Describe and explain Brownian motion in terms of random molecular bombardment

2.1.2 Particle Model – Brownian Motion

What is Brownian Motion?

Brownian motion is the random, jittery movement of tiny particles suspended in a fluid (liquid or gas). It was first observed by the botanist Robert Brown in 1827 when he watched pollen grains in water wobble all over the place. The key idea is that the particles are constantly hit by much smaller molecules of the fluid, which are moving fast and chaotically. These collisions give the particles a random “kick” that makes them jiggle.

Why Does It Happen?

1. Random Molecular Bombardment – The fluid molecules are in constant motion. Each collision transfers a tiny amount of momentum to the suspended particle. Because the collisions are random in direction and strength, the particle’s path looks like a zig‑zag. 2. Thermal Energy – The higher the temperature, the faster the molecules move, so the particle jiggles more vigorously. This is why a cup of hot tea makes the pollen move faster than a cup of cold tea. 3. Size Matters – Smaller particles experience more noticeable motion because the relative impact of each collision is larger compared to their mass.

Mathematical Insight

The average distance a particle travels in a time interval $t$ can be described by the mean square displacement: $$\langle x^2 \rangle = 2 D t,$$ where $D$ is the diffusion coefficient. For a spherical particle of radius $r$ in a fluid with viscosity $\eta$, the Stokes–Einstein relation gives: $$D = \frac{k_B T}{6 \pi \eta r},$$ with $k_B$ being Boltzmann’s constant and $T$ the absolute temperature. This formula shows how temperature, viscosity, and particle size control the jittery motion.

Analogy: The Windy Playground

Imagine a playground on a windy day. The wind (fluid molecules) blows in all directions. A small kite (the suspended particle) is tossed around by gusts that come from random angles. Sometimes the wind pushes it forward, sometimes sideways, sometimes back. The kite’s path looks unpredictable, just like a pollen grain in water. The stronger the wind (higher temperature), the more the kite flutters.

Key Takeaways

• Brownian motion is caused by random collisions between fluid molecules and suspended particles.
• Temperature, viscosity, and particle size all influence the extent of the motion.
• It provides evidence for the existence of atoms and molecules.
• The phenomenon can be described mathematically using diffusion equations.

Quick Quiz

1. What happens to the jitter of a particle if the temperature of the fluid is increased? (Answer: It increases.)
2. Which of the following factors does NOT affect Brownian motion: mass of the particle, size of the particle, viscosity of the fluid? (Answer: Mass of the particle – it has a very small effect compared to size and viscosity.)
3. Write the Stokes–Einstein equation for the diffusion coefficient. (Answer: $D = \frac{k_B T}{6 \pi \eta r}$.)

Data Table: Example Particles