Brownian Motion Lab
Watch a suspended particle jostled by invisible fluid molecules. Trace its random path, measure how far it wanders over time, and verify the Einstein relation connecting diffusion to temperature and particle size.
Guided Experiment: Measuring Brownian Motion
If you increase the temperature of the fluid, what do you predict will happen to how far the particle wanders?
Write your hypothesis in the Lab Report panel, then click Next.
Controls
Results
Mean Squared Displacement vs Time
The MSD grows linearly with time. The slope equals 4D — verifying the Einstein relation.
Data Table
(0 rows)| # | Trial | Time(s) | X Position(px) | Y Position(px) | Displacement(px) | MSD(px²) |
|---|
Reference Guide
Brownian Motion
Brownian motion is the random movement of a particle suspended in a fluid, caused by constant collisions with the much smaller fluid molecules. Discovered by botanist Robert Brown in 1827 and explained theoretically by Albert Einstein in 1905.
The particle's path is unpredictable — each step is independent of the last. This is a hallmark of a stochastic (random) process.
Einstein Relation
Einstein derived an expression for the diffusion coefficient D using thermodynamic principles and Stokes' drag law:
Where is Boltzmann's constant, T is temperature (K), is fluid viscosity (Pa·s), and r is the particle radius (m).
Mean Squared Displacement
Because the path is random, we average over many steps using the mean squared displacement (MSD). In two dimensions:
MSD grows linearly with time. Plotting MSD vs time gives a straight line with slope 4D — this is how D is measured experimentally.
Diffusion Coefficient
The diffusion coefficient D describes how quickly a particle explores space. Larger D means faster diffusion. From the Einstein relation:
- Higher temperature increases D (more energetic collisions)
- Higher viscosity decreases D (more resistance to motion)
- Larger particle radius decreases D (harder to move)
For a 1 µm particle in water at 293 K, .