The Brownian jiggle of a grain too big to be a molecule — does it actually let you weigh the unseeable molecule and count Avogadro's number?
▶ Launch the interactive simulationTake a resin grain of radius a = 0.5 µm suspended in water (η, T known) and use Einstein's (1905) Stokes–Einstein bridge between the visible random walk and the molecular world: D = R·T/(6πη·a·N_A). Forward-model 4000 grains as independent 2-D Gaussian random walks at water's real diffusion coefficient (seeded → reproducible), record the mean-square displacement ⟨r²⟩(t), and least-squares fit its slope through the origin (= 4D in 2-D). Then invert the relation for the one unknown.
Avogadro's number N_A = 6.022×10²³ /mol — recovered as N_A = R·T/(6πη·a·D) from the measured D WITHOUT being told it, and with it Boltzmann's constant k_B = R/N_A. That a purely *mechanical* jiggle of micron grains yields the molecular bookkeeping constant — the same N_A chemistry gets from moles — is the whole point: it pinned a number to the atom and ended the 19th-century debate over whether matter is continuous or made of discrete molecules. Unlike the lab's abstract ?world=diffusion (⟨r²⟩=4Dt in arbitrary units), this one is in real SI and extracts a fundamental constant. Perrin's 1908–1913 measurements (Nobel 1926), the experimental confirmation of Einstein's 1905 Brownian-motion theory