Brownian Motion and Evidence for the Atomic Model

The existence of atoms and molecules was not universally accepted until the early 20th century. Brownian motion provided compelling experimental evidence for the particle nature of matter and for the kinetic theory of gases. This lesson covers the observations, explanation, and significance of Brownian motion.

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Historical Background

In 1827, the Scottish botanist Robert Brown observed through a microscope that tiny pollen grains suspended in water moved in a random, jerky, unpredictable manner. Initially, Brown thought this might be a sign of life in the pollen, but he found that the same motion occurred with clearly non-living particles such as ground-up rock and glass.

The motion remained unexplained for decades. In 1905, Albert Einstein published a theoretical paper explaining Brownian motion mathematically, and in 1908, Jean Perrin carried out experiments that confirmed Einstein's predictions and provided strong evidence for the existence of atoms. Perrin's work was instrumental in convincing the remaining sceptics and earned him the Nobel Prize in Physics in 1926.

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Observing Brownian Motion: The Smoke Cell Experiment

The classic A-Level demonstration of Brownian motion uses a smoke cell:

Apparatus:

• A glass cell (small enclosed chamber)
• A microscope
• A bright light source (illumination from the side)
• Smoke (produced by burning a match or straw and trapping the smoke)

Procedure:

1. Fill the glass cell with smoke.
2. Illuminate the cell from the side with a bright lamp.
3. View the cell through the microscope.

Observations:

• Bright specks of light are visible — these are smoke particles reflecting the light.
• The specks move in a random, jerky, unpredictable path with constant changes of direction.
• The motion never stops (as long as the temperature is above absolute zero).
• No two particles follow the same path.
• If the cell is heated, the motion becomes more vigorous.

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Explanation of Brownian Motion

The visible smoke particles (typically ~1 μm in diameter) are much larger than air molecules (~0.1 nm), but they are still small enough to be affected by molecular bombardment.

The explanation is:

1. Air molecules (which are invisible even under the microscope) are in constant random motion.
2. They bombard the smoke particle from all sides.
3. At any instant, the bombardment is not perfectly balanced — there are slightly more collisions from one side than another, creating a net force in a random direction.
4. This net force causes the smoke particle to accelerate briefly in that direction.
5. Almost immediately, the imbalance shifts, and the net force changes direction.
6. The result is the characteristic random, jerky path.

Why Not Larger Particles?

Larger particles (such as dust) are too massive to show noticeable Brownian motion. The molecular impacts produce forces that are negligible compared to the inertia of the large particle. Brownian motion is most visible with particles that are small enough to be buffeted by molecular collisions but large enough to be seen under a microscope.

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Evidence Provided by Brownian Motion

Brownian motion provides strong evidence for the following claims:

1. Matter is made up of discrete particles (molecules/atoms). The jerky motion of the visible particles can only be explained by collisions with invisible smaller particles.

2. These particles are in constant random motion. The ceaseless, unpredictable nature of Brownian motion shows that the invisible molecules never stop moving.

3. The kinetic energy of the molecules increases with temperature. Heating the cell makes the Brownian motion more vigorous — the smoke particles move faster and change direction more abruptly. This is consistent with molecules having greater kinetic energy at higher temperatures.

4. The motion is truly random. There is no pattern or preferred direction in the paths of the smoke particles, consistent with the random motion of the bombarding molecules.

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Einstein's Theoretical Analysis (1905)

Einstein's 1905 paper made several key predictions:

1. The mean square displacement of a Brownian particle is proportional to time: ⟨x²⟩ ∝ t. This distinguishes Brownian motion from directed motion (where displacement ∝ t) or ballistic motion (where displacement ∝ t²).

2. The diffusion coefficient of the Brownian particle is related to temperature, viscosity, and particle size:

D = kT / (6πηr)