# Modelling for Brownian motion

#### Apparatus and materials

Metal tray lined with cork mat

Marbles, coloured, 20 - 24, about 1 cm diameter

Marbles, large, several, about 2 cm diameter

Three-dimensional kinetic model kit

Power supply, low-voltage, variable

Retort stand, boss, and clamp

Polystyrene, expanded, piece of

#### Health & Safety and Technical notes

See apparatus entry for Electric motor, fractional horsepower.

Beware of marbles on the floor.

If a different vibrator is used with the original tube and rubber-sheet base from the 3-dimensional kinetic model kit, the base can soon be damaged. However, the life of the base can be prolonged considerably by sticking a small disc of aluminium foil on the rubber.

Alternative methods:
1 Adapt the experiment Kinetic theory model for a gas by adding a small piece of expanded polystyrene and following its path.

2 Closely observe a suspension containing mm scale polystyrene spheres, projected onto a screen using a visualiser with a data projector. This demonstration video, from the National STEM Centre eLibrary, shows you how to do it.

#### Procedure

a Add to the tray of marbles one or two larger marbles used in the experiment Kinetic theory: two-dimensional model, and compare their motion with that of the smaller ones.

b Alternatively, add a small piece of polystyrene to the 3D model, as used in the Kinetic theory model for a gas experiment.

#### Teaching notes

1 The random path of a larger marble buffeted by the smaller ones suggests what you might see if you looked at, say, bits of ash in the air.

2 Similarly, the movement of the small piece of expanded polystyrene in the tube used for the experiment Kinetic theory model for a gas shows a similar effect. However, here 'buoyancy' and gravity play more noticeable parts than they would for ash in air. Nonetheless, taking the opportunity to try different sized scraps of expanded polystyrene, the students can predict the ways that smaller and larger fragments of ash will be seen to move in air, and even to realise why Brownian motion is only observed with microscopically small particles.

This experiment was safety-checked in December 2004