Brownian motion
The incessant random jitter of a small particle suspended in a fluid, driven by molecular collisions — the visible proof that atoms are real.
Definition
Brownian motion is the perpetual, irregular motion of a microscopic particle suspended in a liquid or gas, caused by the imbalanced bombardment of the particle by the surrounding molecules. At any instant slightly more molecules strike one side than the other, and the resulting random kicks, millions per second, drive the particle on an erratic random walk that never settles.
Its defining quantitative signature is that the mean-square displacement grows linearly with time, ⟨x²⟩ = 2Dt along one axis, rather than as t² as for steady motion. The diffusion coefficient D is given by the Einstein relation D = k_BT/(6πηr) for a sphere of radius r in a fluid of viscosity η. Measuring the spreading therefore yields k_B, and through R = N_A k_B, Avogadro's number.
Robert Brown observed the motion in 1827 in pollen grains and showed it was not biological. Einstein explained it quantitatively in 1905, and Jean Perrin's measurements in 1908 confirmed Einstein's predictions and ended serious doubt about the existence of atoms.
History
Observed by the botanist Robert Brown in 1827; explained quantitatively by Albert Einstein in 1905 (and independently by Smoluchowski in 1906); measured by Jean Perrin in 1908, earning him the 1926 Nobel Prize.