Brownian Motion - Random Dance of Atoms

Particles jitter randomly as invisible molecules bombard them from all sides

Controls

Parameters

Temperature (K) 300

Particle size 8

Number of particles 5

Trail length 200

Statistics

Steps 0

Mean displacement 0

√(Mean sq. disp.) 0

Diffusion coeff. -

Einstein's Relation

⟨x²⟩ = 2Dt
Mean square displacement ∝ time

DIFFUSION COEFFICIENT

D = k_BT / 6πηr

Robert Brown (1827)

Scottish botanist Robert Brown observed pollen grains of Clarkia pulchella jittering in water. He ruled out life by showing inorganic dust did the same! For 80 years, no one could explain why. The motion was random, continuous, and affected by particle size.

Einstein's 1905 Miracle

In his "annus mirabilis," Einstein explained Brownian motion as bombardment by invisible water molecules. His equation let Jean Perrin (Nobel 1926) calculate Avogadro's number from observations—finally PROVING atoms exist! Skeptics like Mach were silenced.

The Key Insight

Mean SQUARED displacement grows linearly with time: ⟨x²⟩ = 2Dt. Not mean displacement (which is zero—motion is random in all directions). This seemingly technical detail let experimenters measure molecular reality from macroscopic observations!

Everywhere in Nature

Brownian motion governs diffusion in biology, stock price fluctuations (Black-Scholes model), polymer chain conformations, heat conduction, and quantum mechanics. The Wiener process (mathematical Brownian motion) is foundational to stochastic calculus!