Particles and their behaviour · Model
Diffusion
Someone opens a bottle of perfume at the far end of a room. Before long you can smell it. Draughts and convection carry it most of the way — so what covers the last stretch?
Start here
No draught. No fan. No one waving.
The windows are shut, the air is dead still, and a candle flame at the centre of the room stands perfectly upright — so there is genuinely no air current to speak of. The perfume still reaches you in the end.
Commit to what moved it.
Nothing carried it. Each perfume particle was already moving — hundreds of metres per second — and it bounced its way outwards off air particles, in a path so tangled that crossing open space on its own is desperately slow. In a real room draughts and convection carry it most of the way; diffusion covers the last stretch. No push was needed, because the movement never stopped in the first place.
Diffusion is the one piece of the particle model that people find hardest to accept, because it looks purposeful. Something spreads out and fills a space, evenly, every time — and evenly-and-every-time is what deliberate things do. This lesson takes the purpose out of it and leaves nothing but random movement, which turns out to be enough.
The random-walk bench · watch one particle, then all of them
No one is steering.
not started
A drop of dye released on the left of a sealed tank of still water. Every particle takes a step in a random direction, over and over. Nothing else is happening.
Commit first. Once the dye has spread out completely and the tank looks even, what are the particles doing?
Crossings left to right
0
Crossings right to left
0
Spread out?
Not yetYes
The drop is sitting on the left. Nothing is pushing it, nothing is stirring, and there is no current in the tank. Press start and watch what randomness alone does — and warm the water if you want it sooner, because hotter particles move faster and the evening out comes on much more quickly.
Early on, more particles cross left-to-right than right-to-left — not because they know where to go, but because there are more of them on the left available to make the crossing. Watch the GAP between the two counters rather than their size: a single particle near the middle crosses the line again and again, so both totals run away. The gap is the net movement, and it is the whole of diffusion.
Evened out — and look at the two crossing counters. They are still climbing, at the same rate as each other. Particles are pouring across the middle in both directions, in equal numbers, forever. Nothing has stopped; the two flows have simply balanced.
The single traced particle is not going anywhere in particular. Its path doubles back on itself constantly — and the tangle is exactly why crossing a few centimetres takes so long when the particle itself is fast.
Key fact
Diffusion is the spreading out of particles from where they are crowded to where they are not, caused by their own random movement. Nothing pushes them and nothing stops when it is finished.
Think again
“The particles spread out because they want to fill the space evenly.”
Every word of that sentence is doing damage, and it is the sentence almost everyone writes. Commit to what is wrong with it.
A particle has no goal, no information about the rest of the tank, and no way to prefer one direction over another. It cannot want anything. The evenness is not aimed at — it is what randomness produces when you start with a crowd on one side.
The counters on the bench are the proof. At the start, far more particles cross left-to-right than right-to-left — not because they are heading that way, but because there are more of them on the left to make the crossing. Once the two sides are even, the two counts climb at the same rate and keep climbing. The spreading has finished; the moving has not. If the particles were trying to fill the space, they would stop when the job was done.
Where this does real work
Hopeless across a room, unbeatable across a cell
Diffusion is hopeless over long distances and unbeatable over short ones, and that single fact shapes a great deal of biology.
Across a cell · 0.01 mm
About a hundredth of a second
Fast enough that a cell needs no delivery system at all. Oxygen simply arrives.
Across a fingertip · 10 mm
About three hours
Already hopeless. This is why you have a bloodstream, and why the blood is never more than a fraction of a millimetre from any cell.
Across a room · 4 m
Far too slow on its own
Gas particles move far faster and travel further between collisions than they do in a liquid — but across a whole room diffusion alone would take days. Draughts and convection carry a smell most of the way; diffusion covers the last stretch.
Double the distance and diffusion takes four times as long, not twice. That is why every cell in your body is microscopic, why lungs are folded into millions of tiny sacs instead of two smooth bags, and why anything larger than an insect needs a heart.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
Diffusion is the movement of particles from where they are…
Rung 2 · The one that catches people
A tank of dye has completely evened out. What is happening to the particles now?
Rung 3 · Explain
Explain how perfume particles move through the air on their own, and why diffusion alone is so slow across a room even though the particles travel at hundreds of metres per second.
Rung 4 · Take it somewhere new
A drop of food colouring is put into a glass of cold water and an identical drop into a glass of hot water. The hot one spreads much faster. Explain why — and explain why the cold one still spreads completely if you wait.
Key note
Random movement, no pushing, no purpose. Particles go from crowded to less crowded because there are more of them to leave the crowded side. Warmer means faster. The movement never stops, even when the spreading looks finished.
Going further
In 1827 the botanist Robert Brown watched pollen grains in water through a microscope and found them jittering about, endlessly, with nothing touching them. He could not explain it and nor could anyone else for nearly eighty years. Then in 1905 Einstein worked out that the jitter was exactly what you would see if the water were made of invisible particles battering the grain from every side, slightly unevenly, millions of times a second — and he predicted precisely how far a grain should wander in a given time. When Jean Perrin measured it and the numbers matched, the last serious scientific doubt that atoms exist was gone. A dancing speck of pollen settled it.
Before this lesson
Next in this unit
At GCSE this becomes
Where to next
Ask Mr Badmus AI
Still feels like something must be pushing them?
Lesson content © MrBadmusAI.