NEW STUDIES ON THE EXCITATION OF LIGHT *

M. Pirani, Berlin

The Problem of the Excitation of Light

For a long time the task of illuminating engineering consisted in reproducing sunlight by means of thermal radiation. The absence of substances with a sufficiently high melting point and low volatility makes this task impossible. Despite the existing small selective deviations, all thermal radiators radiate according to laws close to those of a black body. Consequently, the maximum attainable efficiency cannot be substantially higher than that calculated for a black body, i.e. at best about 15%.¹

In order to make further progress in this field possible in principle, it was necessary to pass to the study of the elementary processes of luminescence. The general problem of illuminating engineering—the production of light close to sunlight—is then divided into the problems: 1) finding a method for the economical production of radiation in the visible part of the spectrum (the problem of quantity), and 2) finding a method for composing radiation of the desired action (the problem of quality).

The Use of the Resonance Line for Light Radiation

The principal path for investigating the first question is the excitation of an individual atom by electron impact. The sodium atom is an example of a simple atom whose radiation lies mainly in the visible part of the spectrum. 99% of the visible radiation of sodium falls at the wavelength \(\lambda = 5890/96\ \text{Å}\), where the sensitivity of the eye is 0.78 of the maximum (for the distribution of Na energy see Table 1).**

* Report delivered by the author in Section VI of the International Electrotechnical Congress in Paris in 1932. Translated by D. Livshits.

* Here an interesting incidental result is obtained at the same time: one can very simply obtain the mechanical equivalent of light by comparison with a receiver graduated directly in radiant energy, while the curve of the sensitivity of the eye for different wavelengths may be regarded as known. Cf. H. Krefft and M. Pirani, Z. techn. Physik 13*, 367, 1932.

TABLE 1

Spectral intensity of Na, at a pressure of \(10^{-3}\) mm and a current density of
\(0.5\ \mathrm{A/cm^2}\)

Sodium, as an alkali metal (the first group of the periodic system), has a simple spectrum: outside the so-called closed electron shells there is only one optical electron². The transfer of energy from a free electron to an electron bound in an atom is determined by a known function of yield³ (Fig. 1). Electrons whose kinetic energy is approximately two to four times greater than the energy needed to excite some line have the greatest probability⁴ of exciting that line to emission. The optimum value of this yield is not the same for different lines, and within the limits of one series, as the number of the line increases, it falls very steeply. After some time⁷ (about \(10^{-8}\) sec.), the excited atom returns all its excitation energy in the form of a light quantum. The yield in the case of unperturbed atoms⁵ reaches 100%, i.e. 100% of all atoms give up the excitation energy in the form of radiation.

Fig. 1. Relative excitation yield of certain spectral lines of helium (excitation potential between 23 and 24 V) as a function of electron velocities in volts.

In the presence of external perturbing factors the yield decreases⁶, since, first, atoms can be quenched in collisions during their excited state (collisions of the second kind). In this case the excitation energy may pass into the kinetic energy of the colliding pair, or may excite an atom which before the collision had not been excited. This occurs the more often, the greater the density of the particles. The transition into kinetic energy occurs chiefly in collisions with electrons, and less often in collisions with atoms (Fig. 1).

Secondly, atoms excited by an electronic impact may receive an impulse toward further quantum transitions (stepwise excitation and inverse emission of other lines),

Thirdly, a light quantum emitted by an atom may be absorbed (although, in essence, there is no loss of energy for a given wavelength here; the apparent losses of energy increase). This occurs at high pressure of the excited sodium vapor or gas and is especially strong for the resonance line.

For greater emission of the resonance line, according to point 3, the pressure of the excited atoms must not be excessively high; the density of the electrons (i.e., the current density), according to point 2, must not be too high either.

But when the pressure of sodium vapor is lowered, some of the electrons having the optimum velocity do not collide with sodium atoms and, accelerating, acquire a high velocity. This phenomenon is combated by adding a noble gas.

Noble gases are distinguished by a very high excitation potential. Electrons that do not possess sufficient energy for this can give up to an atom of a noble gas only an insignificant part of their energy in accordance with the law of momentum, undergoing a simple elastic reflection ⁷.

Since, according to experiment, the pressure of the noble gas may be taken to be \(10^3\) times greater than the pressure of the sodium vapor, a larger number of such elastic collisions is obtained, which lengthen the path of the electron from anode to cathode, for example, by a factor of 100. Thus the possibility of collision of an electron on its way from anode to cathode with a sodium atom increases considerably. According to the laws of mechanics, the loss of energy in an elastic collision is inversely proportional to the mass of the noble-gas atom. Therefore heavy noble gases should be more advantageous than light ones. But experiment shows that the difference, at least among the heavy noble gases, is small*.

An economical sodium discharge tube is constructed as follows: it is filled with a noble gas at a pressure of several millimeters; the sodium-vapor pressure in it ranges from 0.001 to 0.1 mm; it has a source of electrons; the voltage necessary for accelerating the electrons is applied to it. To obtain sodium vapor of the desired pressure, the discharge tube is heated to a definite temperature; for example, to obtain 0.005 mm it is heated to 260°, 0.05 mm—to approximately 330°, 0.5 mm—to 420° C.

It turns out that 70–80% of the expended electrical energy ⁸ is transformed into light, which corresponds to 370–420 lm/W (not counting heating, i.e., the power expended to obtain the required sodium-vapor pressure). This highly economical type of lamp is used for television. This experiment, for the first time in the history of lighting engineering, actually showed the correctness

* Experiment has shown that helium gives better results than heavy gases. This fact does not fit into Pirani’s simple scheme and has not yet been fully explained (editor’s note).

of the frequently expressed assumption^9 that electrical energy can be converted into light with a high efficiency. This also marked out the path of further technical development. But before transfer to production, the following problems still had to be solved^10: 1) fabrication of an economical and stable source of electrons, 2) the most economical heating for producing vapors, 3) a secondary, but necessary, condition: the fabrication of glass that is not destroyed by sodium.

Fig. 2. Small Osram sodium lamps for direct and alternating current.

Sodium discharge tubes appeared as a result of the solution of these problems (Fig. 2). Oxide electrodes, made of a compacted pressed mixture of tungsten with barium oxide, serve as the source of electrons. The discharge tube is made of a special “sodium-resistant” borosilicate glass. The tube is loaded with such high current densities that the losses at the electrodes and in the tube itself cause strong heating, rapidly increasing with the increase of current density, and quite sufficient for obtaining vapors^11.

The discharge tube proper is surrounded by an evacuated envelope, serving for thermal insulation. The luminous output of such a sodium lamp (the \(D\)-lines) is \(60\ \mathrm{Lm/W}\). Sodium lamps find application, first, where monochromatic light is necessary (spectroscope, polarimeter, signals, etc.) and, second, where monochromatic light does not interfere but is even desirable (the growing resolving power of the eye), for example, in lighting streets for automobile traffic.

Application of higher excited states for obtaining light.

In those atoms in which, in contrast to sodium, the strongest visible lines are emitted in transitions between excited levels—for example in Mg, Cd, Zn, Hg, Ne, He (Fig. 3, scheme of Hg terms)—at increasing current densities and vapor pressures the stronger manifestation of the higher members of series, or of the series corresponding to transitions between these excited levels, plays a large role.

Here one may expect in advance, at low current density and low pressure (about \(50\ \mathrm{mA}\) with Ne at a pressure of \(1\ \mathrm{mm}\))

poor visual efficiency which is in fact observed. But in all these atoms those levels which emit chiefly visible lines have a very long lifetime of the excited state (10–100 times greater than that characteristic of the initial levels of the \(D\)-lines); they are partly “metastable.” A sufficiently weak excitation, or in other words a low current density (about \(200\ \mathrm{mA}/\mathrm{cm}^2\) for Ne at a pressure of \(1\ \mathrm{mm}\)), is enough to attain these levels in such a way that the visible lines behave in the same manner as the resonance lines. Consequently, even at comparatively small current densities and vapor pressures one can obtain a satisfactory luminous yield; as the current density and vapor pressure increase, it begins soon to decrease. In mercury, where the pressure can readily be raised to \(1\ \mathrm{atm}\), an increase in luminous yield is again observed at large current densities and pressures,¹² running parallel with the quenching of the mercury arc. At the same time the relative intensity of the resonance line is greatly diminished. From the intensity distribution of the low-pressure tube (Fig. 4) and the high-pressure tube (Fig. 5) it is seen that the color of the high-pressure discharge approaches “white” (the selective character of the mercury spectrum, however, is not basically changed). The mechanism of this phenomenon, observed so far mainly in metallic vapors, is not yet entirely clear, nor are the grounds for a further increase in economy.

Fig. 3. Term scheme for mercury.

We have in mercury, in contrast to sodium, a case in which high pressure and a large specific load lead to a higher efficiency. Tech-

nical application of these results led to a lamp of 50 Lm/W, which can be used for street lighting (Fig. 6). The improvement in the color of this lamp in comparison with a low-pressure lamp is of great technical importance, since, in general, what is required of a light source is not only economy, but also that the objects illuminated by it should not deviate very much from the appearance familiar to us in daylight. For this it is required first of all

Fig. 4. Distribution of intensity over the spectrum of a mercury discharge at low pressure in a quartz tube. For comparison, the spectrogram of the same lamp is given. The strong predominance of the resonance line 2537, the II subordinate series ($\lambda = 5461,\ 4358,\ 4047$) is more intense than the 1 subordinate series ($\lambda = 3663/50,\ 3132/26,\ 2967\ \text{Å}$). Excitation, chiefly, of the principal level (1 s).

Fig. 5. Distribution of intensity over the spectrum of a high-pressure mercury discharge. For comparison, the spectrogram of the same lamp is given. The resonance line $\lambda = 2537\ \text{Å}$ is relatively weak; the great intensity of the 1 subordinate series ($\lambda = 3663/50\ \text{Å}$), which is now more intense than the II subordinate series ($\lambda = 5461$).

that it should have a spectrum physically close to the solar one^18 or well-distributed emission lines over the general spectrum. A high-pressure mercury lamp emits almost nothing in the red part of the spectrum. Therefore, in order to obtain illumination close to daylight, the mercury lamp must be combined with other light sources that emit a large amount of energy in the red part of the spectrum; such are, for example, a discharge in Ne or incandescent lamps.

The theoretical and experimental premises mentioned above for making a light source with a high efficiency, explained using sodium and mercury as examples, are also valid for the noble gases, as, for example, for the spectrum of helium (the lines of the subordinate series in the visible region, the “resonance line”—\(1.08\,\mu\)) and for the spectrum of neon*.

Fig. 6. Osram high-pressure mercury lamp.

Forbidden transitions and the use of recombination spectra in the excitation of light

At rarefying current and vapor density, the appearance of so-called forbidden transitions and recombinations of electrons and ions is observed for a whole series of metals. From the scheme of the terms of the atom it is seen that only a limited number of combinations of two energy levels (lines) is “allowed”; the rest constitute the so-called forbidden transitions or lines. Forbidden transitions may appear if the atom undergoes a strong perturbation, for example, enters an electric field. In a gas discharge at high densi-

Fig. 7. Light emission of thallium in the positive column; wavelengths are given in Å.
Left: scheme of Tl terms with “normal” transitions: I and II subordinate series, main series and Bergmann series.
Right: scheme of Tl terms with “forbidden” transitions caused by ionic fields in the positive column.

* To what extent these radiation sources will be good sources of light depends on the distribution of the spectral lines, determined by the properties of the atom.

of electrons and ions, extraordinarily large intermolecular fields arise, and emission of forbidden lines becomes probable (Fig. 7). In this case the spectrum of the atom is “supplemented” in a characteristic way.

Fig. 8. Diagram of the recombination spectrum (satellite series of gallium).
Lines corresponding to individual transitions in the term diagram are marked on the spectrogram by numerals. The appearance of the limiting continuum is shown schematically by arrows \(A\), \(B\), and \(C\), which denote transitions of electrons of various kinetic energies to the level \(2P_1\).

Further, from the scheme of the atom’s terms it is seen that the discontinuous energy levels tend toward a definite limit. This limit corresponds to the separation of the luminous electron from the atom—ionization. The reverse combination of an electron with an ion is called recombination. For ionization, as well as for recombination, as for all excitation processes, there exists a definite dependence on the velocity of the electrons, determined by the entrance function. Experimental material and theoretical considerations show that recombination predominates at the walls of the vessel; inside the vessel it had not been observed until recently. Only in investigations in the positive column of mixtures of metal vapor with a noble gas, carried out by Kraft\({}^{14}\), first with Tl and then with K, Cs, Rb, etc., were conditions obtained (a high concentration of ions and electrons caused by strong ionization of the metal vapor) under which recombination was observed inside the vessel. In recombination, as experiment shows, preference is given to those levels at which the strongest excitation and ionization are obtained.

Upon recombination at the γ-walls, the released energy is for the most part imparted to the walls. If recombination occurs inside the vessel, radiation may take place. The wavelength of the emitted light corresponds to the energy of the atomic level on which recombination occurs, plus the kinetic energy of the liberated electron (Fig. 8). In the spectrum at the series limit there is seen an exclusively continuous band, the intensity of which decreases toward the shorter waves (Fig. 8). If this limiting continuum lies in the visible part of the spectrum, as, for example, in the alkali metals, then it increases the light emission. As a result of the superposition of the continuum on the line spectrum, the color of the light changes. Simultaneously, the higher members of the series are intensified, since the concentrations of atoms at high levels increase owing to recombination of the latter; because of this, a further filling-in of the spectrum occurs, and one can sometimes obtain white light, for example, with Cs (Fig. 9). Finally, the “smearing” of the spectrum occurs as a result of emission by the band, namely both by the molecules of the metal and by the molecules of the metal with the noble gas.¹⁵

Fig. 9. Influence of pressure on the distribution of energy over the spectrum in a discharge in cesium and rubidium.
At high pressure the limiting continua and higher series become very intense [side series (Cs γ = 5100 Å, Rb γ = 4950 Å) and the Bergmann series (Cs γ = 6200 Å, Rb γ = 6500 Å)]. The spectrum is “filled in”—it approaches daylight.

The considerations set forth above, illustrated by several examples, have already been realized technically for many vapors and gases, for example, for He, Ne; Na, K, Rb, Cs; Mg, Zn, Cd, Hg; C, In, Te; N₂, CO₂.

Application of excitation of the radiation of photoluminescence of molecular gases, liquids, and solids for obtaining light

Upon a similar examination of the excitation of luminescence of liquids and all sorts of solids for the purpose of obtaining light, the picture changes considerably. Usually the bond of an atom in a molecule strongly depends on the configuration of the electrons, and upon excitation of an electron transition the energy levels that determine the bonding forces change. This change usually occurs,

at the expense of excitation energy, so that the energy efficiency coefficient already for a single molecule under known circumstances may become less than 100% (Stokes’ rule). Part of the energy goes to raising the temperature of the molecular gas. With increasing density the efficiency coefficient will deteriorate still further, since in collisions an exchange of energy takes place between the moving nuclei of individual molecules. In especially unfavorable cases—from the point of view of the rational excitation of light—the excitation does not entail reemission at all; for example, when excitation leads to dissociation. A characteristic example of a poor efficiency coefficient of radiation is carbon monoxide.

These considerations apply all the more to liquids and solids. In general, here one has to reckon with such a large dissipation of energy that rational excitation of luminescence is scarcely possible. But there are certain exceptions, for example, fluorescing liquids.

With thermal excitation, on the contrary, there can be no question of energy dissipation, since solid and liquid substances can be excited by heating and emit their own oscillations.

With the appearance of new levels in the transition from atoms to molecules, and then to the liquid and solid states, a substantial modification of the spectrum occurs. The newly appearing energy levels again lead to periodic processes of comparatively low frequency, since they usually have to do with heavy atomic nuclei; their effect is manifested in the fact that electron transitions are divided into a large number of partial levels. In liquids and solids one usually obtains a spectrum covering the region from infrared rays to the far ultraviolet (absorption and fluorescence spectra), consisting for the most part of continuous bands with places of greater transparency lying between them. In rare cases solids and liquids give non-continuous spectra, for example benzene, certain aniline dyes, and certain rare-earth elements.

Essentially new phenomena occur in metals. In passing from the gaseous state to the liquid, the metal atom partly or completely gives up its optical electrons. The remaining metal ions, together with the free electrons, give a picture possessing entirely different physical properties: “metallic” conductivity, “metallic” reflection, and continuous (with few exceptions) absorption, which is so great that metals are already opaque in very thin layers.

In any case, in the region of the spectrum in which the characteristic optical properties of metals are concentrated (therefore not in the region, for example, of short X-ray waves), all

absorbed energy is converted into heat, i.e., a 100% scattering of the excitation energy occurs. Here it is appropriate to raise the question whether, in addition, there exist hitherto unknown properties of metals that make it possible to excite luminescence.

The result of our general considerations may be reduced to the statement that the attainment of a considerable efficiency for the radiation of definite wavelengths required for obtaining light is the more probable, the more favorable are the conditions for the formation and existence of individual highly excited particles and the smaller is the scattering of energy. Therefore, in principle, the best possibility for the excitation of light is discharge in atomic gases and vapors.

LITERATURE

1. Cf. Geiger-Scheel, Handb. d. Phys. 19, S. 19, Berlin 1928.
2. For the term scheme see W. Grotrian, Graphische Darstellung der Spektren von Valenzelektronen, Berlin 1928.
3. R. Seeliger, “Ann. Physik”, 59, 613, 1919.
4. W. Hanle, “Z. Physik” 54, 94, 1919.
5. Cf. P. Pringsheim, Fluoreszenz u. Phosphoreszenz, S. 38, Berlin 1928.
6. Cf., for example, B. N. Krefft, M. Pirani, R. Rompe, Tech. wiss. Abh. Osram-Konz., 2, 24, 1931.
7. G. Hertz, Verh. dtsch. physik. Ges., 1917; “Z. Physik” 32, 298, 1924.
8. M. Pirani, “Z. techn. Physik” 11, 482, 1930.
9. II. Ebert, “Wiedemanns Ann.” 53, 160, 1894; Mc. F. Moore, ETZ 1896, S. 637.
10. M. Pirani, ETZ 1930, S. 889.
11. M. Pirani, “Z. angew. Chem.” 44, 395, 1931.
12. Küch u. Retschinsky, “Ann. Physik” 22, 515, 1907.
13. Cf. E. Lex u. M. Pirani, Künstliches Tages und Sonnenlicht, Vortr. Int. Illuminat. Congr. 1931.
14. H. Krefft, “Naturwiss.” 19, 269, 1930; “Physik Z.” 32, 948, 1931.
15. Cf. H. Krefft u. R. Rompe “Z. Physik”, 73, S. 681 (1931) and R. Rompe, “Z. Physik”, 74, S. 175 (1932).