Brownian motion provides direct, visible evidence that matter consists of tiny, constantly moving particles. Random movement of smoke particles in air reveals the ceaseless collisions of gas molecules.

Understanding Brownian Motion

Historical Context

The phenomenon of Brownian motion was first observed in 1827 by botanist Robert Brown, who noticed pollen grains moving erratically in water. Although he initially thought this movement was biological, later research proved it was a physical effect caused by collisions with invisible molecules. This discovery was crucial in supporting the kinetic theory of matter, providing strong experimental proof for the existence of atoms and molecules.

The Nature of Brownian Motion

Random Molecular Collisions

Brownian motion occurs because microscopic particles suspended in a fluid (liquid or gas) are constantly bombarded by the much smaller, rapidly moving molecules of that fluid.

• The molecules move randomly at high speeds due to their thermal energy.

• These collisions are uneven — molecules do not strike the suspended particle uniformly from all directions at any instant.

• The imbalance of forces causes the larger visible particle to move in an irregular, zig-zag path.

Schematic illustration of Brownian motion: the red particle executes a jagged path as blue molecules collide with it from random directions. This directly visualises uneven molecular impacts producing the observed jerky motion. The layout is intentionally minimal to emphasise the mechanism. Source.

This visible movement provides macroscopic evidence for molecular motion that cannot be directly seen.

Key Features of Brownian Motion

• Randomness: Each step in the motion is unpredictable in direction and speed.

• Continuous movement: The particle never comes to rest because molecular collisions never cease.

• Dependence on temperature: As temperature increases, molecular kinetic energy rises, causing more vigorous collisions and faster particle motion.

• Scale: Brownian motion is most easily observed for particles between about 1 μm and 10 μm in diameter.

Demonstrating Brownian Motion

The Smoke Cell Experiment

A standard laboratory demonstration uses a smoke cell to show Brownian motion of smoke particles in air.

Apparatus:

• A small, enclosed chamber filled with smoke from a burning source (e.g., smouldering paper).

• A microscope or optical microscope lens to magnify the particles.

• A light source such as a lamp or microscope illuminator that makes the tiny smoke particles visible.

Procedure:

1. Smoke is introduced into the chamber and illuminated.

2. The observer views the smoke particles through the microscope.

3. Each visible smoke speck appears to move in a random, jerky path.

Explanation:

• The visible smoke particles are much larger than the air molecules but still small enough to be moved by them.

• Air molecules move at speeds of several hundred metres per second, but because they are so tiny, their impacts are unseen.

• Unequal numbers of molecular impacts on different sides of a smoke particle cause it to shift irregularly.

This experiment illustrates that gas molecules are in constant motion and that collisions transfer momentum between molecules and larger particles.

Connection to the Kinetic Model of Matter

Evidence for Molecular Motion

The simple kinetic model of matter states that:

• All matter is made of particles (atoms or molecules).

• These particles are in continuous, random motion.

• Their kinetic energy depends on temperature.

Brownian motion confirms these ideas because the irregular movement of smoke particles directly results from molecular collisions. Without moving air molecules, the smoke particles would remain still.

Microscopic Explanation

On the microscopic scale, each collision transfers a small amount of momentum to the suspended particle. Because molecular impacts occur from all directions, the net force at any instant is typically not zero, producing the observed erratic motion. Over time, the directions of movement average out to zero displacement, but at short intervals, the path is chaotic and unpredictable.

Factors Affecting Brownian Motion

Temperature

Raising the temperature increases the average kinetic energy of the gas molecules.

• Molecules collide more energetically and more frequently.

• Smoke particles move more rapidly and with greater amplitude.

  This relationship supports the link between temperature and molecular kinetic energy described by kinetic theory.

Particle Size

Smaller particles experience larger changes in velocity from each molecular impact, leading to more vigorous motion. Larger particles move less because each collision imparts proportionally less momentum change.

Medium

The density and viscosity of the medium also influence the motion:

• In a less dense gas, fewer collisions occur, but each has greater effect.

• In a denser or more viscous fluid (e.g., water), collisions are more frequent but the fluid’s resistance slows motion.

Theoretical Interpretation

Einstein’s Contribution

In 1905, Albert Einstein provided a mathematical explanation of Brownian motion, linking it to the random thermal motion of molecules. His analysis allowed scientists to estimate Avogadro’s number and thereby confirm the molecular nature of matter. Einstein’s model treated the suspended particle as being jostled by molecular impacts, resulting in a diffusion-like motion over time.

Statistical Behaviour

Although each movement is random, the overall distribution of particle positions over time follows predictable statistical laws. This behaviour supports the interpretation that macroscopic randomness arises from the vast number of microscopic collisions occurring each second.

EQUATION
—-----------------------------------------------------------------
Mean square displacement (⟨x²⟩) = 2Dt
⟨x²⟩ = Mean of the squares of particle displacement over time
D = Diffusion coefficient (m² s⁻¹)
t = Time (s)
—-----------------------------------------------------------------

This equation shows that the average squared distance moved by a Brownian particle increases proportionally to time, consistent with experimental observations.

Random-walk trajectories (top) and mean-square displacement vs time (bottom) illustrating the linear MSD ∝ t dependence used to characterise Brownian motion. The plot reinforces the statistical interpretation introduced in the notes. The log-scaled axes and multiple paths add context beyond the minimum syllabus requirement. Source.

Importance in Physics

Evidence for Atomic Theory

Brownian motion provided crucial experimental confirmation that atoms and molecules exist and behave according to kinetic principles. Before its explanation, the atomic model of matter was still debated; Brownian motion offered direct observational support for the molecular nature of substances.

Modern Applications

Understanding Brownian motion is important in fields such as:

• Colloid science, where suspended particles interact with fluids.

• Nanotechnology, analysing the motion of nanoparticles.

• Statistical physics, modelling diffusion and random processes.

Through its demonstration and theoretical understanding, Brownian motion remains a foundational concept linking the microscopic world of molecules to the macroscopic properties of gases and fluids.