Jean Perrin and Avogadro’s Number

Regular readers of this blog may recall that last summer I visited Paris for my 25th wedding anniversary, which was followed by a string of blog entries about famous French scientists. During this trip, my wife and I toured the Pantheon, where we saw the burial site of French scientist Jean Baptiste Perrin (1870–1942). Russ Hobbie and I mention Perrin in a footnote on page 85 of the 4th edition of Intermediate Physics for Medicine and Biology.

The Boltzmann factor provided Jean Perrin with the first means to determine Avogadro’s number [N_A]. The density of particles in the atmosphere is proportional to exp(−mgy/k_BT), where mgy is the gravitational potential energy of the particles. Using particles for which m was known, Perrin was able to determine [Boltzmann’s constant] k_B for the first time. Since the gas constant R was already known, Avogadro’s number was determined from the relationship R = N_Ak_B.

This brief footnote does not do justice to Perrin’s extensive accomplishments. He played a key role in establishing that matter is not a continuum, but rather is made out of atoms. He performed experiments not only on the exponential distribution of particles (described above, and also known as sedimentation equilibrium), but also on Brownian motion. Russ and I describe this phenomenon in Chapter 4:

This movement of microscopic-sized particles, resulting from bombardment by much smaller invisible atoms, was first observed by English botanist Robert Brown in 1827 and is called Brownian motion.

Molecular Reality:
A Perspective on the
Scientific Work of Jean Perrin,
by Mary Jo Nye.

One can learn more about Perrin in the book Molecular Reality: A Perspective on the Scientific Work of Jean Perrin, by Mary Jo Nye. I would not rank this book with the best histories of science I have read (my top three would be The Making of the Atomic Bomb, The Eighth Day of Creation, and The Maxwellians), or among the best scientific biographies (such as Subtle is the Lord: The Science and Life of Albert Einstein). However, it did provide some valuable insight into Perrin’s achievements. Ney states in her introduction that

What has struck me in a perusal of the literature on these topics [discoveries in physics during the early 20th century] is the tendency to assume what so many of the physical scientists of this pivotal period did not for one minute assume—the discontinuity of the matter which underlies visible reality. In looking back upon the discoveries and theories of particles, one perhaps fails to realize that the focus was not simply upon the nature of the molecules, ions and atoms, but upon the very fact of their existence…

In analyzing the role of Jean Perrin in the eventual acceptance of this assumption among the outspoken majority of the scientific community, I have concentrated upon the period of experimental, theoretical, philosophical and popular science which climaxed with the Solvay conference of 1911 and with the publication of Perrin’s book Les Atomes [read an online English translation here] in 1913…

In conclusion, I have discussed the reception of Perrin’s scientific experimentation and propagandisation on the subject of molecular reality, especially his work on Brownian movement, which climaxed in 1913 with the completion of a number of national and international conferences and the publication of Les Atomes. Though Perrin himself did not view his task as completed at that time, the question was no longer central to the basic working assumptions of scientists, and polemics on this question were no longer an impediment or impetus to the progress of general scientific conceptualization. That Perrin’s role was historically essential to this denouement cannot, in my opinion, be doubted.

Nye’s first chapter on 19th-century background contains a little too much philosophy of science for my taste. But her historical review does indicate that, despite what our footnote says, Perrin did not provide the first estimate for Avogadro’s number, but rather provided a definitive early measurement of that value. Her second chapter about Young Perrin: Initial Investigations was better, and the book really captured my attention in the third chapter on The Essential Debate.

The exponential law which Perrin announced in 1908, describing the vertical distribution of a colloid at equilibrium, was the fruit of laborious experiments on Brownian movement after several years of apprenticeship in the study of colloids. Included in his first 1908 paper on Brownian movement was a successful application of the concepts of osmotic pressure and mean kinetic energy to the visible Brownian particles, as well as a convincing calculation of Avogadro’s number. These endevours were but the prelude to a five-year drama devoted to the erection of an unassailable edifice to house the dictum of molecular reality, a structure buttressed at its most vulnerable point of criticism by the observed laws of visible Brownian movement.

I was particularly fascinated by how Perrin knew the mass of the particles he studied.

In order to find m, Perrin utilized Stoke’s law [see Section 4.5 of Intermediate Physics for Medicine and Biology], applying it to a column of the emulsion in a vertical capillary tube, and observing the fact that when the emulsion is very far from equilibrium, the Brownian granules in the upper layers of the column fall as if they were droplets of a cloud. Using Stokes’ formula relating the velocity of a spherical droplet, its radius, and the viscosity of the medium, Perrin found the radius of the granules [on the order of a micron].

Then from the known density, he could determine the mass. Perrin had to go to great lengths to obtain particles with a uniform distribution of radii, starting with 1200 grams of particles and, after repeated centrifugation, ending with less than a gram of uniform particles.

In 1926, Jean Perrin won the 1926 Nobel Prize in physics “for his work on the discontinuous structure of matter, and especially for his discovery of sedimentation equilibrium.”