Physicist Richard Feynman, in his Lectures on Physics, asked us to imagine that somehow all knowledge about nature, except for a single fact, was to be destroyed.  What fact, he asked, should scientists choose to pass on to their successors?  His choice was “Everything is made of atoms”. This, Feynman said, is the most important single piece of scientific knowledge that we have.

I thought of this recently when I read Steven Weinberg’s book The Discovery of Subatomic Particles (an excellent book, by the way, and written for a general audience).  At various places in the book, Weinberg describes the experiments and reasoning that lead from simple speculation about atoms to the eventual certainty that they exist. This post is a summary of that chain of thought.

1. Antoine Lavoisier, 1743-1794, a French chemist formulated the principle that mass is conserved in chemical reactions.  For example, when iron rusts, the mass of the rust equals the mass of the iron and oxygen originally present.  This law does not directly support the existence of atoms, but it is an essential principle in subsequent work on atomic theory.
2. John Dalton, 1766-1824.  Dalton was an English schoolteacher and amateur chemist. By 1800, he had thought through the implications of a remarkable fact: when substances combine chemically to form a new substance, the constituents combine in a precise ratio of masses. For example, Dalton knew that one gram of hydrogen combines with 8 grams of oxygen to form 9 grams of water. As Weinberg points out, this type of behavior is contrary to ordinary human experience.  If we bake a cake, and we use a bit more butter or a bit less flour than the recipe calls for, the result is still a cake, just a slightly different one.  However, with the water example, one gram of hydrogen and 9 grams of oxygen form the same 9 grams of water, with a gram of uncombined oxygen left over.
   Dalton concluded that the simplest explanation for this phenomena was that oxygen and hydrogen consisted of small, indivisible particles (atoms) which combined individually to form a unit of water.  This combination of atoms he called a molecule. We now know, of course, that a water molecule consists of two hydrogen atoms and one oxygen atom, but Dalton assumed that the pairing was probably one-to-one, meaning that an oxygen atom had eight times the mass of a hydrogen atom.  He was similarly wrong for other compounds, but his atomic hypothesis was a powerful idea. Any extra atoms present had nothing to combine with, and remained in their free state.
3. Joseph Louis Gay-Lussac, 1778-1850, was a French chemist. In 1808, he discovered experimentally what is now called Gay-Lussac’s Law:  when gases react chemically, the volume of the reactants and the product are in the ratio of simple whole numbers.  For example, two volumes of hydrogen and one volume of oxygen combine to form two volumes of gaseous water.  This is obviously similar to Dalton’s results about the ratio of masses in chemical reactions, but neither he nor Dalton made use of the law in support of atomic theory.
4. Amedeo Avogadro,  1776-1856, was an Italian scientist.  Avogadro combined Dalton’s and Guy-Lussac’s results by propounding, in 1811, what is now called Avogadro’s Law: equal volumes of gas (at the same temperature and pressure) contain the same number of particles.  These particles could be either atoms or molecules. For the law to hold true, Dalton’s water molecule would necessarily consist of two atoms of hydrogen for every one of oxygen, because that was the ratio of volumes that Guy-Lussac had determined. That in turn would mean that an oxygen atom had 16 times the mass of a hydrogen atom, because the two volumes of hydrogen had 1/8^th the mass of one volume of oxygen.
   There was problem, however. The water-creating reaction produced two volumes of water.  Three atoms had combined into one molecule, so it would seem that the water vapor should have one-third the volume of the original gases, not two-thirds. In a brilliant intuitive leap, Avogadro said that the original oxygen and hydrogen must exist not as individual atoms, but as pairs of atoms combined into a single molecule (that is, H₂ and O₂). To see how this solves the problem, let’s count the atoms involved in the reaction. If A is the number of particles in a unit volume, then the starting number of oxygen atoms is A x (1 volume) x 2 atoms/molecule = 2A. The starting number of hydrogen atoms is A x (2 volumes) x 2 atoms/molecule = 4A. These oxygen and hydrogen atoms combine to form 2A molecules of H₂O, which is 2 volumes.
   The constant A is Avogadro’s number, which we now know is 6.023 x 10²³ particles per liter.
5. Rudolf Clausius, 1822-1888 (German) and James Clerk Maxwell 1831-1879 (Scottish) together created the Kinetic Theory of Gases, starting about 1860. The theory starts with the assumption that a gas consists of a large number of particles in rapid motion, which collide elastically with each other. Kinetic theory predicts that gases will behave in the same way that the empirical gas laws call for. Gas pressure, for example, is a result of collisions of the gas molecules with the walls of the container. Because of this agreement with experiment, the Kinetic Theory of Gases strongly supports the existence of atoms and molecules.

All of this evidence, and more, was not sufficient to persuade everyone that atoms exist. Supposedly, the great physicist Ludwig Boltzmann committed suicide in 1906 in part because of depression related to his failure to have his kinetic theory accepted universally.

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