Frederick Soddy

How to use this course

Frederick Soddy was a chemist in a field that physicists were inventing. His great decade ran from 1902, when he and Ernest Rutherford explained radioactivity as the transmutation of atoms, to 1913, when he showed where the dozens of new radioactive substances belonged in the periodic table and coined the word isotope. After that he turned away from the laboratory toward economics, social reform and, unexpectedly, geometry. This course follows all three.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Modern names and half-lives are used alongside the historical names (thorium X, emanation, mesothorium, ionium, UX), since Soddy’s papers use the latter throughout.

Timeline

Eastbourne, Aberystwyth, Oxford, 1877–1900

Frederick Soddy was born on 2 September 1877 at Eastbourne on the Sussex coast, the son of Benjamin Soddy, a London corn merchant, and Hannah Green. He attended Eastbourne College, where a science master encouraged his interest in chemistry, and then at the University College of Wales in Aberystwyth before going up to Oxford.

In 1895 he won a scholarship to Merton College, Oxford, and in 1898 he graduated with first-class honours in chemistry. Oxford chemistry at the time was strong in careful analysis and weak in the new physical chemistry, and Soddy, who stayed on for two years of research, found it confining. He was independent, outspoken and sure of his own judgment, traits that served him well in Montreal and badly in later academic politics.

In 1900 he applied for a chair at the University of Toronto. He did not get it, but in May 1900 he accepted a post as demonstrator in the chemistry department of McGill University in Montreal. In the same building, the new Macdonald Physics Laboratory, Ernest Rutherford was studying the strange radiation and gaseous emanation given off by thorium.

Montreal and London, 1900–1904

Rutherford needed a chemist. The radioactivity of thorium compounds behaved erratically, and the emanation, a radioactive gas, seemed to come and go. In the autumn of 1901 Soddy joined him. In a little over a year of intense work they separated from thorium a strongly active substance they called thorium X, followed the decay of its activity and the recovery of the thorium’s activity, and showed that the emanation was an inert gas of the argon family produced by thorium X. Their conclusion, published in 1902, was that radioactivity accompanies the spontaneous transformation of one kind of atom into another (Lesson 04).

Soddy later recalled the moment of realization in the laboratory, when he said to Rutherford that this was transmutation, and Rutherford told him not to call it that, or they would be dismissed as alchemists. Whatever the exact words, they wrote cautiously of radioactive change and let the experiments speak. In 1903 they also condensed the radium and thorium emanations with liquid air, showing that they were gases that could be trapped and released.

Helium with Ramsay

In early 1903 Soddy went to London to work with William Ramsay at University College, the discoverer of the noble gases and the master of handling tiny gas samples. Helium had been found trapped in uranium and thorium minerals, and Rutherford suspected a connection. In July 1903 Ramsay and Soddy collected the gases given off by a radium salt, purified them, and saw the spectrum of helium. Then they collected the radium emanation alone; at first it showed no helium lines, but after a few days the helium spectrum appeared. A new element was being born from the decay of another, before their eyes (Lesson 05).

Soddy wrote one of the first books on the subject, Radio-activity: an elementary treatise from the standpoint of the disintegration theory (1904), and lectured widely. In 1904 he was appointed lecturer in physical chemistry and radioactivity at the University of Glasgow.

Glasgow, 1904–1914

The ten Glasgow years were Soddy’s most productive. With a small group of students and assistants, among them Alexander Fleck, Alexander Smith Russell, Ruth Pirret and Ada Hitchins, he worked through the chemistry of the radioelements: which ones could be separated from which, and which could not. He also pursued the slow growth of radium in purified uranium salts, a long experiment designed to find the missing link between uranium and radium.

In 1908 he married Winifred Beilby, daughter of the Glasgow industrial chemist George Beilby. The marriage was close, and Winifred took part in his scientific and social interests. It was at a dinner at the Beilbys’ house in 1913 that the physician and writer Margaret Todd, hearing Soddy explain that different radioelements occupied the same place in the periodic table, suggested the Greek word isotope, “same place”. He adopted it in a letter to Nature of 4 December 1913.

In 1909 he published The Interpretation of Radium, lectures for a general audience on the energy stored in atoms. H. G. Wells read it and dedicated his 1914 novel The World Set Free, which imagines atomic bombs, to the book. Soddy was elected a Fellow of the Royal Society in 1910. His treatise The Chemistry of the Radio-Elements (1912–14) set out the state of the field. In 1913 he stated the displacement law and the isotope concept (Lessons 06–07), and he received the Cannizzaro Prize. In 1914 he left Glasgow for the chair of chemistry at Aberdeen.

Thorium X and the theory of transformation

For the general reader. In 1902 Rutherford and Soddy took a thorium salt, removed a small, intensely radioactive part of it, and watched what happened. The part they removed lost its activity day by day; the thorium they left behind regained activity at exactly the same rate. Thorium was making something new, which then died away. Their explanation was that atoms of one element were spontaneously turning into atoms of another.

The experiment

Precipitating thorium from solution with ammonia, Soddy and Rutherford found that a large part of the activity remained in the filtrate. They called the active substance thorium X (now known to be radium-224, half-life 3.6 days). Freshly separated thorium X lost half its activity in about four days. The purified thorium, meanwhile, recovered its activity along a curve that was the mirror image of the decay curve. The sum of the two activities remained constant.

The complementary curves

Let thorium (parent, decay constant \(\lambda_1\)) produce thorium X (decay constant \(\lambda_2\)), with \(\lambda_1\ll\lambda_2\). In the unseparated salt, thorium X is in equilibrium: its activity \(\lambda_2N_2\) equals the parent’s \(\lambda_1N_1\), which is effectively constant. At \(t=0\) the thorium X is removed. The separated sample obeys \(\dot N_2=-\lambda_2N_2\), so its activity is \(A_X(t)=A_0e^{-\lambda_2t}\). In the thorium left behind, new thorium X grows according to \(\dot N_2'=\lambda_1N_1-\lambda_2N_2'\) with \(N_2'(0)=0\), so

The constant sum expresses conservation: the separation only moved atoms from one vessel to the other, and each atom of thorium X continued to decay on its own schedule. The theory predicts not only the shape of each curve but the identity of the two time constants, which was the decisive check.

(In the real salt the thorium retains a second product, radiothorium, and the thorium X itself supports the short-lived emanation and its products, so the measured curves had small initial irregularities that Soddy and Rutherford explained in their 1902 papers.)

Helium, emanation and the energy of radium

For the general reader. A grain of radium keeps itself warmer than its surroundings year after year. In 1903 Rutherford and Soddy calculated that the energy released by radioactive change is enormously larger than in any chemical reaction. In the same year Ramsay and Soddy caught one of the products of that change, helium, appearing in a sealed tube. Soddy saw at once that atoms contain a vast store of energy, and spent years explaining what that might mean.

Helium from radium

The emanation from radium (radon-222, half-life 3.8 days) was freed from a radium salt, condensed in a small tube cooled by liquid air, and the uncondensed gases pumped away. A spectroscopic examination of the fresh emanation showed no helium lines. Over the next few days the yellow D₃ line of helium appeared and strengthened. Since radon is an inert gas and the tube was sealed, the helium could only have been produced from the emanation itself. This was the first observation of one element being generated from another, and it confirmed the transformation theory chemically. It also supported Rutherford’s suspicion that the alpha particle is a helium atom, which he proved with Thomas Royds in 1908–09.

The modern accounting is simple. The energy released per decay is the mass difference \(Q=(m_{\rm parent}-m_{\rm products})c^2\), typically 4 to 9 MeV for an alpha decay, compared with a few eV per molecule in a chemical reaction. In 1903 neither \(E=mc^2\) nor the nucleus was known; Rutherford and Soddy estimated the energy from the measured speed and charge-to-mass ratio of the alpha particles.

Chemically inseparable elements

For the general reader. By 1910 some forty radioactive substances were known, each with its own half-life and radiation, but the periodic table had room for only about a dozen elements between lead and uranium. Chemists found that some pairs simply could not be separated by any chemical means. Soddy drew the radical conclusion that they were not merely similar but chemically identical: different atoms that were the same element.

The evidence

Several pairs resisted every attempt at separation. Ionium, the parent of radium, could not be separated from thorium (found by Bertram Boltwood and confirmed by others around 1907–09). Willy Marckwald reported that mesothorium 1 could not be separated from radium, and Soddy confirmed it with careful fractional crystallization. Radiothorium resisted separation from thorium, and radium D from lead. Soddy argued in 1910–11 that these were not cases of unusual chemical similarity, like the rare earths, but of complete chemical identity.

Why fractionation fails

Fractional crystallization separates two salts when they partition differently between crystal and solution. If a step leaves fractions \(f_A\) and \(f_B\) of species A and B in the crystals, the ratio \(A/B\) in the crystals is multiplied by \(\alpha=f_A/f_B\) relative to the starting material. After \(n\) steps of a simple cascade the enrichment is \(\alpha^n\). Chemical identity means \(\alpha=1\) exactly, and no number of steps helps. Separation of the rare earths, by contrast, works because \(\alpha\) differs slightly from 1. (Isotopes do differ in mass, and tiny mass-dependent effects give \(\alpha-1\) of order \(10^{-3}\) or less for heavy elements, far beyond the reach of the methods of 1910.)

The displacement law and the decay series

For the general reader. In early 1913 Soddy and, independently, Kazimierz Fajans found a simple rule. When an atom gives off an alpha particle, the product sits two places lower in the periodic table. When it gives off a beta particle, the product sits one place higher. With this rule every radioactive substance found its place, and the three great decay chains, from uranium, thorium and actinium, all ended in lead.

Soddy had noticed in 1911 that alpha emission moved an element two groups back. The beta rule came from the careful chemistry of his assistant Alexander Fleck on the short-lived beta emitters, from Russell’s suggestion in January 1913, and from George de Hevesy’s work. Soddy published the full law in February 1913; Fajans published it the same month from Karlsruhe. Fajans tied his version to a different interpretation of the radiations, and Soddy’s formulation, with its explicit statement of chemical identity, became the standard one.

In 1913 the atomic number had not yet been identified with nuclear charge; Henry Moseley’s X-ray measurements of that year and the next did so. The displacement law in its modern form is then just charge and nucleon conservation: the alpha particle carries away charge \(2e\) and four nucleons, the beta particle charge \(-e\) and no nucleons.

The \(4n+r\) rule

Neither decay changes \(A\) modulo 4. So every natural chain stays in one residue class: the thorium series has \(A=4n\) (thorium-232 to lead-208), the uranium series \(4n+2\) (uranium-238 to lead-206), and the actinium series \(4n+3\) (uranium-235 to lead-207). A fourth class, \(4n+1\), has no long-lived parent on Earth; its longest-lived member, neptunium-237, has a half-life of about 2 million years, and its stable end is thallium-205 (after the very long-lived bismuth-209).

Isotopes and the atomic weight of lead

For the general reader. If lead made from uranium and lead made from thorium are different isotopes, they should weigh differently. In 1914 several laboratories measured the atomic weight of lead taken from radioactive minerals. Lead from uranium ores was lighter than ordinary lead and lead from thorium ores heavier, exactly as Soddy had predicted. An element’s atomic weight, the most carefully measured constant of nineteenth-century chemistry, turned out to be an average.

Theodore William Richards at Harvard, Otto Hönigschmid and Stefanie Horovitz in Vienna, and Soddy himself in Glasgow measured radiogenic lead in 1914. Richards found 207.15 for ordinary lead and 206.40 for lead from a North Carolina uraninite; Hönigschmid and Horovitz obtained about 206.74 for lead from pitchblende. Soddy measured lead from thorite and found it heavier than ordinary lead. The departures from 206 and 208 were explained by the ordinary lead and the uranium or thorium lead mixed in each mineral.

In 1913 J. J. Thomson had found two parabolas for neon, at masses 20 and 22, in his positive-ray apparatus. His assistant Francis William Aston built the first mass spectrograph in 1919 and showed that most stable elements are mixtures of isotopes with nearly whole-number masses. Isotopes, first a fact about the radioelements, became a fact about matter in general.

Mixture atomic weights

If an element consists of isotopes with masses \(m_i\) and atom fractions \(x_i\), its chemical atomic weight is

Protactinium and the actinium series

For the general reader. The displacement law left a gap. Actinium, element 89, must have a long-lived parent in element 91, a place in the periodic table still empty in 1913. In 1917–18, two teams found it: Otto Hahn and Lise Meitner in Berlin, and Soddy and John Arnold Cranston in Glasgow and Aberdeen. The element was later named protactinium, “before actinium”.

Actinium was found in uranium ores in a fixed small proportion, so its chain had to start from uranium. Its own half-life, about 22 years, was far too short to persist on its own. Element 91 had already been met: in 1913 Fajans and Oswald Göhring found a short-lived beta emitter of that atomic number in the uranium series (now protactinium-234m, half-life about 1.2 minutes), called brevium. The parent of actinium had to be a long-lived isotope of the same element. The prediction from the displacement law was that it would be chemically like tantalum, the element above it in group V.

Soddy and Cranston heated pitchblende with carbon tetrachloride vapour and collected a volatile fraction carrying the tantalum-like element; over months the fraction developed the activity of actinium. Hahn and Meitner used a tantalum carrier and followed the alpha activity of their preparation. Hahn and Meitner gave a fuller characterization and their name, protactinium (originally protoactinium), was adopted. The parent of the whole chain, uranium-235 (historically actino-uranium), was identified by Arthur Dempster with the mass spectrograph in 1935.

The Kiss Precise: circles and the hexlet

For the general reader. Four circles can touch each other in pairs, like coins pressed together. There is a simple rule connecting their sizes, first found by René Descartes in 1643 and forgotten several times. In 1936 Soddy rediscovered it and published it in Nature as a poem, The Kiss Precise. He then found a chain of six spheres, the hexlet, that always closes up.

The curvature (Soddy’s word was bend) of a circle of radius \(r\) is \(k=1/r\). In a configuration where one circle encloses the others, that circle is given negative curvature; a straight line has curvature 0.

Proof sketch. Both sides change in the same way under similarities, and the relation is preserved by inversion when curvatures are suitably transformed. Invert in the tangency point of circles 1 and 2: they become parallel lines, at distance \(2\rho\) apart say, and circles 3 and 4 become two equal circles of radius \(\rho\) between the lines, tangent to each other. One checks the identity directly in this configuration (curvatures \(0,0,1/\rho,1/\rho\)), and an algebraic argument with the inversion formula transfers it back. A cleaner proof writes each circle as a vector \((\bar k,k,kx,ky)\), with \(\bar k\) the curvature of the inverted circle, in a four-dimensional space with a Lorentzian quadratic form; tangency becomes a linear condition and the theorem becomes a statement about a Gram matrix.

Soddy’s poem included a third stanza for spheres in space. Thorold Gosset extended the poem and the theorem to \(n\) dimensions in Nature in 1937:

The hexlet

Take three mutually tangent spheres A, B, C with curvatures \(a,b,c\). Soddy showed in 1936–37 that a chain of spheres \(S_1,S_2,\dots\), each tangent to A, B, C and to its predecessor, always closes after exactly six. (The configuration had appeared on a Japanese temple tablet, or sangaku, by Irisawa Hiroatsu in 1822.)

Proof. Apply the Soddy–Gosset theorem with \(n=3\) to A, B, C, \(S_i\) and an unknown sphere of curvature \(x\) tangent to all four. Writing \(s=\sigma+k_i\) and \(q=a^2+b^2+c^2+k_i^2\), the condition \((s+x)^2=3(q+x^2)\) is the quadratic \(2x^2-2sx+(3q-s^2)=0\). Its two roots are the curvatures of the two spheres tangent to A, B, C and \(S_i\), namely \(k_{i-1}\) and \(k_{i+1}\). Their sum is \(s\), so \(k_{i-1}+k_{i+1}=\sigma+k_i\). Iterating from \(k_0,k_1\): \(k_2=\sigma+k_1-k_0\), \(k_3=2\sigma-k_0\), \(k_4=2\sigma-k_1\), \(k_5=\sigma-k_1+k_0\), \(k_6=k_0\). The curvature sequence returns after six steps, and \(k_i+k_{i+3}=2\sigma\). (That the spheres themselves, and not only their curvatures, close up follows from inverting in the tangency point of A and B, which turns the hexlet into six equal spheres around a central one between two parallel planes.)

Aberdeen, Oxford and the Nobel Prize, 1914–1936

Soddy moved to the chair of chemistry at Aberdeen in 1914. The war broke up his research plans: students and assistants left for the forces or for war work, and he turned part of his laboratory to problems set by the war effort. The long-running study of the growth of radium from uranium, carried on with Ada Hitchins, and the search for the parent of actinium with Cranston (Lesson 09) were the last radiochemical work of importance he did.

In 1919 he was elected the first Dr Lee’s Professor of Chemistry at Oxford. He hoped to modernize Oxford chemistry and to bring physical chemistry and radioactivity into the curriculum. He found the college system obstructive, quarrelled with colleagues over laboratories and teaching, and built no research school comparable to Rutherford’s. Isotope research had in any case passed to physicists with mass spectrographs.

The Nobel Prize in Chemistry for 1921, reserved that year and presented in 1922, was awarded to Soddy for his contributions to the chemistry of radioactive substances and his investigations into the origin and nature of isotopes. Aston received the 1922 prize at the same ceremony. Soddy’s Nobel Lecture, on the origins of the conceptions of isotopes, gave a careful account of who had contributed what, including Fleck, Russell, Fajans and Hevesy.

Winifred Soddy died in 1936. Soddy retired from his chair the same year. He lived on for twenty years, writing on economics, science and society, and on geometry. The Royal Society of Arts gave him its Albert Medal in 1951. He died in Brighton on 22 September 1956. The lunar crater Soddy and the uranium mineral soddyite are named after him.

Wealth, debt, and legacy

Soddy’s interest in economics began from physics. If wealth is ultimately physical, made from matter and energy, it obeys the laws of thermodynamics: it decays, wears out and cannot grow without limit. Debt, by contrast, is a number. At compound interest it grows exponentially forever. In Cartesian Economics (lectures of 1921) and Wealth, Virtual Wealth and Debt (1926) he argued that much of the economic trouble of his time came from confusing the two, and from a banking system that created money as interest-bearing debt.

His proposals included full reserve backing for bank deposits, so that banks could not create money by lending, a monetary policy aimed at a stable price index, and floating exchange rates. Most professional economists ignored him in his lifetime, and his manner did not help; some of his later pamphlets were polemical and conspiratorial in tone. Several of his specific proposals later reappeared in mainstream work, notably full-reserve banking in the Chicago Plan of the 1930s, and the ecological economist Herman Daly treated him as a precursor in the economics of physical limits.

Legacy

• Radiochemistry: with Rutherford, the transformation theory of radioactivity; with Ramsay, the production of helium from radium.
• Isotopes: the concept, the name, the displacement law, and the prediction of the atomic weights of radiogenic lead, the basis of uranium–lead dating.
• Public understanding: early, vivid writing on atomic energy that shaped how H. G. Wells and a generation of readers imagined it.
• Mathematics: the Soddy circles, the Soddy–Gosset theorem and the hexlet, rediscoveries that started a modern literature on Apollonian packings.
• Economics: a physicist’s critique of debt-based money, now cited in ecological economics.

Connections

People linked to Frederick Soddy across this collection. A name without a link has no page here yet. See Frederick Soddy in the network of all 337 lives →

Students

• Bertrand Russell
• Alexander Fleck 1911-1913

Influenced by

• René Descartes
• William Crookes

Influenced

• H. G. Wells
• Thorold Gosset

Colleagues and collaborators

• Ernest Rutherford 1901-1903
• J. J. Thomson
• Otto Hahn
• William Ramsay 1903-1904
• Ada Hitchins
• Bertram Boltwood
• Francis William Aston
• George de Hevesy
• John Arnold Cranston 1915-1918
• Otto Hönigschmid
• Ruth Pirret
• Theodore William Richards

Rivals

• Lise Meitner
• Otto Hahn
• Kazimierz Fajans 1913

Family

• George Beilby

Also mentioned in this life

• Stanislao Cannizzaro
• Henry Moseley
• Pierre Curie

Fields

• radiochemistry 6 lives
• physical chemistry 9 lives
• geometry 32 lives

On CoursesHub

• Physical Chemistry

Sources and further reading

Biography

1. Frederick Soddy, Wikipedia.
2. Frederick Soddy, Biographical, NobelPrize.org; and his Nobel Lecture, The origins of the conceptions of isotopes, 12 December 1922.
3. A. Fleck, Frederick Soddy, 1877–1956, Biographical Memoirs of Fellows of the Royal Society 3 (1957).
4. T. J. Trenn, Soddy, Frederick, Dictionary of Scientific Biography; online at Encyclopedia.com.
5. M. Howorth, Pioneer Research on the Atom: The Life Story of Frederick Soddy, New World, 1958.
6. G. B. Kauffman (ed.), Frederick Soddy (1877–1956): Early Pioneer in Radiochemistry, Reidel, 1986.
7. L. Merricks, The World Made New: Frederick Soddy, Science, Politics, and Environment, Oxford University Press, 1996.

Science and mathematics

1. E. Rutherford, F. Soddy, The cause and nature of radioactivity, Phil. Mag. 4 (1902); Radioactive change, Phil. Mag. 5 (1903).
2. W. Ramsay, F. Soddy, Experiments in radioactivity, and the production of helium from radium, Proc. R. Soc. Lond. 72 (1903).
3. F. Soddy, The radio-elements and the periodic law, Chemical News 107 (1913).
4. F. Soddy, Intra-atomic charge, Nature 92 (1913), the letter introducing “isotope”.
5. K. Fajans, Radioactive transformations and the periodic system of the elements, Berichte 46 (1913).
6. F. Soddy, J. A. Cranston, The parent of actinium, Proc. R. Soc. Lond. A 94 (1918).
7. F. Soddy, The Interpretation of Radium, Murray, 1909.
8. F. Soddy, The Kiss Precise, Nature 137 (1936), 1021; T. Gosset, The Kiss Precise, Nature 139 (1937), 62.
9. Descartes’ theorem and Soddy’s hexlet, Wikipedia.
10. J. C. Lagarias, C. L. Mallows, A. R. Wilks, Beyond the Descartes circle theorem, Amer. Math. Monthly 109 (2002).
11. History of isotopes, LibreTexts Chemistry.
12. F. Soddy, Wealth, Virtual Wealth and Debt, Allen & Unwin, 1926.