Jean Perrin

How to use this course

In 1900 serious scientists could still doubt that atoms exist. Chemists used atomic weights, and physicists used the kinetic theory of gases, but leading figures such as Wilhelm Ostwald and Ernst Mach regarded atoms as a convenient fiction. By 1913 the doubt was gone. More than anyone, Jean Perrin made the difference. He took Albert Einstein’s theory of Brownian motion and turned it into a set of measurements, then showed that a dozen unrelated phenomena all gave the same number of molecules in a mole. He named that number after Avogadro.

Perrin was also the founder of much of modern French research: the CNRS, the Palais de la découverte, the Institut de biologie physico-chimique and the Institut d’astrophysique. This course covers both sides of his work.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Numbers in the exercises are realistic but rounded; where Perrin’s own values are quoted, they come from his 1926 Nobel lecture.

Timeline

Lille, Lyon, Paris, 1870–1891

Jean Baptiste Perrin was born in Lille on 30 September 1870, in the first weeks of the Franco-Prussian War. His father, Captain Jean Baptiste Perrin of the 66th infantry regiment, was captured with the army at Metz. The family later moved to Lyon, where the father died in 1880, when Jean was ten.

Perrin was educated in Lyon at the lycée Ampère and then went to Paris to prepare for the competitive examinations at the lycée Janson-de-Sailly. In 1891 he entered the École normale supérieure, the school that trained France’s scientific elite. He was drawn to physics, and to the debate then dividing it: whether the theories of matter should rest on atoms and molecules, or on directly observable quantities such as energy, as the “energeticists” argued.

The École normale and cathode rays, 1891–1897

Perrin passed the agrégation in physics in 1894 and stayed at the ENS as agrégé-préparateur, a laboratory assistant post, in the physics laboratory directed by Jules Violle. He chose a topical subject. Cathode rays, the glow emitted from the negative electrode of an evacuated tube, were either particles (the British view) or waves in the ether (the view of most German physicists). In 1895 Perrin caught the rays in a metal cylinder inside the tube and showed that they deposit negative charge. Lesson 04 describes the experiment.

Röntgen’s discovery of X-rays at the end of 1895 gave him a second subject. He studied how X-rays make gases conducting. The Royal Society awarded him its Joule Prize in 1896, and in 1897 he defended his thesis, Rayons cathodiques et rayons de Röntgen : étude expérimentale. The same year he married Henriette Duportal. Their daughter Aline was born in 1899 and their son Francis in 1901.

Physical chemistry at the Sorbonne, 1897–1910

In 1897–98 the Paris faculty of sciences created a course in physical chemistry and gave it to Perrin, then 27; Pierre Curie had also been a candidate. For thirteen years he taught and built a laboratory on a modest budget. He also taught at the École normale supérieure for girls at Sèvres from 1900. His research moved through electrical double layers at interfaces, electrosmosis, and the stability of colloids, the suspensions of tiny particles that would become his main tool.

He was a convinced atomist. In a public lecture in 1901 he suggested that an atom might consist of a positive core with negative corpuscles orbiting it like planets, a decade before Ernest Rutherford’s nucleus. He also wrote a textbook of physical chemistry, Les Principes. In Paris he joined a close circle of scientists, including Paul Langevin, Marie and Pierre Curie and the mathematician Émile Borel, who shared holidays, a cooperative school for their children, and republican politics.

In 1905 Einstein published his theory of Brownian motion. Perrin realized that colloidal grains of known size could serve as giant molecules, visible under a microscope, and that their behaviour would test both Einstein’s theory and the existence of molecules. From 1907 he set to work. In 1910 he was appointed professor of physical chemistry at the Sorbonne, a chair he held until 1940.

Cathode rays carry negative charge

For the general reader. If cathode rays are a stream of charged particles, they should carry electric charge into whatever they hit. Earlier attempts to detect that charge had failed. In 1895 Perrin put a shielded metal cup inside the tube, aimed the rays into it, and found it charging negatively. When a magnet bent the rays away, the charge stopped. Two years later J. J. Thomson used the same idea to measure the ratio of charge to mass and announced the electron.

The experiment

A metal cylinder, closed except for a small opening facing the cathode, was placed inside the vacuum tube and connected to an electroscope. A second, earthed cylinder surrounded it to shield it from stray charges. A beam of cathode rays passing through the opening charged the inner cylinder negatively. A magnet that deflected the beam away from the opening stopped the charging. Perrin concluded that the charge travels with the rays and moves wherever the magnet sends them.

In 1897 Thomson repeated the experiment with the cup off the axis, so that the rays reached it only when bent by a magnetic field, closing a loophole. A charged particle of speed \(v\) in a field \(B\) perpendicular to its motion moves on a circle of radius

If the particles have been accelerated through a potential \(V\), so that \(\tfrac12mv^2=eV\), then \(r=\frac1B\sqrt{2mV/e}\). Combining deflection with a measurement of energy gives \(e/m\). Thomson found it about a thousand times larger than for the hydrogen ion in electrolysis.

Sedimentation equilibrium

For the general reader. The air thins with height because gravity pulls the molecules down while their thermal motion spreads them out. Perrin reasoned that grains in a liquid, if they share the thermal energy of the molecules, should form a miniature atmosphere. He made grains of uniform size, let them settle, and counted them at different heights under the microscope. They thinned out exponentially, as an atmosphere does, but over a few hundredths of a millimetre instead of several kilometres. The rate of thinning gives Avogadro’s number.

The law

Grains of volume \(V\) and density \(\rho_g\) in a liquid of density \(\rho_\ell\) feel an effective weight \(V(\rho_g-\rho_\ell)g\). If they behave as molecules of a gas at temperature \(T\), each carries mean kinetic energy \(\tfrac32k_BT\) and the grains’ osmotic pressure is \(p=nk_BT\). Balancing the pressure gradient against the weight of a thin slab gives

The same law follows directly from the Boltzmann factor \(e^{-U/k_BT}\) with potential energy \(U=V(\rho_g-\rho_\ell)gh\). Perrin’s point was that it uses only quantities measurable on the grains plus the gas constant \(R\). If molecules did not exist, there would be no reason for the measured \(N_A\) to agree with values from gases.

The practice

Perrin made his emulsions from gamboge, a yellow gum resin, and later mastic. Dissolved in alcohol and poured into water, the resin precipitates as tiny spheres. He sorted them by size with repeated centrifuging, a process like fractional distillation: from one kilogram of gamboge, after several months, he kept a few decigrams of grains about 0.75 micrometre across. He found grain density by suspending grains in a solution dense enough that centrifuging could not separate them, and grain radius by several independent methods. He then counted the grains visible in a thin field of view at successive levels, taking many photographs to average. In his most careful series the density halved for every 6 micrometres of rise and gave \(N_A\approx68\times10^{22}\). The Nobel committee singled out this discovery of sedimentation equilibrium in the 1926 citation.

Brownian displacement and rotation

For the general reader. Einstein predicted that a grain’s wandering grows with the square root of time, at a rate fixed by temperature, the liquid’s viscosity and the grain’s size. Perrin’s team followed individual grains, marking their positions at regular intervals with a drawing device attached to the microscope. They confirmed every feature of the prediction. They also watched large grains turn, and found that the rotation obeys its own version of Einstein’s law.

Translation

The proof combines Stokes’s drag \(6\pi\eta a v\) with equipartition; the Langevin module gives a short derivation. Perrin’s tests went beyond the average. He checked that \(\langle\Delta x^2\rangle\) is proportional to \(t\) and independent of the grain’s mass at fixed radius, that it varies as \(1/\eta\) when glycerine is added to the water, and that the displacements follow the Gaussian law. With his students he obtained values of \(N_A\) between \(55\) and \(72\times10^{22}\), with a careful mean of \(64\times10^{22}\). He also noted that the tracks were so irregular that no tangent could be drawn, a physical example of the continuous nowhere-differentiable curves of the mathematicians.

Rotation

Rotation is slow and hard to see. Perrin used large mastic spheres of about 13 micrometres containing small inclusions that served as markers, suspended in a urea solution of matching density so they would not sink. The rotations gave \(N_A\approx65\times10^{22}\).

Molecular reality: the agreement of methods

For the general reader. One measurement of Avogadro’s number could be a coincidence. Perrin’s decisive argument was that many completely different phenomena, from the blue of the sky to the counting of alpha particles, give the same number. In Les Atomes (1913) he tabulated them. He wrote that the theory of atoms had triumphed, and almost all its opponents agreed. Ostwald announced his acceptance of atoms in 1909.

The table

In his 1926 Nobel lecture Perrin listed these values of \(N_A\), in units of \(10^{22}\ \mathrm{mol^{-1}}\):

The modern value is \(60.22\times10^{22}\). The kinetic theory of gases, the only earlier source, had given values uncertain by a factor of two.

Two of the routes

Electrolysis and the electron. The Faraday constant \(F=96\,485\ \mathrm{C/mol}\) is the charge carried by a mole of monovalent ions. Robert Millikan measured the elementary charge \(e\). Then \(N_A=F/e\).

Black-body radiation. Max Planck’s law contains \(h\) and \(k_B\). Fitting it to measured spectra gives \(k_B\), and \(N_A=R/k_B\). Planck did this in 1900 and obtained \(N_A\approx6.2\times10^{23}\), a result that received little attention until Perrin’s experiments confirmed it.

Hydrogen into helium: the energy of stars

For the general reader. What keeps the Sun shining? Contraction under gravity could supply heat for only tens of millions of years, far less than geology required. In 1919, in a long essay called “Matière et lumière”, Perrin proposed that stars turn hydrogen into helium. Four hydrogen atoms weigh slightly more than one helium atom, and by Einstein’s formula the missing mass becomes energy. Arthur Eddington made the same proposal independently in 1920. It was correct, though the detailed nuclear reactions were found only in the late 1930s.

Francis Aston’s mass spectrograph measured the helium mass defect in 1919–1920, making the figure reliable. Perrin argued that a star that began as hydrogen could shine for billions of years. He also reasoned that the reactions would require the high temperatures of stellar interiors, a point that quantum tunnelling, discovered by George Gamow in 1928, later made quantitative.

The radiation hypothesis of chemical reactions

For the general reader. Some molecules fall apart on their own, at a rate that depends on temperature but, puzzlingly, not on pressure. If collisions supplied the energy, crowding the molecules together should speed things up. In 1919 Perrin proposed that the energy comes instead from the heat radiation that fills any warm vessel. The idea was soon abandoned in favour of a collision mechanism, but it posed the question that shaped chemical kinetics, and it turned out to be right for some large molecules at very low pressure.

Irving Langmuir and others objected that the predicted frequencies, for typical activation energies of 100 to 250 kJ/mol, lie in the near infrared to ultraviolet, where the molecules in question do not absorb, and that the radiation flux is far too small. In 1922 Frederick Lindemann proposed instead that molecules are activated by collisions and then wait a while before reacting. At high pressure activation is in equilibrium and the rate is first order; at low pressure it falls off. The fall-off was soon observed, and the Lindemann–Hinshelwood theory became standard. In 1998 Robert Dunbar and Terrance McMahon showed that large ions held in a trap at very low pressure do dissociate by absorbing the infrared radiation of the walls, a case where Perrin was right.

Fluorescence and resonant transfer

For the general reader. After the war Perrin and his son Francis studied fluorescence, the light that some molecules give off after absorbing light. Jean Perrin noticed that in concentrated solutions the light is weaker and can pass from one molecule to another. In 1927 he proposed that an excited molecule can hand its energy to a neighbour without emitting light, by a resonance between the two, like coupled tuning forks. Theodor Förster made the idea quantitative in 1948. Today this energy transfer, called FRET, is a ruler that biologists use to measure distances inside proteins.

Resonant transfer

Jean Perrin’s 1927 proposal of “induction moléculaire par résonance” treated donor and acceptor as classical oscillating dipoles coupled by their near fields. Francis Perrin gave a quantum treatment in 1932. Both overestimated the range because they ignored the spread of molecular frequencies. Förster included the overlap of the donor’s emission and acceptor’s absorption spectra and obtained the law now used.

The \(r^{-6}\) law comes from the dipole–dipole interaction energy, which falls as \(r^{-3}\), entering the transition rate squared.

Depolarization and rotation

Fluorescence excited by polarized light is itself polarized, unless the molecule turns before emitting. Francis Perrin derived in 1926 the relation, now called the Perrin equation, between the anisotropy \(r\) of the emission and the rotation of the molecule:

where \(\tau\) is the excited-state lifetime, \(r_0\) the anisotropy without rotation, and \(\theta\) the rotational correlation time of a sphere of volume \(V\). It is the rotational Brownian motion of Lesson 06, measured with light on the scale of single molecules.

Building French science, 1919–1939

During the First World War Perrin served as an officer in the engineer corps and worked on acoustic detection: listening devices to locate enemy guns, aircraft and submarines. The war convinced him that France needed organized, publicly funded research. At a ceremony for Marie Curie in 1921 he set out a programme for national science policy, and he spent the rest of his life carrying it out.

Recognition came in the 1920s. He was elected to the Académie des sciences in 1923. The 1926 Nobel Prize in Physics was awarded to him for his work on the discontinuous structure of matter, and especially for his discovery of sedimentation equilibrium. With funding from the banker Edmond de Rothschild he helped create the Institut de biologie physico-chimique, an early laboratory for physical approaches to biology, and he also built the Institut de chimie physique. In 1933 a petition he led produced the Conseil supérieur de la recherche scientifique. His laboratory trained, among others, Pierre Auger, who discovered the Auger effect there and defended his thesis in 1926.

Politics gave him the means. In the autumn of 1936, in Léon Blum’s Popular Front government, he succeeded Irène Joliot-Curie as under-secretary of state for scientific research, and served again in 1938. He created a central research service, pushed for the Institut d’astrophysique in Paris and the Observatoire de Haute-Provence, and for the 1937 International Exposition conceived the Palais de la découverte, a museum where working scientists showed experiments to the public. His plan to merge the research bodies became, on 19 October 1939, the Centre national de la recherche scientifique.

Exile, death and the Panthéon, 1940–1948

When the German army entered France in June 1940, Perrin, a known opponent of fascism, left Paris for Bordeaux and sailed for Casablanca. He spent many months in North Africa and the unoccupied zone, then travelled through Spain to Lisbon and crossed to New York on the SS Excambion, arriving in December 1941. In New York he worked with exiled French scholars to found the École libre des hautes études, a French university in exile, and became its president. He died at Mount Sinai Hospital on 17 April 1942, aged 71, a few weeks after its inauguration.

In 1948 his remains were carried home on the cruiser Jeanne d’Arc. On 17 November 1948, in a single national ceremony, his ashes and those of his lifelong friend Paul Langevin were placed in the Panthéon.

Legacy

• Atomism: the experiments that made the reality of molecules an observed fact, and the name “Avogadro’s number”.
• Methods: colloids as model atoms, which led to modern soft-matter physics and single-particle tracking; sedimentation equilibrium, used in the ultracentrifuge.
• Astrophysics and chemistry: the hydrogen-to-helium proposal for stellar energy; the question of unimolecular activation.
• Photophysics: resonant energy transfer, the root of FRET.
• Institutions: the CNRS, the Palais de la découverte, the Institut de biologie physico-chimique, the Institut d’astrophysique de Paris.
• Writing: Les Atomes (1913), translated widely; about 30 000 copies had been sold by 1936.
• Honours: Joule Prize (1896), La Caze Prize of the Académie des sciences (1914), Nobel Prize in Physics (1926), Commander of the Legion of Honour (1926), membership of the Royal Society and many academies.

Connections

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

Students

• Pierre Auger 1926

Influenced by

• Albert Einstein
• Amedeo Avogadro
• Ludwig Boltzmann

Influenced

• Irène Joliot-Curie
• J. J. Thomson
• Wilhelm Ostwald 1908
• Theodor Förster

Colleagues and collaborators

• Arthur Eddington
• Frédéric Joliot-Curie
• Irène Joliot-Curie
• J. J. Thomson
• Louis de Broglie
• Pierre Curie

Rivals

• Wilhelm Ostwald

Friends

• Marie Curie
• Paul Langevin
• Émile Borel

Family

• Francis Perrin

Also mentioned in this life

• André-Marie Ampère
• Michael Faraday
• George Gamow
• Hermann von Helmholtz
• James Prescott Joule
• William Thomson, Lord Kelvin
• Ernst Mach
• Robert Millikan
• Max Planck
• Ernest Rutherford
• Frederick Soddy
• George Gabriel Stokes

Fields

• physical chemistry 9 lives
• experimental physics 16 lives

On CoursesHub

• Physical Chemistry

Sources and further reading

Biography

1. Jean Baptiste Perrin, biographical, NobelPrize.org.
2. Jean Perrin, Wikipedia; and the more detailed French article.
3. Perrin Jean (1870–1942), Encyclopædia Universalis.
4. M. J. Nye, Molecular Reality: A Perspective on the Scientific Work of Jean Perrin, Macdonald and American Elsevier, 1972.
5. M. Charpentier-Morize, Perrin, savant et homme politique, Belin, 1997.

Physics

1. J. Perrin, Nouvelles propriétés des rayons cathodiques, C. R. Acad. Sci. Paris 121 (1895) 1130.
2. J. Perrin, Mouvement brownien et réalité moléculaire, Annales de chimie et de physique 18 (1909) 5–114. English translation by F. Soddy, Brownian Movement and Molecular Reality, 1910.
3. J. Perrin, Les Atomes, Alcan, 1913; English translation Atoms, 1916.
4. J. Perrin, Discontinuous structure of matter, Nobel lecture, 11 December 1926.
5. J. Perrin, Matière et lumière, Annales de physique 11 (1919).
6. A. Einstein, Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Annalen der Physik 17 (1905) 549.
7. F. A. Lindemann, Discussion on the radiation theory of chemical action, Trans. Faraday Soc. 17 (1922) 598.
8. Perrin’s hypothesis reborn, Physics World, 1998, on R. C. Dunbar and T. B. McMahon, Science 279 (1998) 194.
9. T. Förster, Zwischenmolekulare Energiewanderung und Fluoreszenz, Annalen der Physik 437 (1948) 55.