THE ELECTRON AND THE LIGHT QUANTUM FROM AN EXPERIMENTAL POINT OF VIEW¹

R. A. Millikan.

The fact that natural science moves forward on two legs—theory and experiment—can best be illustrated by the example of two fields in whose development I have taken some part, for which you have honored me by awarding the Nobel Prize.

At one time one leg, at another time the other, moves forward; but sustained progress is possible only when both are in motion: either by the establishment of theories and their subsequent verification, or by the discovery of new experimental relations and then the drawing up of the theoretical leg, which at that moment lags behind, and so on without end.

Your protocol states that the prize is awarded “for work on the elementary quantity of electricity and on the photoelectric effect.” In both of these fields my work was that of a pure experimenter, whose most noble task consists in setting up, as far as possible, irreproachable experimenta crucis in order to test the correctness of theories put forward by other investigators.

The assumption of electrical particles, or atoms, is already 170 years old and belongs to Benjamin Franklin, who in 1750 wrote: “Electrical matter consists of exceedingly fine particles, since it can penetrate through ordinary matter, even the densest, with such ease that the latter offers no appreciable resistance.”

These theoretical conceptions were developed in particular parts by Wilhelm Weber² in works of 1871. The numerical value of the elementary electrical unit was estimated within known limits by Johnstone Stoney³ in 1881, and in 1891 this physicist gave the elementary quantity of electricity the name “electron.”

¹ Nobel lecture. Zeitschr. für physikalische Chemie, 116, p. 65, 1925.
² Werke, IV, p. 281.
³ Phil. Mag., 11, 384, 1881.

In 1897 an experimental foot advanced: J. J. Thomson and Zeeman found the so-called specific charge by two entirely different methods. These and analogous experiments within a few years brought the theory of electrons almost universal recognition among physicists.

Nevertheless, for at least two decades there still existed, even among men of science, skeptics who held the view that the seemingly uniform character of electricity is merely a statistical phenomenon. As for educated non-specialists, among them even now there is widespread a great misconception concerning the significance of our exhaustive proofs of the existence of the electron. One prominent man of letters recently spoke of the electron as of “the latest natural-historical hypothesis, which, in its turn, will give way to the abracadabra of tomorrow.”

Therefore, perhaps, it will be useful to try today to illuminate, in its main outlines, as accurately as possible, the present experimental state of the question and to make an attempt to draw a sharp distinction between theory and certain newly established facts.

As the most direct and unambiguous proof of the existence of the electron, it is apparently customary to consider one experiment, which I, for convenience, shall call the experiment with oil droplets. But before I turn to discussing the significance of this achievement, I shall ask you to hear the experimenter’s answer to the fundamental and often posed question: what is electricity? This answer has been found, but at the same time it is simple and definite. The experimenter states first of all that, as to the ultimate essence of electricity, he knows nothing.

He then turns to certain simple and well-known experiments and gives certain definitions, which are merely descriptions of the experiments and therefore contain nothing hypothetical.

First of all he notes the fact that a pith ball or a piece of paper, after contact with a glass rod previously rubbed with silk, acquires new and striking properties. The ball or piece of paper, with a considerable and easily measurable force, moves away from the rod. The experimenter describes this fact and at the same time adds that, apart from the existence of this force, he knows nothing more; he makes this description in such a way that he introduces a new word and says that the ball has been brought into a state of positive electrization, or, more simply, that the ball receives a positive electric charge. He then determines the dimensions of this charge by the magnitude of the observed force.

In a similar way the experimenter finds that another little ball, after contact with an ebonite rod previously rubbed with cat’s fur, is attracted by the first little ball, and describes this experiment by saying that the latter little ball has received a charge of negative electricity. If it is now possible to discover that an elder-pith ball, after contact with some body or by some other means, is brought into such a state that, as a result, it exhibits the properties described, then it, by definition, acquires a charge of positive or negative electricity. All our thinking about electricity proceeds from these simple experiments and these two definitions.

In order to be able to draw an entirely unambiguous conclusion as to the correctness or incorrectness of Franklin’s hypothesis, it was clear what was needed: 1) to reduce the charge on the elder-pith ball to the smallest possible magnitude; 2) to vary this charge by the smallest possible steps; and 3) to ascertain whether the forces acting on the ball at a known distance from the glass rod (i.e., in a constant field) reveal any tendency to increase or decrease by uniform steps.

The success of the experiment, which was first carried out in 1909, depended exclusively on the design of the apparatus, i.e., on the mutual arrangement of its parts.

The ball itself, which was to receive the smallest possible charge, naturally had to be a very small spherical body, whose mass in this case had to remain constant; for a continuously varying gravitational force, in its effect on the motion of a charged body, would be indistinguishable from a continuously varying electric charge.

Likewise, it was impossible to use a nonuniform or nonspherical body, since the force acting on the ball had to be measured from the velocity which it imparted to it, and this force can be calculated from the velocity only when the surface is spherical and the density absolutely constant. Therefore, instead of elder-pith balls, a single oil droplet was used, approximately \(0.001\) mm in diameter, which was produced in an ordinary atomizer and placed in an atmosphere completely freed from convection currents by suitable thermostatic devices. The glass rod, which created a constant electric field, was, of course, replaced by plates \(C\) and \(D\) of an air condenser (Fig. 1); one plate was connected with the positive pole, the other with the negative pole of a battery through a switch, so that the field could be turned on or off at will.

In order that the force acting on the oil droplet could be measured very accurately, it was necessary to be able to

measure the velocity over a path of approximately \(1\ \mathrm{cm}\). This is one of the most important requirements imposed on the apparatus; underestimating it introduced an error into the measurements of some later observers. This path of \(1\ \mathrm{cm}\) and the constancy of the field determined the approximate dimensions of the plates, whose diameter was in fact \(22\ \mathrm{cm}\) with a spacing between them of \(16\ \mathrm{mm}\).

Likewise the field strength—approximately \(6000\) volts per cm—was substantial, and constituted a requirement that was new for work of this kind. This field strength was a factor that turned possible failure into success. In fact, nature proved extremely kind here, for it provided a certain, though narrow, range of field strengths within which such experiments were possible.

Fig. 1. A sprayed oil drop is blown out over the plate \(C\). It falls through an opening in \(C\) into the space between \(C\) and \(D\), where it moves up or down as a consequence of the electric field between \(C\) and \(D\) being switched on or off. Its charge can be changed by ionizing the air with X-rays, which pass through the lead diaphragms \(L'\) and \(L\).

The drops had to be large enough that the so-called Brownian motion could almost be neglected; they had to be spherical and homogeneous, they had to be light and not evaporate; the distance had to be sufficiently large so that the time intervals in the motion of the drops could be determined accurately, and the electric field had to be strong enough to overcome the force of gravity when a drop charged with one or two electrons moved upward under the influence of the field. Hardly any other combination of dimensions, field strengths, and nature of materials could have yielded the results obtained. If the charge of the electron had been \(0.1\) of its actual value, or if the so-called sparking potential in air had been only \(0.1\) of its true value, the experimental facts reported here could never have been established.

The observations that gave an unambiguous answer to the question of the atomistic structure of electricity were carried out as follows. A drop was charged, for the most part, as a result of the friction associated with spraying. The charged drop slowly fell through a small opening in the middle of the plate \(C\) into the space between \(C\) and \(D\). Then the velocity of its fall under the action of gravity with the electric field switched off was measured, as well as the velocity of its rise against gravity with the electric field switched on; and the measurements were repeated after the charge of the drop had been changed by several different methods. This change of charge was achieved, for example,

ELECTRON AND LIGHT QUANTUM

by ionizing the air directly beneath the drop with \(\alpha\)-, \(\beta\)-, or \(\gamma\)-rays of radium, by illuminating the drop itself with ultraviolet light, by illuminating either the drop itself or the air beneath it with X-rays, etc. The now generally known results of this change of charges are set out in the following table:

1. It was possible to discharge the droplet completely, so that, within the limits of observational error—small fractions of a percent—one centimeter in the field of gravity, with a potential difference of 10,000 volts applied between \(C\) and \(D\), was traversed by the droplet in the same time as without the field.

2. A definite velocity could be imparted to it in the electric field (in our special case, 67.7 seconds), which, at will, could be reproduced and which was the smallest velocity imparted to the droplet by the given field. This change of velocity, which was due to the capture of one electron, was by no means so small as to make it difficult to observe and measure. On the contrary, it was often greater than the velocity imparted by the force of gravity, and was associated, as in the case cited, with a change of direction, so that it was wholly indisputable.

3. Velocities greater by two, three, four, five, etc. times (always within the limits of observational error—not more than one percent) could

R. A. MILLIKAN

be imparted to a droplet, but velocities equal to fractional parts of the smallest one were never encountered.

Whoever has seen this experiment—and hundreds of investigators have observed it—has, in the literal sense of the word, seen the electron. For he has measured (by means of velocity) the smallest electric force which a given electric field can in general exert upon an elder-pith ball—the very ball by whose motion he defines electricity itself. Further, he has found that the thing which he has agreed to call electricity can be imparted to his ball, or removed from this ball, only in such quantities that this moving force either falls to zero or increases by definite integral multiples of the smallest observable force.

If anyone were to see a football, about which another person told him that this is an electron, he would be far less certain that this corresponds to reality than if he were to become acquainted with the experiment described. With the aid of this experiment the observer can—as the table shows—count the number of electrons in a given small charge with precisely the same certainty with which he counts his fingers. It should be added that when he has counted up to 200 electrons in his charge, the errors of observation do not allow him to distinguish between 200 and 201; so that the conclusion that larger electric charges are built up in the same way as the charges which he can count is, of course, a generalization, but one which is evidently entirely plausible.

But the electron itself, which the observer measured, as is shown by the case given in the table, is not something doubtful or hypothetical. It is a new experimental fact, which our generation has seen for the first time, but which from now on anyone who wishes can see.

The measurement of the electron in absolute electrostatic units, and not through velocity, as was given above, includes observations of the kind described on thousands of droplets of different sizes, made of different substances, surrounded by different gases, at pressures varying over wide limits from atmospheric pressure down to \(1.5\) mm of mercury.

This measurement required a number of years in order to find the exact value of the internal friction of the gas and to establish how Stokes’s law must be modified in order to represent the law of fall of a particle through a gas at any pressure. All this interests us here because it shows how, without exception, observations in all gases and with all substances lead to one and the same absolute value of the electron, which is a point

ELECTRON AND LIGHT QUANTUM

intersection of all the straight lines on the \(e^{2/3}\) axis of our Fig. 21. This point of intersection directly gives the numerical value of the electron:

\[ e = 4.774\ (\pm 0.005)\times 10^{-10}\ CGSE \]

After ten years of work by other laboratories, in which the methods and results obtained in connection with the study of oil droplets were tested, practically general agreement has now been reached as to their correctness, despite the fact that these methods and results had first been driven through the ranks of severe criticism.

Thus electrons, both positive and negative, are merely observable electric force centers, like charged pith balls, the study of which gave our initial determination of the electric charge, with the difference that electrons are invariable in their charge, whereas the charges of pith balls vary, since these charges consist of different numbers of electrons. Further, Rowland long ago showed that electric currents are simply electric charges in motion. Therefore the proof that electric charges consist of a definite number of discrete electrical particles, electrons, also includes the proof that electric currents are nothing other than streams of an enormous number of electrons moving in a conductor.

Fig. 2. All these straight lines converge at one and the same point of intersection on the vertical axis, thereby providing excellent proof that one and the same electron takes part in the construction of all atoms.

Strictly speaking, we know nothing about the dimensions of electrons, so that for practical purposes electrons of either sign may be regarded as point charges, although it is well known that the positive electron has a mass 1,845 times greater than the negative one. Why this is so—no one knows. It is a further experimental fact.

It is well known that we can now accurately count the number of positive and negative electrons in each atom; that we imagine all positive electrons as being located in the nucleus; that we partly distribute the negative electrons in the outer

in part, we find bound in the nucleus; that the number of external negative electrons changes in uniform steps from one in hydrogen to 92 in uranium, and that the number of negative electrons in the nucleus is determined by the difference between the atomic weight and the atomic number.

Will we ever discover that the positive or negative electron is divisible? This, too, no one knows; but we can draw certain conclusions on the basis of the history of the chemical atom. It is sometimes rashly said of it that it has been blown up; but, of course, every natural scientist knows that the atom has not lost one iota of its former reality and its former vitality. From the experimental point of view, the chemist’s atom is completely embodied in the laws of constant proportions and multiple ratios. For those purposes for which the concept of the atom was originally employed—namely, for understanding chemical compounds—it still represents the very same ultimate unit that it was before.

Likewise, it does not seem probable that in the field in which the electron has been found as a unit—namely, in problems connected with the structure of the atom—there will ever be a need to make use of another unit. The new facts discovered by our generation constitute a solid inheritance for posterity. If the electron should ever be subdivided, this will probably occur when humanity, with new means—as unlike X-rays and radioactivity as the latter are unlike ordinary chemical forces—opens with these new means a region in which the electron can be destroyed. In that event, however, it will not lose its character as a structural unit, which it reveals in those relations in which we have investigated it hitherto.

The second field in which I, in accordance with your protocol, attempted to take a further step forward and to help the experimental leg catch up with the theoretical one is the field of ether waves. In this field I had already been trying since 1904 to find unequivocal proof for the Thomson–Planck–Einstein conception of localized radiant energy.

This conception, in its most general form, was used in 1903 by J. J. Thomson1 to explain two newly discovered experimental facts. Namely:

1. That X-rays pass through all the atoms of the portion of space illuminated by them, with the exception of an insignificantly small fraction—approximately 1 in 1000 billion—without giving up their energy; however, here and there an atom is encountered from which they eject an electron with enormous velocity.

ELECTRON AND LIGHT QUANTUM

2. That ultraviolet light possesses, as discovered in 1902 by Lenard¹), the remarkable ability to tear electrons from the surface of a metal with an energy that remains the same regardless of whether the distance of the light source is large or small, i.e. regardless of the intensity of the incident light.

This semicorpuscular conception of Thomson concerning localized radiant energy was accepted in 1905 by Einstein²). Proceeding from this conception and in connection with the existence of quanta, discovered by Planck as a result of the analysis of black-body radiation, the latter obtained an equation which, in Einstein’s opinion, should govern the exchange of energy between ether waves and electrodes. This equation reads:

\[ \frac{1}{2}mv^{2}=h\nu-p. \]

Here the left-hand side represents the energy of the flying electron, the first term on the right-hand side is the Planck energy quantum³) for light of the given frequency, and the last term is the work necessary to remove the electron from the metal.

All efforts were initially directed toward an exact experimental measurement of the energy of the emitted electrons, now as a function of temperature, now as a function of wavelength, now as a function of the nature of the material (the role of the contact potential). After ten years of trials, measurements, study, and also some errors, the work of 1914, contrary to my own expectations, gave the first direct experimental proof of the strict validity of Einstein’s equation within narrow limits of observational error⁴). From this there also resulted the first photoelectric determination of the Planck constant \(h\). The accuracy achieved was about \(0.5\%\), and at that time was the best. Fig. 3 gives a diagram of the apparatus used. Figures 4 and 5 depict the results of the most exact investigation on a definite metal (sodium) and show the complete unambiguity of the result. — And this work, like the work on the electron, withstood severe criticism, for until 1916 not only lively

![Fig. 3 diagram]

Fig. 3. Monochromatic light falls through the opening \(O\) onto the metal \(A\), from which it tears out electrons. The kinetic energy with which these electrons leave \(A\) is measured by the positive potential difference which must be applied between \(A\) and \(F\) in order that they reach the electrode \(F\). The resulting electron current is read from the indications of \(E\).

¹) Ann. d. Phys., 8, 149, 1902.
²) Ann. d. Phys., 17, 132, 1905; 20, 199, 1906.
³) Verh. d. Deutsch. Phys. Ges., 2, 202, 237, 1900.
⁴) Phys. Rev., 4, 73, 1914; 6, 55, 1916; 7, 362, 1916.

R. A. MILLIKAN

Fig. 4. The figure shows how clearly the energy of the photoelectrons emitted by [[unclear: object/source]] (see Fig. 3) decreases as the wavelength increases in five steps (or as the frequency correspondingly decreases). These steps correspond to the spectral lines of the mercury spectrum from the extreme ultraviolet line \(\lambda = 2535\) to the bright green line \(\lambda = 5461\). The decrease in energy is manifested in the fact that the points of intersection of the photocurrent curves shift farther and farther to the right. (The lower part of the diagram represents the right end of the upper part; they are printed one under the other solely for convenience.)

The question of whether there exists in general a limiting velocity of emission was discussed, but even some other observers, who admitted

Fig. 5. The figure shows not only that between the energy of the electron (the points of intersection in Fig. 4) and the acting frequency of the light there exists a linear relation, but in the lower right-hand corner it is also shown that the numerical value of the ratio is equal to \(6.56 \cdot 10^{-27}\), which agrees well with other determinations of Planck’s constant \(h\). This was the first direct determination of this fundamental constant.

that there exists a linear relation between energy and frequency, did not find the universal constant \(h\) as a factor. However, it will not now be an exaggeration to say that, indeed, exhaus-

proving the strict validity of Einstein’s equation and its very broad applicability, which has now already been obtained, within the narrow limits of experimental error, by the experiments of many observers, by several methods, in the most diverse laboratories,—so that this proof may perhaps constitute the most outstanding and most astonishing achievement of experimental physics in the last ten years.

The history of this remarkable success, in brief, is as follows. One or two years after the completion of the above-mentioned photoelectric investigations, Duane1 and his collaborators found an unambiguous proof of a relation that represents the inverse of Einstein’s relation. They bombarded a metal disk with electrons of known and constant energy and found that the limiting frequency of the excited ether waves (in most cases X-rays) is determined very accurately by the equation

\[ \frac{1}{2}mv^2=h\nu. \]

D. L. Webster2 then showed that the characteristic X-ray frequencies of an atom are excited precisely at those potential differences at which the energy of the electron current bombarding the atoms reaches the value determined by the relation \(h\nu=\frac{1}{2}mv^2\), where \(\nu\) is now the frequency of the so-called edge of the absorption band.

On the other hand, de Broglie3 in France and Ellis4 in England measured with great accuracy the velocity of electrons torn out by high-frequency radiation from different atoms and from different energy levels of one and the same atom, and thus confirmed, in this region of high frequencies, the strict applicability of the same Einstein equation

\[ \frac{1}{2}mv^2=h\nu-p, \]

whose validity for ultraviolet and visible rays I found.

In parallel with this development there proceeded an extensive elaboration of the field of the so-called ionization and resonance potentials. Here, too, the same relation between the frequency and the energy of the electron was used and confirmed, the relation asserted by Einstein’s equation and the inverse of which constitutes the cornerstone of Bohr’s theory of spectral lines. All these works on ionization

R. A. MILLIKAN

potentials trace their origin to the fundamental experiments of Franck and Hertz1; however, since 1916 this field has also been studied very zealously in America, in particular by Foote and Mohler, Wood, Davis and Goucher, MacLennan, and others2.

I believe that, in view of all these methods and investigations, the general validity of Einstein’s equation is now everywhere confirmed, and therefore the reality of Einstein’s light quanta may be regarded as experimentally established. This alone, together with the consequences that follow from it, represents an achievement of exceptional importance. It gives to present-day physics the greatest appeal. The facts of the theory of relativity, in comparison with this, appear of minor importance. Whatever conceptions may have led to Einstein’s photoelectric equation, the fact that ether waves can be absorbed by electrons in atoms and that these electrons are ejected with an initial energy \(h\nu\) (\(\nu\) is the frequency of the incident ether waves), and the converse fact that when electrons of known energy

\[ \frac{1}{2}mv^2 \]

bombard atoms, they excite ether waves whose frequency can be exactly calculated from the relation considered—these facts constitute a new experimental discovery of the same significance for physics as the discovery of the atomistic structure of electricity itself. If the light quantum is defined as the ultimate quantity of energy, transmitted and in this sense unitary, \(h\nu\), then the existence of the light quantum is a proven experimental fact. However, the conception of spatially bounded light quanta, from which Einstein obtained his equation, could not for a long time be regarded as proven, since up to the present it has not been possible to reconcile it with the numerous well-confirmed phenomena of interference. Whether the mechanism of interaction between ether waves and electrons is hidden in unknown states and laws within the atom, or whether it should be sought in the corpuscular-in-essence views of Thomson–Planck–Einstein—this is one of the exciting unresolved problems of modern physics.

In 1921 I took one more step toward solving this problem3, showing that in the photoelectric process the light energy \(h\nu\) is received not only by atomic electrons, but also by free electrons (i.e., conduction electrons) of the metal. Thereby the mechanism of absorption was evidently removed entirely from the atom, and the capacity to impart the energy \(h\nu\) to free or bound electrons had to be attributed to a property of light itself.

ELECTRON AND LIGHT QUANTUM

However, a year later the excellent discovery of Klein and Rosseland¹) made such a conclusion superfluous. Klein and Rosseland showed that—as P. Epstein first emphasized—there exists an intermediate process, namely, a collision of the second kind, by means of which energy from the source can be transferred without loss to a conduction electron by an indirect route, so that the need for a direct transfer of energy disappears. It follows from this that the process of absorption may be an atomic process, while the absorbed energy will only subsequently, by means of a collision of the second kind, be transferred to a free electron. Thus, this important discovery left our knowledge of spatially bounded light quanta in its former state.

However, quite recently the young American physicist Arthur Compton²), making use of the conception of discrete light quanta, pointed to a phenomenon which at least testifies to the fruitfulness of Einstein’s hypothesis. Compton went one step further than Einstein and admitted not only the existence of light quanta, but also proposed that, in a collision between a light quantum and a free electron, the laws of conservation of energy and momentum remain valid. These assumptions enabled him to calculate exactly how much the frequency of those ether waves which collide with free electrons is decreased. For he could calculate the amount of energy which the ether wave gives to the electron in the collision; hence the loss of energy of the wave, i.e. the decrease in \(h\nu\), is obtained directly. Experimentally he found that, in the scattering of monochromatic molybdenum X-rays by carbon, there is obtained a decrease of frequency approximately coinciding with the calculated one. Subsequently Ross³) confirmed this result photographically.

Fig. 6. The Compton effect. This photograph was made by Becker, Smid, and Stosson in April 1924. It shows X-ray lines \(\alpha\) and \(\beta\), and also the lines \(\alpha_0\) and \(\beta_0\), respectively shifted toward the red side. These latter arise as a result of the collision of the quantum of the \(\alpha\)- and \(\beta\)-lines with the electrons of aluminum. This important phenomenon was qualitatively predicted by A. Compton on the basis of the simple assumption that the usual laws of impact are valid in the collision of Einstein’s light quantum with an electron. Here before us is the latest success of Einstein’s theory.

¹) Zeitschr. für Physik. 1922.
²) Phys. Rev. 21, 483, 1923; 22, 409, 1923.
³) Proc. Nat. Acad. 9, 246, 1923.

Since Duane and his collaborators were unable to find any traces of the Compton effect, quite recently Becker, Watson, and Smyth1 carried out experiments analogous to Ross’s experiment. They used aluminum as the scattering substance, and on the photographic plate on which the X-ray spectrum had been recorded at high dispersion, they found that each of the lines of the so-called molybdenum $\alpha$-doublet was noticeably doubled, with the satellites shifted toward the longer wavelengths. Here it was possible to measure the magnitude of the displacement with an accuracy of up to 1%, and within these narrow limits it proved to coincide with the magnitude predicted by Compton’s equation. In Fig. 6 one of these new photographs is shown, where it is seen that the $\alpha$- and $\beta$-lines of molybdenum are shifted toward the longer wavelengths $\alpha_c$ and $\beta_c$, as a result of scattering by aluminum. Thus it may safely be said that here we have before us an exceptional success not only of Einstein’s equation, but also of Einstein’s views. However, until it proves possible to explain by means of these views interference and other phenomena that stand in contradiction with them, one should refrain from final recognition of the truth of these views. It is possible that, as a result of the latest attempts of Duane, Compton, Epstein, and Ehrenfest, it will be possible even to include interference within the circle of phenomena explained by spatially bounded light quanta. But for the present—the path is dark.

1. Proc. Phys. Soc., April 1924 and Phys. Rev., June 1924. ↩↩↩↩↩

2. Report Photoelectric. Con. National Research Council 1921; also Foote and Mohler. The Origin of Spectra. ↩↩

3. Phys. Rev. 18, 236, 1921. ↩↩

4. Proc. Roy. Soc. 99, 261, 1921. ↩