Atoms and molecules

Black-and-white portrait of an elderly man with white hair and a white beard. — The French physicist Jean Perrin, Nobel Prize winner, photographed in 1926 by the Meurisse press agency. Agence Meurisse, Public domain, source

A little over a hundred years ago, some leading scientists did not believe in atoms.

Not out of narrow-mindedness, but because nobody had ever seen one.

A reasonable objection

Around 1900, atomic theory worked very well. It made it possible to predict chemical reactions, to calculate proportions, to explain the behaviour of gases.

But two renowned scientists — Wilhelm Ostwald and Ernst Mach — refused to accept that atoms really exist.¹

Their argument: it is a convenient fiction. A way of calculating that gives the right results, without any need to believe in the reality of these little balls. After all, not a single one had ever been measured.

These were not obtuse minds. Their demand was: “Show it to me some other way than by saying that it works.”

It was this demand that made the proof necessary. The proof, when it came, was magnificent.

Brownian motion

Very fine grains suspended in water — pollen, a drop of ink — observed under the microscope, do not stay still: they jiggle about in every direction, constantly and for no apparent reason.

In 1905, Einstein proposed a mathematical explanation: these grains are bombarded from all sides by water molecules, invisible and countless. By chance, the impacts never quite balance out, and the grain is knocked off course.²

From this he derived precise formulae: how far a grain should move, on average, depending on its size, on the temperature, on the thickness of the liquid.

But Einstein was a theorist: he had no experiments to hand.

Perrin, gamboge and patience

Between 1908 and 1913, a French physicist, Jean Perrin, carried out the experiments. At first, he did not even know of Einstein’s paper.

The work was tedious. Perfectly regular grains were needed, otherwise the measurements meant nothing. Perrin used gamboge, a yellow pigment taken from the latex of Asian trees, and he developed a method for obtaining grains of uniform size from it — a skill that almost nobody else had mastered.³

Then he counted, measured and started again.

From this he derived a number: how many molecules there are in a given quantity of matter. This is what is called Avogadro’s number.⁴

What won the argument

Perrin could have stopped there. He did something else, and that is the reason this page exists.

In his book Les Atomes, published in 1913, he brought together thirteen different ways of calculating this same number. Thirteen methods that have nothing to do with one another:⁵

The viscosity of gases;
Radioactivity;
The radiation of heat;
The charge of oil droplets;
Brownian motion;
And even — this is our favourite — the blue of the sky.

These phenomena have no connection with one another. They belong to different branches of physics. They are measured with different instruments, by different people.⁶

They give the same number. All thirteen values obtained lie between 60 × 10²² and 75 × 10²².⁷

Perrin marvels at this in his book, in terms that deserve to be quoted:

“One is seized with admiration before the miracle of such precise agreement arising from such different phenomena. That, first, the same magnitude should be found again for each of the methods, while varying the conditions of its application as much as possible, and then that the numbers thus defined without ambiguity by so many methods should coincide — this gives molecular reality a likelihood very close to certainty.”⁸

This sentence contains two arguments, not just one. First: each method, taken on its own, gives the same result when its conditions are changed as much as possible. Second: the methods, compared with one another, agree.

Finally, the last words are significant. Perrin does not write “certainty”. He writes “very close to certainty”.

Ostwald, one of the best-known opponents, declared himself convinced as early as 1909. Mach, for his part, never was. The proof did not convince everyone, and that is in the nature of things.⁹

Why this is the best possible proof

This reasoning is worth dwelling on, because it holds far beyond this case.

At the time, nobody had seen an atom. Nor had anyone found a method so good that it would make everyone agree.¹⁰

What was found was thirteen methods, none of which would have been enough on its own — and which agree.

Now, if atoms did not exist, each method would be measuring something else — a flaw peculiar to its instrument, to its subject, to its branch. Why would these flaws all give the same number?

There is only one simple explanation: they are all measuring the same real thing.

This reasoning turns up elsewhere on this site, a century later. To produce the first image of a black hole, the scientists were divided into four teams that worked for seven weeks without talking to one another, using different methods. The four images differed in their details. All of them contained the same ring (1.10).

The idea is exactly the same: if independent paths arrive at the same place, it is probably not the path that created it.

Molecules, or why arrangement matters

An isolated atom is rare. Most of the time, atoms are attached to one another, in small groups or in vast networks: these are molecules.

A surprising fact: the same atoms, put together differently, do not do the same thing.

Diamond and pencil lead are made of the same atom, carbon, and nothing else. In diamond, each atom is firmly bonded to four neighbours in all directions: it is the hardest natural material. In the graphite of a pencil, the atoms are bonded in sheets that slide over one another: that is what leaves a mark on paper.¹¹

Same ingredient, two arrangements, two materials. What matters is not only what a thing is made of, but how it is made.

The drawing of the atom

The drawing is familiar: a ball in the centre, and little beads circling around it on rings. It appears in textbooks, logos, signs, on the covers of exercise books.

It corresponds to a model proposed in 1913 by Niels Bohr, and superseded as early as 1925-1926.¹²

What Bohr did, and why it was not foolish

We should not draw the wrong conclusion from this.

In 1913, this model was a considerable advance. Before it, classical physics predicted that an electron orbiting a nucleus should lose its energy and crash into it almost instantly. Yet atoms exist and endure.

Bohr solved the problem by imposing a new rule: the electron can only occupy certain tracks, not just any. It does not radiate as long as it stays on them; it emits or absorbs light only when it changes track.¹³

It was the first time that the idea that certain quantities come in packets rather than continuously had been brought into the atom. This model can be compared to a signpost on a footpath: it does not show the destination, it shows the direction.

It had its limits, which were known: it could not explain atoms with several electrons; it worked well only for hydrogen.¹⁴

What replaced it

In 1926, Erwin Schrödinger established an equation that describes the behaviour of the electron far better. What it states is disconcerting.¹⁵

The trajectory of the electron cannot be given. It is not that we do not yet know how to measure it: it is that there is none, in the usual sense of the term.

What can be calculated is the probability of finding it in one place rather than another. The result looks like a cloud: dense where the electron is very likely to be, thin elsewhere.

By convention, the region in which there is a 90% chance of finding it is often marked out, and it is this shape that is drawn.¹⁶

The right picture, then, is not a bead on a rail. It is a map of the places where the electron is likely to be.

And a word that still gives it away

One detail strikes us as remarkable.

Chemists call these regions of probability orbitals.¹⁷

The term can be misleading: to the ear, the word “orbital” suggests that the electron has an orbit. In other words, precisely what it does not have, as we have just seen.

The word has kept the ghost of the old model.

This mechanism often comes up on this site: a word that manufactures a fact. But this one is unusual, and that is why it is worth telling.

This time, the problem lies in the very vocabulary of chemists.

Should we abandon the drawing, then?

No. That is the conclusion of this page.

Bohr’s drawing remains useful: it makes it possible to count electrons, to understand why some atoms bond and others do not, to reason quickly. It is still taught deliberately, for its simplicity.

The problem is not that it is used. The problem is that nobody says what it is.

A drawing presented as a picture of the atom plants a false idea that dies hard. The same drawing presented as a tool for reasoning, which dates from 1913 and was superseded in 1926, plants nothing at all: it does its job and steps aside when it is no longer needed.

It is not the model that misleads. It is the silence about its status.

Note 1

However, it was not always the case, and the hypothesis of a continuous structure of matter was relentlessly defended until the end of the nineteenth century by famous names such as Duhem, Ostwald, and Mach.

Duplantier, Bertrand, “Brownian Motion, "Diverse and Undulating"”, in Damour, Thibault, Darrigol, Olivier, Duplantier, Bertrand and Rivasseau, Vincent (eds), Einstein, 1905-2005. Poincaré Seminar 2005, Progress in Mathematical Physics, vol. 47, Birkhäuser, Basel, 2006, p. 201-293