Kinetic TheoryMolecular Nature of Matter
Richard Feynman, one of the great physicists of the twentieth century, was once asked which single sentence he would pass on if all scientific knowledge were about to be lost. His choice was the atomic hypothesis: all things are made of atoms, little particles that move around in endless motion, attracting each other when they are a little distance apart, but repelling when squeezed into one another.
Drag atom B and feel the force for yourself.
The amber curve is the force on B: above the axis it pushes B away, below it pulls B in. Far apart, the atoms hardly notice each other. A few ångströms apart (1 Å = 10⁻¹⁰ m) they attract. Squeezed closer than about 2 Å they repel very strongly. So the force between atoms has a long-range attraction and a short-range repulsion, and the atoms settle where the two balance.
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Atoms in ancient India and Greece. Long before modern science, thinkers guessed that matter cannot be divided forever. In India, Kanada, who founded the Vaiseshika school around the sixth century B.C., argued that if things could be cut up without end, a mustard seed and the mighty Mount Meru would both be made of an endless number of parts, and there would be nothing to tell them apart. He imagined eternal, indivisible smallest particles, the paramanu, of four kinds (earth, water, fire and air), joining in twos (dvyanuka) and threes (tryanuka) to make the substances around us. The Lalitavistara, a life of the Buddha from around the second century B.C., even gives a size for them close to the modern 10⁻¹⁰ m. In Greece, Democritus (fourth century B.C.) called the particles atoms, "uncuttable", and explained properties by their shapes: smooth round atoms of water slide past each other, rough jagged atoms of earth lock together. These were brilliant guesses, but nobody tested them by measurement, and testing is what turns a guess into science.
Equal Volumes, Equal Numbers
The modern atomic theory is credited to John Dalton, about 200 years ago. Chemists had found two rules. A compound always contains its elements in a fixed proportion by mass (law of definite proportions). And when two elements form more than one compound, the masses of one that combine with a fixed mass of the other are in a ratio of small whole numbers (law of multiple proportions). Dalton explained both: each element is made of identical atoms, different from the atoms of other elements, and a few atoms join to make a molecule of a compound.
Around the same time, Gay Lussac found that when gases react to give another gas, their volumes are in ratios of small whole numbers. Avogadro's law (or hypothesis) explains why: equal volumes of all gases at the same temperature and pressure contain the same number of molecules. Watch hydrogen and oxygen make steam.
The two jars of hydrogen and the one jar of oxygen held three molecules each, and the reaction gave six water molecules: exactly enough for the two jars of steam. So 2 volumes of hydrogen and
Dalton's atoms plus Avogadro's law turn Gay Lussac's whole-number volumes into whole-number molecules. Since elements often exist as molecules (H₂, O₂, N₂), Dalton's theory is also called the molecular theory of matter. It is now beyond doubt, although even at the end of the nineteenth century some famous scientists refused to believe in atoms.
How Far Apart Are They?
Today electron microscopes and scanning tunnelling microscopes let us actually see atoms. An atom is about an ångström across. In a solid, atoms are packed a few ångströms apart (about 2 Å), and in a liquid they are about as close, though free enough to slide past each other, which is why a liquid flows. In a gas they are tens of ångströms apart. The average distance a gas molecule travels before it hits another one, the mean free path, is thousands of ångströms. Put these four lengths in order, smallest first.
On a scale where each step is ten times the last, the size of an atom and the spacing in a solid sit side by side, the spacing in a gas is ten times further on, and the mean free path is a hundred times further still. In solids and liquids the atoms are close enough for the attraction and repulsion to matter. In a gas they are free: let the gas out of its container and it spreads away.
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A gas that looks perfectly still is anything but. Its molecules keep colliding and changing their speeds; only the averages stay constant. This is a dynamic equilibrium. And atoms are not the end of the story: they contain a nucleus and electrons, the nucleus contains protons and neutrons, and these are made of quarks. In this chapter we stay with whole molecules and ask how a crowd of them in endless motion behaves.