Ladenburg, Rudolf Walther

(b. Kiel, Germany, 6 June 1882; d. Princeton, New Jersey, 3 April 1952)

physics.

Ladenburg was the second of three sons of the eminent chemist Alber Ladenburg and his wife, Margarete Pringsheim.

After his early education in the schools of Breslau, where his father was professor of chemistry in the university, Ladenburg went in 1900 to the University of Heidelberg. He returned to Breslau in 1901 and in 1902 went to Munich, where he took his Ph.D. in 1906 under Roentgen with a thesis on viscosity, a subject that held his interest until he began work in spectroscopy in 1908. From 1906 to 1924 he was on the staff of the University of Bresolau, first as privatdocent and from 1909 as extraordinary professor. He married Else Uhthoff in 1911. He served in 1914 as a cavalry officer but later in the war did research in sound ranging. In 1924, at the invitation of Haber, he moved to the Kaisr Wilhelm Institute in Berlin as head of the physics division and remained there until going to Princeton in 1931.

Ladenburg is well known for his research in many fields of physics, but his most original work was done in the elucidation of anomalous dispersion in gases, in the period before 1931. To understand the originality of that work it is necessary to remember that the quantum theory had been proposed by Planck in 1901 but that its application to atomic phenomena did not become possible until after Bohr’s paper on hydrogen in 1913. It was in the interim that Ladenburg started his important work.

A paper of considerable significance to an understanding of Ladenburg’s mind must be discussed at this point. It is a sixty-page review of the photoelectric effect, published in 1909 in the Jahrbuch der Radioaktivitàt und Elektronik. Much of the experimental elucidation of that effect was the work of Erich Ladenburg, an older brother, whose tragic death by drowning in 1908 affected Rudolf very seriously. The paper is especially noteworthy because in it Ladenburg became one of the first physicists to accept Einstein’s view of the constitution of radiation, at least as applied to the photoelectric effect. At that time there were two competing theories of that effect, the commonly accepted resonance theory due to Lenard and the theory which depended on the acceptance of Einstein’s idea that radiation consisted of indivisible packets of energy hv. Ladenburg gives a masterly discussion of the two theories and shows conclusively that Lenard’s theory is in difficulties in explaining several of the known facts, whereas Einstein’s fits all of them in a quite natural way. At the same time, Ladenburg definitely recognized that Einstein’s theory is in contradiction to the classical theory of radiation and gives no explanation of the mechanism of the release of the electrons. In other words, Ladenburg was face to face with the fundamental problem that led to the invention of quantum mechanics some sixteen years later.

The research undertaken by Ladenburg in the early part of his university career was published in five papers on viscosity, including his thesis. He then turned to spectroscopy, which was just becoming of major interest to physicists. His first effort in that new field was directed to a solution of the problem of whether electrically excited hydrogen could absorb the light of the Balmer lines, a question about which there was much conflicting evidence. Ladenburg solved it very quickly and definitely by an experiment in which he ensured that the source of the Balmer lines and the absorbing column of gas were both excited at the same instant, by simply having the two tubes in series in the same induction-coil circuit. He then proceeded to resolve the question by demonstrating that anomalous dispersion could be detected in the close neighborhood of the lines by placing the absorption tube in one arm of a Jamin interferometer. The only existing theory, based on classical electromagnetism, yielded a rough value of 씑_e = 4 X 10¹² oscillators per cubic centimeter, equivalent to about one in 50,00 atoms. A further confirming experiment was carried out to measure the magnetic rotation of the plane of polarization of the light passing in the immediate neighborhood of the absorption lines. The small but measurable effect distinguished definitely between two current theories, confirming Voigt’s theory based on the Hall effect. It also demonstrated that the oscillators were negatively charged particles. Ladenburg discussed these results in detail in a paper in Annalen der Physik (38 [1912], 249–318).

Although Ladenburg’s research had shown unequivocally that the Balmer lines were the seats of anomalous dispersion, the appearance of Bohr’s theory of hydrogen in 1913 led surprisingly to attempts by theorists to base the theory of dispersion on the frequencies of the Bohr orbits rather than those of the lines. Ladenburg, of course, knew that the contrary was correct, and after World Was I he set himself the task of finding the theoretical relations connecting the constant 픑_e with the radically new way of describing emission and absorption. Using a correspondence-principle argument he found the following expression for 픑_e (which is essentially correct except for the absence of a small correction term that was derived later by Kramers and that leads to negative dispersion):

in which g_k and g_i are the statistical weights of the upper and lower states and a_ki is the probability of spontaneous transition from state k to state i. Ladenburg applied this formula to his observations of both hydrogen and sodium. In the latter element the density of oscillators appeared to be nearly equal to the number N of atoms per cubic centimeter. In hydrogen it was possible to find an approximate value of about four for the ratio of 픑_e for H _αH _β. This is a quantity that is not calculable from the Bohr theory. The equivalent ratio in sodium and other alkalies is very much greater.

With the advent of quantum mechanics a number of theoretical physicists developed a valid form of the equation for anomalous dispersion in gases involving in particular the factor mentioned above

which depends on the ratio of the number of atoms in the upper state to the number in the lower state. It appears that increasing excitation of a gas could increase that ratio and so produce a decrease in the refractive index, and effect usually referred to as negative dispersion.

During the years 1921–1928 Ladenburg performed a number of experiments with the aid of his students Kopfermann, Carst, and Levy that led to an important series of eight papers under the general title “Untersuchungen über die anomale Dispersion angeregte Gase.” They are concerned mainly with the dispersion in electrically excited neon around the familiar strong yellow to red lines that result from transitions between levels p₁ to p₁₀ and the lower levels s₂ to s₅. The new work was done with much improved techniques and gave results of outstanding importance.

The changing characteristics of the discharge through the absorption tube as the current was increased were studied in detail and revealed a close similarity between the curves for 픑_e for all the lines with the same lower level up to a current of about 50 milliamperes. This showed that the population of the lower level was the dominant influence in that range of currents. However, with increasing current the curves of 픑_e fell and diverged in a regular way, showing an unmistakable effect of the upper levels. this is exactly what should be expected from the factor

which gives the effect of negative dispersion. From the effects of that factor it is possible to derive a specific temperature for each level, all of which lie in the region of 20,000° C. for currents of about 700 milliamperes through the tube.

A further series of five papers, written with G. Wolfsohn, under the title “Untersuchungen ü die Dispersion von Gasen und Dāmpfen und ihre Darstellung durch die Dispersionstheorie”was published between 1930 and 1933. A new quartz Jamin interferometer made it possible to extend the measurements in mercury through the ultraviolet line 2536 Å using Rozhdesvensky’s “hook”method, which had also been used in the work on neon. The value of f = ℜ_e/N was found to be constant at .0255 ± .0005 for all pressures form .01 to 200 millimeters of mercury in radical disagreement with previous measurements by R. W. Wood and others. A further paper carries measurements of the refractive index of mercury down to 1890 Å and makes possible an approximate calculation of the ∫-values at 1849 Å and 1413 Å which are the first and second member of the singlet principal series. New measurements were also made of the refractive index of oxygen down to 1920 Å, allowing the construction of a three-term formula depending on certain band frequencies as the centers of anomalous dispersion.

Ladenburg’s experimental work on hydrogen and, especially, neon was very important for the theory of dispersion. In addition, it showed for the first time the possibility of obtaining definite results in the extremely difficult field of electrical discharges in gases. His successful formula for anomalous dispersion, which ignored the Bohr orbital frequencies in favor of the line frequencies, was of critical importance to the later development of the new quantum theory during the 1920’s.

In 1931 Ladenburg was a visiting professor at Princeton and in 1932 accepted the appointment to the Cyrus Fogg Bracket professorship of physics, a position he held until his retirement in 1950. When he accepted call to Princeton, he was probably insufficiently aware of the radical differences in the organization of departments of physics in Germany and the United States; furthermore, it may have come as a shock to find that the research professorship did not give him the control over graduate work that it would have given in Germany. The difficulty of reorientation was increased by the change of his chief interest to nuclear physics, a field that was then rapidly displacing spectroscopy.

For Ladenburg’s use the Princeton physics department purchased, with funds from the Rockefeller Foundation, a transformer-rectified set with a capacity of 400,000 volts and thirty mililamperes. It was considered that the high current would compensate for the low voltage, but unfortunately this hope was not realized because of the limitations in the available accelerating tubes and ion sources.

The apparatus was initially used for experiments on the light elements and eventually exclusively for the production of neutrons from the D-D reaction for a number of experiments including a determination of the relative cross sections for fission of uranium and thorium in the energy range 200 to 300 kilovolts.

World War II , which disrupted all physics research at Princeton, brought Ladenburg into contact with the Army Ballistic Laboratories, for which he developed a flash suppressor for rifles. This later led him to his postwar research on gas dynamics.

Refractivity changes accompanying density changes in a compressible flow field permit the use of optical methods in laboratory research. It was here that Ladenburg made the contribution for which he is best remembered by fluid dynamicist—the introduction in the United States of optical interferometry as a quantitative tool to map the density distribution in high-speed flows. He and his associates were the first to made systematic interferometric studies of over-and underexpanded supersonic jet flows and channel flows. The method was quickly adopted by many research laboratories for use with wind tunnels, shock tubes, ballistic ranges, and similar devices and in plasma dynamics. It is evident that the method will remain a major tool for the study of the physics of gases and gas flows.

In his social relationships Ladenburg was an extremely agreeable and hospitable person, but professionally he could be a very severe taskmaster, both to his students and to himself. An enthusiastic experimenter, he did not spare himself when great efforts were necessary. He was a very good teacher indeed and spent a great deal of time providing his graduate students with advice as well as instruction.

As early as 1933, the plight of German scientists under Hitler was causing great concern, and many had had to emigrate from Germany to other countries. The sympathy aroused in Ladenburg and E. P. Wigner by that situation led them to address an appeal to many physicists in American institutions for definite pledges of support for displaced colleagues, listing many by name. The work thus started was carried on by Ladenburg throughout the 1930’s and 1940’s by correspondence with scientists in many countries, including Germany. It was a work of the heart and showed that the human side of his nature was more important to him that the professional side. Einstein wrote after Ladenburg’s death: “Ladenburg has been caught very suddenly by illness. He was a good human being who did not take things easily. During his last years he even fled from newspaper reading because he could not stand any more of the hypocrisy and mendacity”(Albert einstein—Masx Born, Briefwechsel 1916–1955 [Munich, 1969, p. 257).

BIBLIOGRAPHY

I. Original Works. Ladenburg’s name appears on 134 scientific papers; 24 other papers published under the names of his students are an integral part of his own principal researches. His doctoral thesis was “Die innere Reibung zäher Flüssigkeiten und ihre Abhängigkeit vom Druck,” in Annaled der Physik, b (1907), 287–309. Also on viscosity are “Über den Einfluss von Wänden auf die Bewegung einer Kugel in einer re9bended Flüssigkeit,” ibid., 23 (1907), 447–458; “Einfluss der Reiburng auf die Schwingunges einer Kuge,” ibid., 27 (1908), 157–185; and “Über die Reibung tropbares Flüssigkeiten,” in Jahresbericht der Schlesischen Gesellschaft für vaterländische Kultur (1908), pp. 1–4.

Ladenburg’s work on dispersion in gases is described in 58 papers, of which the most important are “Über die Dispersion des Leuchtended Wasserstoffs,” in Physikalische Zeitschrift, 9 (1908), 875–878; “Über die anomale Dispersion und die magnetische Drehung der Polarisationebene des leuchtenden Wasserstoffs, sowie über die Verbreitering von Spektrallinien,” in Annalen der Physik, 38 (1912), 249–318; “Über selektive Absorption,” ibid., 42 (1913), 181–209; “Die Quantentheoretische Deutung dee Zahl der Dispersionselektronen,” in Zeitschrift für Physik, 4 (1921, 451–468; 8 papers (I to VIII) under the title “Untersuchungen über die anomale Dispersion angeregte Gase,” written with H. Kopfermann, A. Carst, and S. Levy, of which no. VIII is Zeitschrift für Physik, 88 (1934), 461–468; and 5 papers under the title “Untersuchungen über die Dispersion von Gasen und Dàmpfen und ihre Darstellung durch die Dispersionstheorie,” written with G. Wolfshohn, of which no. V is Zeitschrift für Physik, 85 (1933), 366–372.

There are 12 papers on anomalous dispersion in sodium, of which the last is “Die Oszillatorenstàreke der D-linien,” in Zeitschrift für Physik, 72 (1931), 697–699.

During World War I Ladenburg did research on problems of sound; his last publication was “Experimentalle Beitràge zur Ausbreitung des Schalled in der freien Atmosphere,” in Annalen der Physik, 66 (1921), 293–322, written with E. von Angerer.

In 1929 Ladenburg undertook work on the cleaning of effluent gases and published a number of papers, the last of which is “Elektrische Gasreinigung,” in Chemie-Inge-nieur, 1 , pt. 4 (1934), 31–81.

In nuclear physics, Ladenburg’s principal papers are “On the Neutrons from teh Deuteron-Deuteron Reaction,” in Physical Review, 52 (1937), 9911–918; “Study of Uranium Fission by Fast Neutrons of Nearly Homogeneous Energy,” ibid., 56 (1939), 168–170, written with M. H. Kanner, H. H. Barschall, and C. C. Van Voorhis; “Mass of the Meson by the Method of Momentum Loss,” ibid., 60 (1941), 129–138, written with H. H. Barschall.

Ladenburg’s interest in the atmosphere led to a number of papers of which the most important are “The Continuous Absorption of Oxygen Between 1750 Å and 1300 Å and Its Bearing Upon the Dispersion,” ibid., 43 (1933), 315–321, written with C. C. Van Voorhis; and “Light Absorption and Distributon of Atmospheric Ozonce,” in Journal of the Optical Society of America, 25 (1935), 259–269,

Ladenburg’s early papers in gas dynamics are “Interferometric Study of Supersonic Phenomena,” written with C. C. Van Voorhis and J. Winckler, in Navy Department Bureau of Ordnance, Washington, D.C. (1946), pt. 1, no. 69–46; (17 Apr. 1946), 1–84; pt. 2, no. 93–46; (2 Sept. 1946), 1–51; pt. 3, no. 7–47; (19 Feb. 1947), 1–22. Other papers of importance in this field are “Interferometric Studies of Faster that Sound Phenomena,” in Physical Review, 73 (1948), 1359–1377 and 76 (1949), 662–677, written with C. C. Van Voorhis and J. Winckler; and “Interfermetric Studies of Laminar and Rurbulent Boundary Layers Along a Plane Surface at Supersonic Velocities,” in Symposium on Experimental Compressible Flow, Naval Ordinance Laboratory Report, no. 1133 (1 May 1950), pp. 67–87, written with D. Bershader.

Ladenburg’s most important monographs include “Die neueren Forschungen über die durch Lichtund Röntgenstrahlen hervorgerufene Emission negative Elektronen,” in Jahrbuch der Radioaktivitàt und Elektronik, 6 (1909), 425–484; “Bericht über die Bestimmung von Planck’s elementaren Wirkengsquantum h,” in Jahrbuch der Radioaktivität und Elektronik, 17 (1920), 93–145; and 17 (1920), 273–276; “Die Deutung der kontinuierlighen Absorptionsund Emissions-spektra von Atomen in Bohr’s Theorie,” ibid., 17 (1920), 429–434; “Methoden zur h-Bestimmung und ihre Ergebnisse,” in Geiger-Scheel, ed., Handbuch der Physik (Berlin), 23 (1926), 279–305; “Die Bestimmung der Lichtgeschwindigkeit in Ruhenden Körpern,” in WienHarms, ed., Handbuch der Experimentalphysik, 18 (1928), 3–34; “Die Methoden zur h-Bestimmung und ihre Ergebnisse,” in Geiger-Scheel, ed., Handbuch der Physik, 2nd ed., 23 (1933), 1; “Dispersion in Electrically Excited Gases,” in Review of Modern Physicy, 5 (1933), 243–256; “On Laminar and Turbulent Boundary Layer in Supersonic Flow,” ibid., 21 (1949), 510–515, written with D. Bershader; and “INterferometry,” in High Speed Aerodynamics and Jet Propulsion, VII, sec. A3 (Princeton, N.J., 1954), 47–75, written with D. Bershader. Ladenburg was also the general editor of vol. VII.

II. Secondary Literature. An obituary notice is Hans Kopfermann, “Rudolf Ladeburg,” in Naturwissenschaften, 13 (1952), 289–290.

A. G. Shenstone