron, for this would cause a decrease in the energy of the latter and its approach to the center of the atom, which is impossible according to the fundamental assertion that the orbit in which the electron is situated before the collision is the nearest possible stable orbit to the nucleus. Consequently, in a collision only the transfer by the external electron of all or part of its energy to the atomic electron is possible. The latter, having received an excess of kinetic energy, will evidently move away from the center of the atom to such a distance that the centrifugal force again balances the attraction. And since, according to Bohr’s theory, not all orbits are possible, but only quite definite ones, it is obvious that the atomic electron can take up not just any energy, but only such an energy as will remove it to one of these orbits. These portions of energy will evidently be equal in magnitude to \(W_n - W_1\), where \(W_n\) can assume a series of values corresponding to the series of possible orbits.

Consequently, the external electron either does not lose its energy at all in a collision, or loses it in portions equal to \(W_n - W_1\). The smallest quantity of energy that an electron can transfer to an atom corresponds to the transfer of the atomic electron from the first orbit to the second. If the energy of the electron \(W_0 < W_2 - W_1\), then, obviously, in a collision the transition of the electron to the second orbit is impossible, and thus—

read, and in general the transfer of energy is impossible. The primary electron, moving with energy \(W_0 < W_2 - W_1\), will be elastically reflected from the atom, without loss of energy, which agrees with the experimental data set forth above and summarized in §1 and §2. An electron possessing energy \(W_0=\dfrac{Ve}{300}=W_2-W_1\) can transfer its energy to an atomic electron; the potential \(V\), determined from the relation \(\dfrac{Ve}{300}=W_2-W_1\), is, evidently, the quantity which we called the resonance potential \(V_R\) (for mercury, 4.9 volts). If \(\dfrac{Ve}{300} > W_2-W_1\) and \(< W_3-W_1\), the electron transfers to the atomic electron only part of its energy in the amount \(\dfrac{Ve}{300}=W_2-W_1\), and retains the excess; this corresponds to the experimental results.

If \(\dfrac{Ve}{300}=W_3-W_1\), a complete transfer of energy to the atomic electron can again occur. The \(V\) determined from this relation is the second resonance potential, denoted above by \(V'_R\) (for mercury, 6.7 volts), and so on. To carry the atomic electron to infinity, or, what is the same thing, to ionize the atom, energy \(W_\infty-W_1\) is necessary. Consequently, the ionization potential is determined from the relation \(\dfrac{V_i e}{300}=W_\infty-W_1\). By definition, potential energy is the work which must be performed in order to bring the given body from infinity to the given orbit. Since the electron is a negatively charged body, while the remaining part of the atom is charged positively (a neutral atom without an electron has a positive charge), then in bringing it from infinity to the given orbit not only is no energy expended, but, on the contrary, energy is liberated: the electrostatic forces attract the electron, and therefore the potential energy has a negative value. One should not be confused by this, since in reality we always deal with the difference of potential energy, and not with their absolute values, and the negative value is simply the result of the definition.

The energy \(W_n=U_n+T_n\), where \(T_n\) is the kinetic and \(U_n\) the potential energy of the electron. From general mechanical considerations one can show that, in rotation under the action of the Coulomb force, \(T_n=\dfrac{1}{2}|U_n|\), where \(|U_n|\) is the absolute value of the potential energy. Consequently, \(W_n=\dfrac{1}{2}|U_n|+U_n\), and since, according to what was said above, \(U_n\) is negative, \(W_n=\dfrac{1}{2}U_n\). Consequently, all \(W_n\) are negative. Moreover, in absolute value \(W_n\) is the smaller, the larger \(n\) is, so that

the differences \(W_n - W_1\) are positive, as is obvious and as indeed must be the case.

For \(n = \infty\), \(W_\infty = 0\), since the potential energy \(W_\infty\) is obviously equal to 0 by the definition of potential energy; the kinetic energy at infinity is likewise \(= 0\). And since \(\dfrac{V_1 e}{300} = W_\infty - W_1\), then, in view of \(W_\infty = 0\), we obtain \(\dfrac{V_1 e}{300} = -W_1\), i.e. it is equal, with the opposite sign, to the energy of the atomic electron on the normal orbit. Since \(W_1\) is a negative quantity, \(-W_1\) is a positive quantity. Thus measurements of ionization potentials make it possible to determine experimentally the magnitude of the energy of the atomic electron in its normal position on the first orbit. If we know \(W_1\), then from the relation \(\dfrac{V_k e}{300} = W_k - W_1\) we find \(W_2\), i.e., knowing the excitation potential \(V_k\), we can determine the energy of the electron \(W_2\) on the second orbit. Knowing the second excitation potential \(V'_k\), we can determine \(W_3\) in an analogous way, and so on. Thus, if Bohr’s theory is correct, the data on the ionization and excitation potentials give us very valuable information about the energy of the electron in the various orbits. We note that the positive quantity \(-W_1\) is greater than any other \(-W_n\).

To what extent, then, is Bohr’s atomic theory confirmed by the experiments described? For the time being this confirmation is only qualitative, namely, the transfer of energy to the atomic electron is observed only in quite definite portions, which agrees with the requirement of Bohr’s theory.

Let us pass to quantitative coincidences. For this let us recall Bohr’s second fundamental assertion. If an atomic electron is excited and is on an orbit with the symbol \(n\), then, as was indicated, it tends to pass to an orbit with lower energy, i.e. to a closer one, with a smaller number, for example to the \(m\)-th, where \(m < n\). Where, then, is the energy \(W_n - W_m\) expended in this case? According to Bohr’s conception, it is transformed into light energy, into electromagnetic energy. With every transition of an electron from a more distant orbit to a closer one, an elementary act of emission of light takes place. Bohr’s second assertion consists in the fact that monochromatic light of frequency \(\nu\) is emitted in this process, and that this frequency is determined by the relation \(h\nu = W_n - W_m\).

It follows from this that the frequency of the light emitted by an electron in transition from the second orbit to the first is determined by the relation \(h\nu_2 = W_2 - W_1\), or, according to what was said above, \(h\nu_2 = eV_k\), where \(V_k\) is the first excitation potential.

We have seen that the experiments showed that electrons with velocities \(V_k\) do indeed cause luminescence upon impact against an atom, that luminescence

it is monochromatic and that the frequency \(\nu_r\) of this oscillation does indeed obey the relation \(h\nu_r = \dfrac{eV_r}{300}\). Thus here we are dealing with a quantitative confirmation of Bohr’s theory.

Many years before that, opticians had arranged all the lines of line spectra emitted by various gas vapors into series. It turned out that all the frequencies \(\nu_n\) of the lines grouped in one series can be expressed by the formula \(\nu_n = -A_n + A_m\), where \(A_m\) is a constant number, while \(A_n\) changes according to a simple law from one line to another. Let us take such a series for which \(A_m\) is greatest, and call it \(A_1\); then for this series \(\nu_n = -A_n + A_1\). The numerical value of \(A_n\) rapidly decreases as \(n\) increases and in the limit is equal to 0. The lines of the series, at first far apart from one another in the spectrum, gradually merge. The limit of the series, i.e. the frequency of the line with the shortest wavelength, is evidently determined by the relation \(\nu_f = A_1\).

It is easy to understand how such series laws are obtained from Bohr’s theory. If we put \(A_1 = -\dfrac{W_1}{h}\) and \(A_n = -\dfrac{W_n}{h}\), then we obtain

\[ \nu_n = \frac{W_n - W_1}{h}, \]

or \(h\nu_n = W_n - W_1\), i.e. Bohr’s formula. Thus

\[ A_1 = -\frac{W_1}{h}. \]

And since the ionization potential

\[ V_J = -\frac{300W_1}{e}, \]

we obtain a relation between the limit of the series and the ionization potential:

\[ V_J = \frac{300hA_1}{e} \]

or

\[ \frac{V_J e}{300} = \nu_f h. \]

It is precisely this relation that the experimental data satisfy.

It should also be noted that the frequency determined by the relation

\[ h\nu_1=\frac{eV_R}{300} \]

and observed when atoms are bombarded by electrons with velocities \(V_R \ge V_r\), must evidently be the first line of that series whose limit is calculated from the relation

\[ h\nu_f=\frac{eV_J}{300}; \]

indeed, in all vapors for which the series laws have been sufficiently studied, this requirement is fulfilled. The series \(\nu_n = -A_n + A_1\) was chosen by us with the greatest value of \(A_1\), i.e. this series must indeed correspond to transitions of electrons from the second, third, fourth, etc. orbits to the first, since it is precisely for this orbit that the quantity \(-W_1\) has the greatest value.

Let us turn to the questions of why, during ionization, emission of the entire line spectrum of the given vapor is observed. The point is that, after some time, the ionized atom encounters one or another electron and attracts it. A phenomenon occurs that is known as recombination. It is precisely in this phenomenon that light is emitted, since here the potential energy of the electron is converted into light. In the act of ionization itself, however, energy is not released, but

is absorbed, and there can be no radiation. As a result of recombination we again obtain an atom with the normal electron orbit and energy \(W_1\). Thus, in recombination the energy \(W_\infty-W_1\) is lost. However, the transition of electrons from outside the atom inward may occur by various paths. The electron may be detained on the way on one or another orbit, or, finally, without detention pass directly to the normal orbit. Depending on this, it will emit different spectral lines. For example, if it is detained on the orbits \(8, 4, 2\), then it will emit four lines corresponding to the frequencies

\[ \nu=\frac{W_\infty-W_8}{h},\quad \frac{W_8-W_4}{h},\quad \frac{W_4-W_2}{h},\quad \frac{W_2-W_1}{h}. \]

With a large number of recombinations we shall obtain all possible frequencies, determined by the relation \(\nu_n=\dfrac{W_n-W_1}{h}\), i.e. all lines of all series of the spectrum of the given vapor. It remains to explain the fact that the frequency of the light emitted under bombardment by electrons with energies \(V_K\), \(V_N\), in all known cases coincides with the lines of the absorption series of the given vapor. Absorption of light by atoms occurs, according to Bohr, especially intensely in the case when the frequency of the incident light is connected with the energies of the orbits by the relation: \(h\nu=\dfrac{W_n-W_1}{n}\). Consequently, if a vapor is illuminated by a continuous spectrum, then, after the passage of the light through the vapor, those lines will be absent from it which satisfy the indicated relation. All absorption lines correspond to transitions of the electron from the normal first orbit to one of the following. Thus, the first absorption line is determined by the relation \(h\nu_1=W_2-W_1\), the second by \(h\nu_2=W_3-W_1\). But, when an electron strikes an atom, the portions of transferred energy \(\dfrac{V_K e}{300}\), \(\dfrac{V_N e}{300}\), \(\dfrac{V_1 e}{300}\) are determined by the same relation \(\dfrac{V_K e}{300}=W_2-W_1\); \(\dfrac{V_N e}{300}=W_3-W_1\), etc.; while the light emitted by atoms under the influence of these impacts is determined by the relation \(h\nu_2=W_2-W_1\), etc.; hence it is clear why these lines must coincide with the absorption lines.

If the atoms are excited very intensely, so that, despite the tendency of the electrons to return to the normal orbit, at every given moment there is nevertheless a sufficient number of excited atoms with electrons located, for example, on the second orbit, then, obviously, such a vapor will absorb not only the series \(\nu_n=\dfrac{W_n-W_1}{h}\), corresponding to the normal state of the atom, but also the series \(\nu_{n2}=\dfrac{W_n-W_2}{h}\), corresponding to the absorption of light by excited atoms (for them, obviously, the second orbit possesses all the properties of the first orbit in the normal state). If the excited atoms have electrons not

only in the second, but also in all the other orbits in sufficient quantity, then all the lines emitted by it will be absorbed by such vapor. Precisely such a phenomenon was observed. Light from a mercury arc was examined through another mercury arc. In the mercury arc there occurs a very strong excitation and ionization of the mercury atoms. It turned out that almost all the lines emitted by the first mercury arc are absorbed, to a greater or lesser degree, in passing through the second, whereas unexcited mercury vapor absorbs only one ultraviolet series. This experiment, despite its qualitative character, is good confirmation of Bohr’s views.

It seems to us that the results of the present paragraph not only confirm Bohr’s theory, but may also be regarded as its experimental substantiation.

§ 4. Some results of experiments in gases.

a) Monatomic gases.

We present the results of measurements in helium and argon. — In helium two critical potentials were obtained: the radiation potential \(V_R = 20.5\) volts and the ionization potential \(V_I = 24.5\) volts. If, from the radiation potential, one calculates the wavelength of the light that should be emitted, it proves to be equal to 606 angstroms. The wavelength of the boundary of the series, calculated from the ionization potential, \(\lambda_g = 490 A\). The first of these lines, according to Bohr’s theory, should be the first member of the series

\[ \nu_n = \frac{W_n - W_1}{h}, \]

and the second—the last. Thus the whole series must lie within wavelengths from 490 to 600 \(A\), i.e. in the extreme ultraviolet part of the spectrum. Experimentation with such short wavelengths is very difficult. However, Lyman succeeded in finding optically the first member of this ultraviolet series of helium, the wavelength proving to be approximately 600 \(A\), which, as is evident, agrees well with the calculated value. Richardson and Bazzoni, by an indirect method (from the velocities of photoelectrons emitted by a metal under the action of luminous helium), found the limiting member of the series, i.e. the shortest wavelength emitted by helium. It turned out that it lies within the limits 420—470 \(A\). The agreement with the value calculated from the ionization potential is not so good here, but is nevertheless satisfactory if one takes into account the difficulty and inaccuracy of Richardson’s experiments.

In argon two critical potentials were likewise found: radiation—11.5 volts, ionization—15.1 volts. The wavelength \(\lambda_g\), calculated from the ionization potential, is equal to 817 \(A\). This wavelength, obviously, must be the shortest in the spectrum of argon. Lyman, investigating the spectrum of argon, found that it ends at a wavelength of 800 \(A\), which agrees very well with the calculated value.

b) Simple diatomic gases.

Hydrogen. In hydrogen, undoubtedly, three critical potentials have been found. In various experiments the numerical values of these potentials vary within the limits of 1.5 volts. Let us take the data of Foote and Mohler. They obtain one radiation potential equal to 10.4 volts, and two ionization potentials \(V_l = 13.3\) volts and \(V'_l = 16.5\) volts.

Here for the first time we encounter the existence of two ionization potentials. This would seem not to fit within the framework of the theory set forth, but it must be remembered that here, for the first time, we are dealing with a diatomic gas. The existence of two ionization potentials is easily explained if we suppose that in the experiments the hydrogen consisted partly of atoms—was partly dissociated. It is known from thermochemistry that diatomic hydrogen at high temperatures breaks up into atoms, being transformed in part into a monatomic gas. Moreover, it is known that the hydrogen liberated in electrolysis consists of atoms, which only with the passage of time combine into molecules. In the experiments described, hydrogen flowed continuously through the measuring apparatus; it either entered the apparatus through a heated palladium thimble, or directly through the tap where the hydrogen was produced by electrolysis. Thus it was always possible that, in addition to diatomic hydrogen molecules, a small number of hydrogen atoms was present in the measuring apparatus. It is precisely to these that the potential \(V_l\) should be assigned, at which the first weak ionization was observed. To verify the correctness of this supposition, let us compare the number 13.3 volts obtained by us with the quantity \(h\nu_0/e\), where \(\nu_0\) is the limit of the Lyman series of hydrogen. By this formula we obtain 13.5 volts. If the experimental error in determining \(\nu\) is taken into account, the agreement must be considered very good. Having calculated the wavelength of the first member of the series \(\nu=\frac{W_n-W_1}{h}\) (the Lyman series), for the hydrogen atom, we obtain from the formula the first radiation potential 10.2 volts, which agrees very closely with the experimental value—10.4 volts. Thus, indeed, \(V_k\) and \(V_l\) pertain to hydrogen atoms.

The second ionization potential \(V'_l\), at which intensive ionization occurs, pertains to the ionization of diatomic hydrogen molecules. In the ionization of a hydrogen molecule, one of the atoms composing it loses an electron. As a result we shall have a molecular hydrogen ion. However, one may think that the electron causing ionization is not limited to the removal of one electron from the molecule, but at the same time also breaks the molecule itself into atoms, so that as a result of ionization we obtain a neutral hydrogen atom and a monatomic hydrogen ion. Experiments on measuring the sizes of hydrogen ions compel one to prefer precisely this second point of view. If this is so,

then for ionization of the molecule the energy of the bombarding electron must be equal to the energy required for splitting the hydrogen molecule into atoms (the so-called work of dissociation, known from thermochemistry), plus the energy necessary for ionization of the hydrogen atom, equal to \(V_j'\), i.e., between the work of dissociation \(D\) volts and the two ionization potentials, \(V_j\) and \(V_j'\), there must exist the relation \(V_j' = V_j + D\), or \(D = V_j' - V_j\). Since \(V_j\) and \(V_j'\) are known to us, we find \(D = 3.2\) volts. According to thermochemical data, for the dissociation of a hydrogen molecule one must expend \(Q = 80{,}000\) calories. For one molecule, consequently, one must expend \(\frac{Q}{N}\), where \(N\) is the number of molecules in a gram-molecule, equal to \(60 \cdot 10^{22}\). Multiplying by the thermal equivalent, we find this energy in ergs and, converting it into volts, obtain \(D\) equal to 3.6 volts, which closely agrees with 3.2 calculated from the ionization potentials. This confirms the hypothesis we have advanced concerning the ionization of diatomic molecules. This point of view, however, is proved much more definitely by experiments in iodine vapor.

Iodine vapor. In iodine vapor, Foote and Mohler found a radiation potential equal to 2.34 volts; Smyth and Compton—two ionization potentials \(8 \pm 0.1\) volts and \(9.4 \pm 0.1\) volts. For the difference they found on the average the value \(1.47 \pm 0.05\) volts. Their experiments were carried out at two different temperatures of iodine vapor: at a temperature of about \(25^\circ\) and \(500^\circ\) C. It turned out that in the first case ionization at 8 volts is very weak, while at 9.4 it is strong. In the second case ionization at 8 volts predominates. From chemical data it is known that at a temperature of \(25^\circ\) iodine vapor consists almost entirely of diatomic molecules. At \(500^\circ\) iodine vapor consists half of monatomic molecules. Comparing the results given, one may say with certainty that the first ionization potential refers to iodine atoms, the second to molecules. As in the case of hydrogen, one can compute the magnitude \(Q\) from chemical data, obtaining for a gram-molecule 35,000 calories. Carrying out the calculation, we obtain \(D = 1.52\) volts. The agreement between the calculated and the observed value is complete.

As for the radiation potential, the wavelength calculated from the relation

\[ h\nu = \frac{eV}{300} \]

turns out to differ by only \(4\%\) from the shortest absorption line of diatomic iodine vapor, found by Wood.

Smyth and Compton performed with iodine vapor one more experiment, well confirming the atomic representations set forth at the end of § 2. As was indicated, in a strongly excited vapor there may be a considerable number of atoms or molecules with electrons not on the normal orbit, but on one of the following ones. Illuminating iodine with a strong light source, we obtain, thanks to the phenomenon of absorption, a large number of molecules with electrons located on the second

orbit. For these molecules the ionization potential will no longer be \(W_1 300/e\), but \(W_2 300/e\). The difference of these two potentials is equal to \((W_2-W_1)300/e\), i.e. \(=V_k\). Smith and Compton determined the ionization potential of illuminated iodine vapor and found that in it there are observed not two, but three ionization potentials. Two of them coincide with the ionization potentials of unilluminated, normal iodine; the third, \(V_j''\), is new, differing from \(V_j'\) by 2.66 volts. Thus the difference between the ionization potentials of unexcited and excited iodine molecules is equal to 2.66 volts, which is very close to the value of the luminescence potential—2.34 volts, as indeed follows from the considerations set forth above.

c) Hydrogen-halide compounds.

Investigations of the ionization potentials have been made for the following compounds: \(HCl\), \(HJ\), and \(HBr\). Before giving the results of the measurements, let us say a few words about the molecular structure of these diatomic compounds. Hydrogen and the halides belong to sharply different chemical groups and combine with one another very energetically. If hydrogen compounds (acids) are dissolved in water, then during electrolysis of this solution hydrogen is liberated at the negative pole. The halides, on the contrary, are always liberated at the positive pole. As is known, when salts and acids are dissolved in water, their molecules dissociate into ions, one of which is positively charged, the other negatively. Hydrogen is always found to be positively charged, the halide atom always negatively. In particular, when \(HCl\), \(HBr\), \(HJ\) are dissolved, the molecules of these substances split into two ions—into a hydrogen atom charged positively, and an atom \(Cl\), \(Br\), or \(J\), charged negatively. The phenomenon of the splitting of neutral molecules in water into charged parts can be easily explained if one assumes that before dissolution a molecule, for example \(HCl\), consists of a hydrogen atom without one electron and a chlorine atom which has attracted to itself the hydrogen electron. From this point of view the chemical bond is effected by electrostatic attraction between oppositely charged atoms. As is known, the force of attraction depends on the nature of the medium in which these charged bodies are located, namely it is inversely proportional to the dielectric constant of the medium. This quantity for water is very large, greater than for all other bodies, and is equal to 81. Therefore the force of attraction of the ions is weakened 81-fold when the molecule is immersed in water. It is easy to calculate that, with such a force, even the thermal impacts of molecules are already sufficient to break the molecule into its constituent parts, i.e. into a positive hydrogen ion and a negative chlorine ion. Thus it is very probable that the vapors of the hydrogen-halide acids have molecules consisting of a positive hydrogen ion and a negative halide ion, held together by the force

of electrical attraction. Bearing in mind such a structure of the hydrogen halides, one may with great probability suppose that, when they are bombarded by electrons of sufficient velocities, the molecule may decompose into its charged parts, since an electron, falling, for example, between the ions of the molecule, thereby makes possible the occurrence of a phenomenon analogous to that which takes place upon dissolution in water, i.e. it weakens the bond and thus makes it possible for the molecule to split into ions. If this were so, then the process of ionization in the hydrogen halides would differ from all the preceding cases. There, as a result of ionization, one electron was liberated, or, in the case of diatomic molecules, one electron was liberated and the molecule dissociated; here, as a result of ionization, no free electron is knocked out, but the molecule itself breaks up into two charged atomic ions. To such a phenomenon one cannot simply apply the considerations of Bohr’s theory. However, here too a theoretical verification of the proposed hypothesis of the ionization of hydrogen-halide compounds is possible. Born calculated, on the basis of his theory of crystal lattices, the work required for the decomposition of hydrogen-halide compounds into two charged ions. To decide whether, under electron bombardment, the molecules \(HCl\), \(HBr\), \(HJ\) actually decompose into a positive hydrogen ion and a negative halide ion, let us compare the experimentally found ionization potentials with the work of dissociation of the hydrogen halides into charged ions calculated by Born. The data are given in Table II.

TABLE II.

	\(HCl\)	\(HBr\)	\(HJ\)
\(V_i\) observed	14.4	13.8	13.4
\(V_i\) calculated	13.9	13.5	13.1

The agreement proves to be remarkable if one takes into account that the observed quantities are taken from ionization experiments, while the calculated ones are obtained from a very complicated formula into which enter all sorts of chemical data on the latent heat of fusion, the heat of dissociation, and similar quantities which, at first glance, have nothing in common with ionizing potentials. This evidently indicates the correctness of the ideas set forth above concerning the process of ionization of hydrogen-halide compounds.

Literature.

1. Franck & Hertz. Messung der Ionisierungsspannung in verschiedenen Gasen. Verh. d. Deutsch. Phys. Ges. 1913, Jan., 34.

By Lenard’s method a loss of velocity by electrons was found in \(He\) at 20.5 V, \(Ne\)—17 V, \(Ar\)—12 V, \(H_2\)—11 V, \(Hg\)—9 V, and \(N_2\)—7.5 V.

1. Franck & Hertz. Über Zusammenstösse zwischen den Elektronen und Molekülen des Quecksilberdampfes und die Ionisierungsspannung desselben. Verh. d. D. Phys. Ges. 1914, May, 457.

By a new method a loss of velocity was found in \(Hg\) vapor at 4.9 V. The frequency \(\nu\), corresponding to the resonance line of mercury \(\lambda = 253.6\,\mu\mu\), when substituted into the quantum relation \(h\nu = eV\), gives \(V = 4.84\) V, a value close to 4.9 V.

1. Franck & Hertz. Über die Erregung der Quecksilberresonanzlinie 253,6 \(\mu\mu\) durch Elektronenstösse. Verh. d. D. Phys. Ges. 1914, Juni, 512.

The authors found the appearance of the line \(253.6\,\mu\mu\) when mercury vapor was bombarded with 4.9-volt electrons.

1. Mc Lennan & Henderson. Ionization Potentials of Mercury, Cadmium and Zinc, and the Single- and Mani-lined Spektra of these Elements. Proc. Roy. Soc. London 1915, Aug. 485.

The authors repeated the experiments of Franck and Hertz with vapors of mercury, and then \(Cd\) and \(Zn\). They obtained the lines \(\lambda\,253.672\,\mu\mu\) in \(Hg\), \(\lambda\,307.599\,\mu\mu\) in \(Zn\), and \(\lambda\,326.017\,\mu\mu\) in \(Cd\), at the corresponding voltages 4.9 V, 3.96 V, and 3.74 V. They observed the appearance of many-line spectra in the vapors of these metals at 12.5 V—in \(Hg\), 11.8 V—in \(Zn\), and 15.3 V in \(Cd\).

1. J. Tate. The Low Potential Discharge Spectrum of Mercury Vapor in Relation to Ionization Potentials. Phys. Rev. 1916, 7, 686.

By a method analogous to that of Franck and Hertz, the author found ionization of mercury vapor at \(10.0 \pm 0.3\) V, by a sudden increase in the current. At the same time a many-line spectrum of \(Hg\) appeared. Beginning with \(\sim 5\) V and up to \(\sim 10\) V, the spectrum consisted only of the line \(253.67\,\mu\mu\). No increase of the current near 5 V was observed.

1. Goucher. Ionisation by Impact in Mercury Vapor and other Gases. Phys. Rev. 1916, 8, 561.

Using Lenard’s method and an equipotential cathode, the author found a current in \(H_2\) at \(10.25 \pm 0.1\) V, in \(N_2\)—at \(7.4 \pm 0.1\), and \(Hg\)—at \(4.9 \pm 0.1\) V. In addition, he observed a strong increase of the current in mercury vapor at \(\sim 10\) V.

1. Bazzoni. Experimental Determination of the Ionisation Potential of Helium. Phil. Mag. 1916, Dec., 566.

The author measured the current between a glowing wire—the cathode—and a coaxial cylinder serving as the anode. The current curves reveal a sudden jump near 20 V. The jump is repeated at voltages that are multiples of 20 V.

1. Mc Lennan. On the Ionisation Potentials of Magnesium and other Metals and on Their Absorption Spectra. Proc. Roy. Soc. London 1916, Oct., 574.

A line \(\lambda\,285.222\,\mu\mu\) was found in \(Mg\) vapor at a voltage close to 4.5 V. This is one of the lines of the absorption spectrum of \(Mg\), namely the first member of the series.

\(\nu=(1,5S)—(mP)\). Further, at about 7.5 V an arc was ignited. The frequency corresponding to the boundary line of the series \(\nu=(1,5S)—(mP)\), \(\lambda 162.17\ \mu\mu\), being substituted into the relation \(h\nu=eV\), gives a potential \(\sim 7.5\) V.

1. Bishop. The Ionisation Potential of Electrons in Various Gases. Phys. Rev. 1917, 10, 244.

By a method analogous to the method of Franck and Hertz of 1914, ionization was observed in \(H_2\) at 11 and 15.7 V, in \(Hg\) at 10.27 V, in \(N_2\) at 7.5 V, and in \(O_2\) at \(\sim 9\) V.

1. Davis & Goucher. Ionisation and Excitation of Radiation by Elektron Impact in Mercury Vapor and Hydrogen. Phys. Rev. 1917, 10, 101.

By a new method, making it possible to distinguish the effects of ionization and radiation, there was obtained an ionization potential of \(Hg \sim 10.4\) V, and two resonance potentials, 4.9 V and 6.7 V, corresponding to the lines \(253.67\ \mu\mu\) and \(184.9\ \mu\mu\). In \(H_2\) there were obtained: ionization and radiation at 11 V, radiation at 13.6 V, and second ionization at 15.8 V.

1. Hughes & Dixon. The Ionising Potentials of Gases. Phys. Rev. 1917, 10, 495.

By two methods, representing a certain modification of Lenard’s method, the authors investigated the ionization potentials of mercury vapor (10.2 V), \(H_2\) (10.2 V), \(O_2\) (9.2 V), \(HCl\) (9.5 V), \(CO_2\) (10.0 V), \(CO\) (7.2 V), \(N_2\) (7.7 V), \(NO\) (9.3 V), \(Cl_2\) (8.2 V), \(Br_2\) (10.0 V), \(S\) (8.3 V?), \(CH_4\) (9.5 V), \(C_2H_6\) (10 V), \(C_2H_4\) (9.9 V), and \(C_2H_2\) (9.9 V).

1. Hebb. The Single-lined and the Mani-lined Spectrum of Mercury. Phys. Rev. 1917, 371.

The author observed a many-lined spectrum in \(Hg\) vapor at an accelerating potential of \(\sim 5\) V. Different densities of the electron discharge required different excitation potentials for the many-line spectrum.

1. Wood & Okano. On the Ionizing Potential of Sodium Vapour. Phil. Mag. 1917, Sept., 177.

In \(Na\) vapor the \(D\)-line appeared at a potential difference between cathode and anode of 0.5 V. At 2.3 V, lines of the subordinate spectral series appeared.

1. Tate & Foote. Resonance and Ionisation Potentials for Electrons in Metallic Vapours. Phil. Mag. 1918, July, 64.

By a method analogous to that of Franck and Hertz, measuring the currents (partial and total) from the inner and outer—two coaxial—cylinders, the authors investigated the critical potentials of \(Cd\), \(Na\), \(K\), and \(Zn\). The results of these investigations are given in the following table.

Metal.	Resonance potential.	Ionization potential.
\(Cd\)	3.88 V.	8.92 V.
\(Na\)	2.12 V.	5.13 V.
\(K\)	1.55 V.	4.1 V.
\(Zn\)	4.1 V.	9.5 V.

1. Hebb. The Ionisation Potential of Mercury Vapor and the Production of the Complete Spectrum of This Element. Phys. Rev. 1918, March, 170.

The author showed that the ionization at voltages less than 10 V, observed by him in \(Hg\) vapor, is not a consequence of obtaining \(\lambda 253.67\ \mu\mu\), which acts photoelectrically on mercury vapor.

1. Hebb. Ionisation of Mercury, Sodium and Potassium Vapors and the Production of Low Voltage Arcs in These Vapors. Phys. Rev. 1918, 12, 482.

The author investigated the minimum voltages at which an arc is ignited in vapors of Hg, Na and K, and also in mixtures of Na and Hg vapors, and K and Hg. He found ionization in K vapor at 1.6 V, in Na vapor at 2.5 V. In a mixture of K and Hg vapors the arc was ignited at 0.5 V, and of Na and Hg—at 1.4 V; in this case the mercury spectrum appeared.

The author considers possible causes of low-voltage arcs.

1. McLennan & Young. On the Absorption Spectra and the Ionisation Potentials of Cadmium, Strontium and Barium. Proc. Roy. Soc. London 1919, Feb., 273.

From the limiting characteristic frequencies \(\nu = (1,5S)\) the authors calculate the ionization potentials Hg(10.45), Zn(9.4 V.), Cd(9.0 V.), Mg(7.65 V.), Ca(6.12 V.), Sr(5.7 V.) and Ba(5.21 V.).

1. Horton & Davies. An Experimental Determination of the Ionising Potential for Electrons in Helium. Proc. Roy. Soc. London, 1919, April, 408.

As the mean of several observations, the resonance potential of He was obtained as 20.4 V, and the ionizing potential as 25.7 V. A second type of ionization was observed at \(\sim 55\) V. A series of grids between cathode and anode at the corresponding potentials makes it possible to distinguish the effects of ionization and radiation.

1. Foote & Mohler. Ionisation and Resonance Potentials for Electrons in Vapours of Magnesium and Thallium. Phil. Mag. 1919, Jan., 33.

As the mean of a series of experiments, the ionization potential of Mg is obtained equal to 7.75 V and the resonance potential to 2.65 V. The frequencies corresponding to these potentials are determined by the limiting terms of the series \(\nu = (1,5S) - (mp_2)\). For thallium there were found a resonance potential of 1.07 V and an ionization potential of 7.3 V.

1. Davis & Goucher. Ionisation and Excitation of Radiation by Electron Impact in Nitrogen. Phys. Rev. 1919, Jan., 2.

On bombardment with 7.5-volt electrons, radiation in \(N_2\) was detected. More intense radiation was observed at 9 V. Ionization sets in at \(\sim 18\) V.

1. Foote, Rognley and Mohler. Ionisation and Resonance Potentials for Electrons in Vapors of As, Rb and Cs. Phys. Rev. 1919, Jan., 59.

Using the former method of measuring the total and partial currents, the authors found for As vapor an ionization potential of 11.5 V and a resonance potential of 4.7 V; for Rb and Cs, respectively, \(V_J = 4.1\) V and \(V_R = 1.6\) V, and \(V_J = 3.9\) V and \(V_R = 1.43\) V.

1. Smyth. The Radiating Potentials of Nitrogen. Phys. Rev. 1919, Nov., 409.

The author found very strong radiation at \(8.29 \pm 0.04\) V, doubtful radiation at 7.3 V, and radiation obtained only at low pressures at \(6.29 \pm 0.06\) V. The lines corresponding to these voltages the author attempts to identify with known spectral lines.

1. Rentschler. Resonance and Ionisation Potentials for Electrons in the Monatomic Gases Argon, Neon and Helium. Phys. Rev. 1919, Dec. 503.

Using the method of Tate and Foote, and also Lenard’s method, the author obtained for Ar, as the mean of the results of both methods, \(V_J = 17\) V and \(V_R = 12.3\) V. For Ne and He, without corrections for the initial velocity, there are obtained respectively \(V_J = 19.5\) V and \(V_J = 26\) V.

1. Franck & Knipping. Die Ionisierungsspannungen des Heliums. Phys. ZS. 1919, 481.

By a method representing a certain modification of Lenard’s method, the ionizing potentials of He were found: one at 25.4 V and the second \(79.5 \pm 0.3\) V, corresponding to double ionization. Further, in agreement with the results of earlier investigations, a resonance potential of 20.5 V was obtained; and, in addition, in very pure He a second resonance potential was observed, exceeding the first by 0.8 V.

1. Holst & Koopmans. The Ionisation of Argon. Proc. Amsterdam 1919, 21, 1089.

Using the Franck and Hertz method, a loss of velocity by electrons at 12 V was discovered. The authors attribute this effect to the photoelectric action of 12-volt resonance radiation on the electrodes. The ionization potential is obtained as equal to 17 V.

1. Compton. On Ionisation by Successive Impact and its Action in Low Voltage arcs. Phys. Rev. 1920, April, 130.

Calculation of the probability of the simultaneous collision of several electrons with a molecule leads to the impossibility of explaining low-voltage arcs by such collisions.

1. Compton. Radiation and Ionisation Produced in Helium by 20-volt Impact. Phys. Rev. 1920, 131.

Ionization, which occurs in helium at high pressures and 20 volts, ceases as the pressure is reduced. This is explained by the decrease in the probability that an electron will encounter an excited atom.

1. Found. Ionisation Potentials of Argon, Nitrogen, Carbon Monoxide, Helium, Hydrogen, Mercury and Iodine Vapors. Phys. Rev. 1920, 132.

The investigation of current curves through certain gases and metal vapors led the author to the following approximate values of ionization potentials: 15–16 V (Ar), \(\sim 16\) V (\(\mathrm{N}_2\)), 13.5–14 V (CO), 20.5 V (He—of doubtful purity), \(\sim 15\) V (\(\mathrm{H}_2\)) and 10–11 V (Hg).

1. Mohler & Foote. Electron Currents in Some non Metallic Vapors. Phys. Rev. 1920, 321.

The investigation of the critical potentials of P, \(\mathrm{J}_2\) and S leads to the following result:

Substance.	First inelastic impact.	Ionization.
P	\(5.80 \pm 0.1\)	\(13.3 \pm 0.5\)
\(\mathrm{J}_2\)	\(2.34 \pm 0.2\)	\(10.1 \pm 0.5\)
S	\(4.78 \pm 0.2\)	\(12.2 \pm 0.5\)

1. Compton, Lilly & Olmstead. The Minimum Arcing Voltage in Helium. Phys. Rev. 1920, Oct., 283.

An arc in He was ignited at 20 V. In the case of a high density of the electron discharge and sufficient pressure, it was possible to obtain an arc at 8 V.

1. Hebb. Arcing Voltage in Mercury Vapor as a Function of the Temperature of the Cathode. Phys. Rev. 1920, Nov. 376.

The investigation of the minimum potential difference at which an arc is ignited in Hg vapors, as a function of the current heating a Wehnelt cathode, led the author to the following dependence between this potential difference and the temperature of the cathode: \(V = 10.5 - kT\), where \(k\) is a constant. The author has not yet found a satisfactory explanation of low-voltage arcs.

1. Smyth & Compton. The Effect of Fluorescence and Dissociation on the Ionising Potential of Iodine Vapor. Phys. Rev. 1920, 501.

The ionization of \(J_2\) vapors was investigated: 1) illuminated by a mercury arc and 2) in the absence of illumination. In the first case three critical potentials were obtained: \(6.42 \pm 0.11\ \mathrm{V}\), \(7.67\ \mathrm{V}\), and \(9.07 \pm 0.42\ \mathrm{V}\); in the second—two: \(7.7\ \mathrm{V}\) and \(9.21\ \mathrm{V}\). Identifying the last two potentials of the first case with the potentials of the second, the authors assign \(6.42\ \mathrm{V}\) to the ionization of fluorescing molecules, the middle one to the ionization of iodine atoms obtained as a result of the dissociation of molecules near a heated filament, and the third to the ionization of normal molecules. The authors find for the work of dissociation of the iodine molecule the value \(1.47 \pm 0.045\ \mathrm{V}\), whereas from the heat of dissociation of 35,000 cal the value \(1.52\ \mathrm{V}\) is obtained.

1. Horton & Davies. Critical Velocities for Electrons in Helium. Phil. Mag. 1920, May, 592.

Measuring the ionization current as a function of the accelerating electron potential, the authors discovered, besides ionization at \(25.6\ \mathrm{V}\), two further types of ionization: at \(\sim 55\ \mathrm{V}\), corresponding to ionization of the He ion, and at \(\sim 80\ \mathrm{V}\), corresponding to double ionization.

1. Mohler, Foote & Stimson. Ionisation and Resonance Potentials, for Electrons in Vapours of Lead and Calcium. Phil. Mag. 1920, July, 73.

By the method of Tate and Foote the authors found for lead \(V_R = 1.26\ \mathrm{V}\) and \(V_J = 7.93\ \mathrm{V}\). According to the quantum condition, \(V_p\) gives \(\lambda\ 980 \pm 80\ \mu\mu\), which agrees with spectroscopic data (Randall). For calcium two resonance potentials, \(1.90\ \mathrm{V}\) and \(2.85\ \mathrm{V}\), and an ionizing potential, \(6.01\ \mathrm{V}\), were obtained, in good agreement with the corresponding potentials calculated theoretically.

1. Horton & Bailey. The Effect of a Trace of Impurity on the Measurement of the Ionisation Velocity for Electrons in Helium. Phil. Mag. 1920, Oct., 440.

In pure He ionization occurs at \(\sim 25\ \mathrm{V}\), while in contaminated He it occurs at \(\sim 21\ \mathrm{V}\), which indicates ionization of impurities at the latter voltage. Whereas at \(\sim 25\ \mathrm{V}\) the complete He spectrum is observed, at voltages between 21 and 25 only mercury lines were visible.

1. Compton. Ionisation and Production of Radiation by Electron Impacts in Helium, Investigated by a New Method. Phil. Mag. 1920, Nov., 553.

Using a new method which permits ionization to be distinguished from radiation, the author found ionization of He at \(25.5\ \mathrm{V}\) and radiation at \(20.2\ \mathrm{V}\), accompanied by weak ionization. This ionization, in the author’s opinion, is due to collisions of electrons with atoms excited by the 20.2-volt radiation.

1. Horton & Davies. An Experimental Determination of the Critical Electron Velocities for the Production of Radiation an Ionisation on Collision with Argon Atoms. Proc. Roy. Soc. London 1920, March, 1.

By the method of Davies and Goucher, the ionizing and resonance potentials of Ar were found, respectively equal to \(15.1\ \mathrm{V}\) and \(11.5\ \mathrm{V}\). From this the limiting frequency of the Ar spectrum is obtained as the corresponding \(\lambda\,81.7\ \mu\mu\), which agrees with the discovery of Lyman, who found that the Ar spectrum breaks off near \(\lambda 80.0\ \mu\mu\).

1. Franck & Knipping. Über die Anregungsspannungen des Heliums. ZS. f. Phys. 1920, I, 4, 320.

In pure He the authors obtained \(V_R = 21.25\ \mathrm{V}\) and \(V_J = 25.25\ \mathrm{V}\). In the presence of impurities, a second \(V_R = 20.45\ \mathrm{V}\) was also observed. Two resonance potentials

correspond to two serial systems of He. Collision with a 20.45-volt electron gives the initial orbit of the infrared and visible series, assigned by Landé to compound He; with a 21.25-volt electron—the initial orbit of the parhelium series. Collision with a 20.45-volt electron does not produce radiation, but transfers the normal three-dimensional helium atom—according to the theory of Franck and Reiche—into a metastable compound state. Any process that returns such an atom to the normal state must liberate 20.45 V. The appearance of \(V_R \cdot 20.45\,V\) only in the presence of impurities is explained by the authors by saying that the compound atom enters into short-lived compounds with foreign impurities, which decompose with the liberation of energy corresponding to 20.45 V. In addition to the critical potentials named, the authors found a whole series of potentials between 20.45 V and 25.25 V.

1. Franck & Einsporn. Über die Anregungspotentiale des Quecksilberdampfes. ZS. f. Phys. 1920, II, 1, 18.

The measurement was carried out by two methods. The first consists in observing the dependence of the photoelectric effect on the velocity of the exciting electrons. Each line excited by the collision of electrons of a given velocity with Hg atoms gave a jump in the photoelectric-current curve. The second method consists in measuring the current due to those electrons which, after collision with the atoms, still retained part of their kinetic energy—as a function of the accelerating potential. In this way the authors succeeded in observing up to 17 resonance potentials between 4.68 V and 10 V, and ionization at 10.38 V. The lines calculated from the potentials obtained are quite close to the lines known from spectroscopy.

1. Compton & Olmstead. Note on the Radiating and Ionising Potentials of Hydrogen. Phys. Rev. 1921, 45.

By a method constituting a modification of Lenard’s, the following were found in hydrogen: ionization and radiation at \(\sim 10.8\) V, radiation at \(\sim 13.4\) V, and strong ionization at 15.9 V. The authors suppose that at about 10.8 V there may occur radiation of the atom, or ionization without dissociation of the molecule; at about 13.4 V—dissociation of the molecule plus radiation of one of the atoms, or ionization of the atom; finally, at 15.9 V—dissociation of the molecule plus ionization of one of the atoms.

1. Franck & Grotrian. Bemerkungen über angeregte Atome. ZS. f. Phys. 1921, IV, 1, 89.

Comparing a whole series of known facts with their own experiments, which consisted in observing the green glow appearing when dense mercury vapor is illuminated by the resonance line \(253.6\,\mu\mu\), the authors come to the conclusion that the existence of \(Hg_2\) molecules is possible.

1. Einsporn. Über die Anregungs- und Ionisierungsspannungen des Quecksilbers. ZS. f. Phys. 1921, V, 4, 208.

Measuring the current between cylindrical electrodes (a filament, two mesh cylinders, and a solid cylinder), the author succeeded in observing, in addition to \(a = 4.9\) V and \(b = 6.7\) V, the effects \(2a + b\), \(a + 2b\), \(4.a,3b\), \(3a + b\), \(2a + 2b\), and \(5a\) volts. Finally, at \(42 \pm 2\) V the author apparently observed double ionization.

1. Knipping. Die Ionisierungsspannungen der Halogenwasserstoffe. ZS. f. Phys. 1921, VII, 4—5, 328.

By a method analogous to Einsporn’s method (42), ionizing potentials were obtained for HCN (15.5 V), HCl (14.4 V), HBr (13.8 V), and HJ (13.4 V), with a maximum error of \(\pm 0.5\) V. From the good agreement of his results with the data of Born and Fajans, the author concludes that the ionization of the named substances consists in the splitting of the molecule into a positive H-ion and a negative halide ion.

1. Brandt. Über die Ionisierungs- und Anregungsspannungen des Stickstoffs. ZS. f. Phys. 1921, VIII, 1, 32.

The author observed ionization of \(N_2\) at \(17.75 \pm 0.1\ \mathrm{V}\), \(25.41 \pm 0.1\ \mathrm{V}\), and \(30.72 \pm 0.2\ \mathrm{V}\). The first inelastic impact was observed at \(8.5\ \mathrm{V}\).

1. Krüger. Ionisations- und Dissotiationsarbeit des Wasserstoffs. Ann. D. Phys. 1921, 64, 288.

By the Davis and Goucher method the following results were obtained with hydrogen: 1) ionization and weak ultraviolet radiation at \(11.5 \pm 0.7\ \mathrm{V}\), 2) radiation at \(13.6 \pm 0.7\ \mathrm{V}\), 3) strong ionization at \(17.1 \pm 0.25\ \mathrm{V}\), and 4) a second type of ionization at \(30.4 \pm 0.5\ \mathrm{V}\). The last potential corresponds to dissociation of the molecule and ionization of both atoms \((2J + D)\); \(17.1\ \mathrm{V}\)—to dissociation of the molecule and ionization of one atom \((J + D)\); \(13.6\ \mathrm{V}\)—to dissociation and radiation of one of the atoms \((R + D)\); finally, \(11.5\ \mathrm{V}\), in the author’s opinion, corresponds to ionization of the hydrogen molecule without its dissociation.

1. Horton & Davies. The Production of Radiation and Ionisation by Electron Bombardment in Pure and Impure Helium. Phil. Mag. 1921. Nov., 746.

The measurements were made by the Davis and Goucher method. In pure He two resonance potentials, \(20.4\ \mathrm{V}\) and \(21.2\ \mathrm{V}\), were found. In contaminated He, ionization was detected at \(20.4\ \mathrm{V}\). Further, by subjecting He to 21.2-volt radiation emitted by atoms when bombarded with electrons at \(21.2\ \mathrm{V}\) in a special tube attached for this purpose to the main one, the authors obtained ionization at \(20.4\ \mathrm{V}\). They interpret this result as ionization by 21.2-volt radiation of atoms excited by 20.4-volt electrons.

1. Horton & Davies. Critical Electron Velocities for the Production Luminosity in Atmospheric Neon. Phil. Mag. 1921, 921. Proc. Roy. Soc. 1921, Oct., 124.

The authors found in Ne three ionizing potentials: \(16.7\ \mathrm{V}\), \(20.0\ \mathrm{V}\), and \(22.8\ \mathrm{V}\), and two resonance potentials: \(11.8\ \mathrm{V}\) and \(17.8\ \mathrm{V}\). At \(16.7\ \mathrm{V}\), ionization was not accompanied by visible radiation; at \(20\ \mathrm{V}\), the principal series appeared; and at \(22.8\ \mathrm{V}\)—the complete Ne spectrum.

1. Foote, Meggers & Mohler. The Excitation of the Enhanced Spectrum of Magnesium in a Low Voltage Arc. Phil. Mag. 1921, Dec., 1002.

On the basis of their analysis of the received Mg, subjected to bombardment by electrons of various velocities, the authors assert that a normal Mg atom absorbs the following energy quanta: \(46.9\ \mathrm{V}\), emitted in the form of L-radiation; \(22.8\ \mathrm{V}\), producing double ionization and emitted in the form of a simple enhanced spectrum and in the form of an arc spectrum; \(7.61\ \mathrm{V}\)—ionizing the atom and giving the arc spectrum; \(4.33\ \mathrm{V}\), giving two, and \(2.70\ \mathrm{V}\)—one spectral line. The ionized Mg atom absorbs: \(14.97\ \mathrm{V}\), producing ionization and giving the simple enhanced spectrum, and \(4.4\ \mathrm{V}\)—a one-line enhanced spectrum.

1. Goucher. The Measurement of the Resonance, Radiation and Ionisation Potentials of Several Gases and Vapors. Phys. Rev. 1922, March, 189.

By a method that is a modification of Compton’s method, the following results were obtained:

Gas or vapor	$V_R$	Radiation	$V_J$
$\mathrm{H_2}$	$10.1 \pm 0.1$	$10.1—13.6$	$13.6;\ 15.6$
$\mathrm{N_2}$	$8.4 \pm 0.1$	$8.4—15.8$	$15.8$
$\mathrm{O_2}$	$8.0$	Radiation not observed	$14.0$
$\mathrm{C_4H_{10}^{0}}$	$6.6 \pm 0.1$	$8.1—10.1$	$13.6$
$\mathrm{C_6H_6}$	$6.0$	Radiation not observed	$9.6 \pm 0.1$
$\mathrm{C_7H_8}$	$6.2 \pm 0.25$	— ” —	$8.5 \pm 0.5$
$\mathrm{C_8H_{10}}$	$6.5$	— ” —	$10.0$
$\mathrm{CHCl_3}$	$6.5$	— ” —	$11.5$

1. Davies. The minimum Energies Associated with the Excitation of the Spectra of Helium. Proc. Roy. Soc. London 1922, March, 599.

When He was bombarded with electrons of various velocities, the appearance of both principal series of helium (orthohelium and parahelium) was observed only at velocities corresponding to the ionization potential, which contradicts the conclusions reached by Franck and Knipping on the basis of their work.

1. Horton & Davies. A Spectroscopic Investigation of the Ionisation of Argon by Electron Collisions. Proc. Roy. Soc. London 1922, Nov., 131.

Observing the luminescence of Ar bombarded by electrons, the authors obtained the following results: $V_R = 11.5$ V, $V_J = 15.1$ V—values they had found earlier. At 15.5 V they observed the appearance of the red spectrum of Ar. Further, at 34 V, double ionization was observed, accompanied by the appearance of the blue spectrum of argon.

1. See, for example, the article by P. Ehrenfest, “Application of the quantum doctrine to the theory of spectral series.” Advances in the Physical Sciences, vol. II, issue 1. ↩