Temperature298 K
Diffusion D0.44 µm²/s
Measured MSD0.00 µm²
Time0.0 s

Brownian Motion

Microscope evidence for invisible molecular motion
Workspace

Experiment

Mission: track one smoke particle and connect its irregular path to unseen molecular impacts.

System controls

298 K
1.00 mPa·s
0.50 µm
14
1×
1.00×

Apparatus key

  1. Lamp: produces the illuminating beam.
  2. Condenser: focuses light through the sample.
  3. Smoke cell: sealed chamber containing suspended particles.
  4. Stage: holds the cell steady.
  5. Objective: magnifies scattered light from tracers.

On small screens, tap a part to show its single leader label.

Live measurements

Diffusion D0.44 µm²/s
Measured MSD0.00 µm²
Elapsed time0.0 s
Collisions0

Fast fluid molecules strike suspended smoke particles from changing directions, producing an irregular path.

Object focus

Tap a tracer particle, fluid molecule, smoke cell, lamp, or microscope objective.

Mean-square displacement

Measured Theory: 4Dt

Teacher tools

The two-dimensional model uses D = kBT ÷ (6πηr) and predicts mean-square displacement = 4Dt. Visual distances and collision sizes are scaled for learning.

Interactive lecture

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1. An irregular microscopic path

What to watch: A tracer changes direction without a visible cause.

Under a microscope, smoke particles move in irregular zigzags. The path is evidence of impacts that are too small to see directly.

Chapters

Learning objectives

  • Connect an irregular tracer path to unequal molecular impacts.
  • Predict how temperature, viscosity, and particle size affect diffusion.
  • Interpret mean-square displacement instead of a single unpredictable path.
  • Identify the lamp, smoke cell, stage, and objective in the apparatus.

Scientific model

Brownian motion is the random movement of a visible suspended particle caused by many invisible fluid molecules colliding with it. Individual steps cannot be predicted, but the spread of many paths can.

Stokes–Einstein relationship: diffusion coefficient D = kBT ÷ (6πηr). Higher temperature increases D. Greater viscosity η or particle radius r decreases D.

Two-dimensional prediction: mean-square displacement = 4Dt.

The simulation uses real parameter relationships. Molecules, distances, collision visibility, and time are enlarged or accelerated for conceptual observation.

The apparatus

A bright lamp sends a narrow beam through a sealed smoke cell. A condenser concentrates scattered light. A microscope objective above the stage magnifies illuminated smoke particles against a dark field.

Suggested experiments

  • Raise temperature while tracking the same particle.
  • Increase viscosity and compare the trail length.
  • Reduce particle radius and observe diffusion.
  • Restart identical settings and compare two different random paths.

Applications & misconceptions

Brownian motion supports kinetic theory and matters in aerosols, colloids, cells, nanoparticle transport, and diffusion-based measurements.

Random motion is not caused by life, a hidden current, or a particle “choosing” directions. Molecules strike from every side, but moment-by-moment impacts are unequal.

Brownian challenge

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