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Put a drop of milk under a good microscope and the fat droplets will not sit still. They jiggle, endlessly, with no current pushing them. Robert Brown was not the first person to see this kind of motion (he himself credited earlier observers), but he checked it so carefully that it now carries his name. This post tells what he did, why it mattered, and how to calculate the motion yourself.
Who was Robert Brown?
The Dictionary of National Biography entry says Brown was born in Montrose, Scotland, on 21 December 1773. In 1801 he sailed with Captain Flinders as naturalist on a survey of the coast of Australia, and returned in 1805 with nearly 4,000 species of dried plants, many new to science. He was elected a Fellow of the Royal Society in 1811, and the entry credits him with discovering the nucleus of the plant cell. He died on 10 June 1858.
What did Brown see in 1827?
Brown described his work in a paper published in 1828, A brief account of microscopical observations. The full text, reprinted in his collected works on Wikisource, says he began in June 1827 with Clarkia pulchella. Its pollen grains were filled with particles "from nearly 1/4000th to about 1/5000th of an inch in length", which he saw moving in water.
One point is often told wrongly: the moving particles were inside the pollen grains, not whole pollen grains. A 2010 paper in the American Journal of Physics, What Brown saw and you can too, describes them as particles ejected by the pollen of Clarkia pulchella, and repeats his observations with a modern microscope and a homemade single-lens one like his.
How did he rule out the obvious explanations?
This is what makes Brown worth studying. At first the motion looked like a kind of life, and Brown wrote of the "seeming vitality" of the particles. So he tested it. He found the same motion in pollen from plants that had been dried, including mosses dried for more than a hundred years, then turned to things that had never lived.
The paper says: "The first substance examined was a minute fragment of window-glass," which gave particles that agreed "in size, form, and motion" with those he had already seen. Rocks of all ages gave them too, including "a fragment of the Sphinx". He also stated that the motions "arose neither from currents in the fluid, nor from its gradual evaporation, but belonged to the particle itself."
In later remarks he went further: he trapped tiny drops of particle-filled water inside almond oil so they could not evaporate quickly, and the motion continued "with undiminished activity".
How did Brownian motion prove atoms are real?
Brown never claimed to know the cause. In 1905 Einstein published a paper in Annalen der Physik showing that the molecular theory of heat predicts that small suspended particles must wander, because fluid molecules hit them unevenly from all sides. It gave a testable formula. Jean Perrin received the 1926 Nobel Prize in Physics, according to the Nobel facts page, "for his work on the discontinuous structure of matter". The 1926 presentation speech said his measurements on Brownian movement showed Einstein's theory "was in perfect agreement with reality" and gave a new value of Avogadro's number. Our post on Einstein's 1905 papers covers the theory side.
How far does a jiggling particle move? A worked example
Einstein's result for a sphere of radius a in a fluid of viscosity η is a diffusion coefficient D = kT ÷ (6πηa). In one direction, the root-mean-square displacement after time t is √(2Dt).
Take a sphere 1 micrometre across (a = 0.5 × 10⁻⁶ m) in water at 293 K, with η = 1.0 × 10⁻³ Pa s and k = 1.38 × 10⁻²³ J/K.
kT = 1.38 × 10⁻²³ × 293 ≈ 4.04 × 10⁻²¹ J.
6πηa = 6 × 3.14 × 1.0 × 10⁻³ × 0.5 × 10⁻⁶ ≈ 9.42 × 10⁻⁹ kg/s.
D = 4.04 × 10⁻²¹ ÷ 9.42 × 10⁻⁹ ≈ 4.3 × 10⁻¹³ m²/s.
After 1 s: √(2 × 4.3 × 10⁻¹³ × 1) = √(8.6 × 10⁻¹³) ≈ 9.3 × 10⁻⁷ m, about 0.9 micrometres.
After 100 s: multiply by √100 = 10, so about 9 micrometres.
What mistakes do students make here?
Assuming distance grows with time. It grows with the square root of time. Four times as long gives only twice the spread.
Using diameter for a. The formula uses the radius.
Thinking the particle is pushed by one molecule. Each water molecule is far too small to be seen. The jiggle is the uneven sum of enormous numbers of collisions.
Calling it a property of life. Brown's own tests with glass and rock showed it is not.
For the gas-molecule side of the same idea, see our guide to kinetic theory of gases. Random motion is easier to understand once you watch it, and the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Redo the worked example for a sphere 2 micrometres across and check that the 1-second displacement falls by a factor of √2.
