Brownian motion: the dance you can see, pushed by what you can't

The problem

Robert Brown, a botanist, looked at tiny pollen particles in water under a microscope. They never stopped moving: jerking left, then right, then back, with no pattern at all. Nothing was stirring the water. So what was pushing them?

The answer: water molecules, far too small to see, hitting the particle from every side. At any instant a few more hit one side than the other, and the particle jumps. Brownian motion is the visible sign of invisible molecular motion.

Brownian motion is the random, irregular, zig-zag motion caused by molecular collisions. Each collision transfers momentum and energy, so the path keeps changing direction.

Key terms

Random collisions

A molecule changes its path after every collision. Many collisions in a row give a random, zig-zag path. That makes Brownian motion one of the simplest models of randomness.

Mass and speed

The speed a particle gets from a kick depends inversely on its mass. Lighter particles obtain greater speeds from the same collisions.

Viscosity

Viscosity is the internal friction of a fluid: its resistance to flow. The lower the viscosity, the faster the Brownian movement. Pollen jiggles more in water than in honey.

Einstein and Perrin

Albert Einstein explained the movement in 1905 as the work of molecules. In 1908 the French physicist Jean Perrin confirmed it experimentally, which earned him the 1926 Nobel Prize in physics.

Short questions with model answers

1. Q1. Explain how a drop of ink in a beaker of water will behave.

   • Water molecules are in constant random motion.
   • They knock the ink particles in random directions.
   • So the ink slowly spreads until the colour is even.

   The drop spreads through the water by itself, pushed by random molecular collisions.

2. Q2. Two particles receive the same momentum kick, Δp. One has mass m, the other 2m. Compare their speeds.

   • v₁ = Δp ÷ m
   • v₂ = Δp ÷ 2m = v₁ ÷ 2

   The lighter particle moves twice as fast: lighter particles jiggle more.

3. Q3. Why is Brownian motion slower in honey than in water?

   • Honey has a much higher viscosity.
   • The particle's speed is inversely related to viscosity.

   Higher viscosity, more internal friction, slower Brownian movement.

Common mistakes

• ✗ Copying the year as printed: “In 1927, Robert Brown…”

  ✓ Brown made his observation in 1827. It must come before Einstein's explanation in 1905, so 1927 is a misprint.

• ✗ Saying the pollen moves because it is alive.

  ✓ Dust particles show the same motion. It is an effect of molecular motion: the fluid's molecules keep hitting the particle.

• ✗ Writing that higher viscosity makes Brownian motion faster.

  ✓ It is inverse: low viscosity gives faster Brownian movement.

MCQs

1. 1. Who explained Brownian motion in 1905?

   1. (a) Robert Brown
   2. (b) Albert Einstein
   3. (c) Jean Perrin
   4. (d) James Clerk Maxwell
   Show answer

   (b) Einstein, in 1905. Brown observed it; Perrin verified the explanation in 1908.

2. 2. Perrin's experimental verification earned him the Nobel Prize in:

   1. (a) 1905
   2. (b) 1908
   3. (c) 1926
   4. (d) 1927
   Show answer

   (c) 1926, for work he did in 1908.

3. 3. Brownian movement is faster when the fluid's viscosity is:

   1. (a) high
   2. (b) low
   3. (c) zero only
   4. (d) unchanged
   Show answer

   (b) Low viscosity: less internal friction to slow the particle down.

4. 4. From the same collisions, which particle gets the greater speed?

   1. (a) the heavier one
   2. (b) the lighter one
   3. (c) both the same
   4. (d) neither moves
   Show answer

   (b) The lighter one: speed from a kick is inversely proportional to mass.

5. 5. Viscosity describes a fluid's:

   1. (a) colour
   2. (b) temperature
   3. (c) internal friction, its resistance to flow
   4. (d) density
   Show answer

   (c) Internal friction: how strongly the fluid resists flowing.

Quick revision

• Brownian motion is the random zig-zag motion caused by molecular collisions; Brown saw it in pollen in 1827 (the book prints 1927).
• Lighter particles and less viscous fluids give faster Brownian movement.
• Einstein explained it (1905); Perrin verified it (1908) and won the 1926 Nobel Prize.