Describe and explain Brownian motion in terms of random molecular bombardment

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – Particle Model: Brownian Motion

Cambridge IGCSE Physics 0625 – Particle Model

2.1.2 Brownian Motion

Brownian motion is the erratic, random movement of tiny particles (typically of the order of a few micrometres) when they are suspended in a fluid (liquid or gas). The motion is observable under a microscope and provides direct evidence for the kinetic theory of matter.

Explanation in terms of random molecular bombardment

According to the particle model, a fluid consists of a huge number of molecules moving constantly in random directions with a range of speeds. When a suspended particle is present, it is continuously struck by these molecules. Because the impacts are:

  • Random in direction,

  • Unequal in magnitude (different molecular speeds), and

  • Occurring at very short time intervals,

the net force on the particle fluctuates rapidly, causing it to jitter about its original position. This jitter is what we observe as Brownian motion.

Key points to remember

  1. Brownian motion provides macroscopic evidence for the existence of molecules.

  2. The intensity of the motion increases with temperature because molecular speeds increase (\$\langle v \rangle \propto \sqrt{T}\$).

  3. Smaller particles exhibit more noticeable Brownian motion than larger ones, since the relative effect of each molecular impact is greater.

  4. The motion is completely random; there is no preferred direction.

Quantitative description (optional)

The mean square displacement \$\langle x^{2} \rangle\$ of a particle undergoing Brownian motion in one dimension after a time \$t\$ is given by:

\$\langle x^{2} \rangle = 2 D t\$

where \$D\$ is the diffusion coefficient, related to temperature \$T\$, fluid viscosity \$\eta\$, and particle radius \$r\$ by the Stokes‑Einstein equation:

\$D = \frac{k_{\mathrm{B}} T}{6 \pi \eta r}\$

Here \$k_{\mathrm{B}}\$ is Boltzmann’s constant.

Evidence supporting the particle model

ObservationInterpretation
Particles suspended in a liquid move erratically.Continuous, random impacts from moving molecules.
Motion becomes more vigorous as temperature rises.Higher molecular kinetic energy → faster, more forceful collisions.
Smaller particles show larger displacements.Force from each collision has a greater effect on a smaller mass.

Suggested diagram: A microscope view showing tiny particles jittering in a fluid, with arrows indicating random molecular impacts.

Common misconceptions

  • Brownian motion is not caused by convection currents; it occurs even in still fluids.

  • The motion is not due to the particle’s own energy; it is driven entirely by external molecular impacts.

  • It is not limited to visible particles; the same principle applies at the atomic scale.

Summary

Brownian motion is a clear, observable phenomenon that demonstrates the particle nature of matter. It arises from the random, incessant bombardment of fluid molecules on suspended particles, and its characteristics (temperature dependence, particle‑size dependence, randomness) are all consistent with the kinetic theory of gases and liquids.