06. How Many Atoms — Proving Matter Is Grainy

A number named after a man who never calculated it

The Avogadro constant is the number of particles in a mole of substance, and since 2019 it has been fixed at exactly 6.02214076 × 10²³ per mole. Amedeo Avogadro proposed in 1811 that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. He never computed how many, and the constant carrying his name was estimated for the first time decades after his death. Josef Loschmidt made an early determination in 1865 from the kinetic theory of gases, working out the number density of molecules in air; German-language usage still calls the related quantity the Loschmidt constant. The figures attributed to Loschmidt in modern secondary sources disagree with each other by about an order of magnitude, which is a warning about tracing an old number through retellings rather than to its paper. What matters is that by the 1860s the size of the graininess of matter had become a quantity somebody could put a value on.

The experiment that ended the argument

Well into the twentieth century, serious scientists held that atoms were a useful bookkeeping fiction rather than objects. Jean Perrin attacked the question through Brownian motion, the jittering of pollen grains suspended in water that Einstein had connected to molecular bombardment. Perrin measured how the grains distributed themselves vertically under gravity, tracked their displacements, and extracted the constant several different ways. The decisive part was not any single value but that his independent methods converged on the same figure, which is very difficult to explain if the underlying particles do not exist. He was awarded the 1926 Nobel Prize in Physics "for his work on the discontinuous structure of matter," a citation that names the real achievement rather than the number. After Perrin, the atomic hypothesis stopped being a hypothesis.

Convergence as the strongest evidence

A single measurement can be wrong in a way its author cannot see, and a repeated measurement can be wrong in exactly the same way. Independent methods failing in the same direction is far less likely, so agreement between unrelated techniques carries more weight than precision within one. This is why the pattern recurs in every later chapter of this book, and why a lone spectacular result should be read as an invitation rather than a conclusion.

Example: One witness describing a stranger may be mistaken; four witnesses who never met describing the same stranger is a different kind of claim.

Verdict. Avogadro's constant was named for a man who did not calculate it and established by Perrin's convergence of independent methods, which is what ended the debate over whether atoms are real.

Overturned if: Perrin's several determinations are shown to share a common systematic assumption, which would collapse the independence that carries the argument.

Sources. 1926 · Nobel Prize in Physics, Jean Baptiste Perrin — NobelPrize.org · 2019 · "Avogadro constant" — Wikipedia