Random Walks
Math · Advanced · Lesson 3 of 7

Brownian Motion

Jiggling pollen and diffusion

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

  • Brownian motion is a random walk driven by molecular collisions.
  • Distance ∝t\propto \sqrt t, so time ∝\propto distance².
  • Diffusion is fast at the scale of cells and slow at the scale of bodies.

Steps

  1. Proof of atoms
  2. Jostled by molecules
  3. A spreading cloud
  4. Diffusion time
  5. Einstein’s formula
  6. Diffusing a metre
  7. Inside a cell