Particles and their behaviour · Model
The particle model
Pour 50 ml of water into 50 ml of alcohol and you get 97 ml. Nothing leaked, nothing evaporated. Where did the three millilitres go?
Start here
Fifty and fifty makes ninety-seven.
Two measuring cylinders, both read to the millilitre. 50 ml of water, 50 ml of pure alcohol. Tip one into the other, wait for the froth to settle and read the level: 97 ml. Do it again tomorrow and you get 97 ml again.
Three millilitres of liquid are missing. Commit to a reason.
Nothing is missing. Every drop you poured is still in the cylinder. The only way 50 and 50 can make 97 is if liquids are not solid stuff all the way through — if there are gaps, and the small particles of one liquid can settle into the gaps between the large particles of the other. That is the whole model, arrived at by arithmetic.
Everything in this unit rests on one claim: matter is not continuous. It is made of separate particles, far too small to see, with nothing at all in between them, and they never stop moving. That claim is worth nothing to you until you have tried to break it — so the rest of this lesson is two attempts to break it.
The cutting bench · attempt one
Keep cutting it in half.
0 of 24 possible cuts
A sugar cube, one centimetre on each side. A knife with a perfect edge, and no limit on your patience. Halve it across, throw the rest away, then halve what is left again — every cut leaves a piece half as wide as the one before.
Commit before you start. With a perfect knife and forever to work, how many times could you cut?
Cuts made
0
Edge of the piece
10 mm
Still sugar?
YesFloor
Twenty-four cuts. Not twenty-four thousand, not forever — twenty-four. The knife has not gone blunt and your hand has not got tired. There is simply no piece of sugar smaller than this one, because this one is a single particle, and halving matter runs out. 0.6 nm is about a millionth of a millimetre: a human hair is a hundred thousand times wider.
The edge has stopped being smooth. What looked like a solid block four cuts ago is a countable number of particles, and you can see the end coming.
A centimetre of sugar. Cut it and watch it go — the size on the ruler and the piece on the bench are the same claim.
Still sugar, still sweet, still white, still behaving exactly like sugar. Halving does not seem to be getting you anywhere. Keep going.
Key fact
All matter is made of particles, far too small to see, with nothing between them, and they are always moving.
Attempt two · the gap
What is between the particles?
Zoom into the sugar until you can see individual particles with spaces between them. Pick what is in the space, then run the test that would tell them apart.
Take the gap away and see what happens
Nothing is the hard answer to accept and the only one that survives. Run a test and see why the alternatives do not.
You have put something in the gap. Now run a test and watch it fail.
With gaps: the particles are pushed closer and the gas takes up a fifth of the space. That is why a bike pump works.
Fill the gaps with air and there is nothing left to squash — the air would need gaps of its own, and so would that air, forever.
With gaps: small particles drop into the spaces between large ones, and 50 + 50 comes out at 97.
Fill the gaps with something and the volumes must simply add. 50 and 50 would make 100, and it does not.
With gaps: a moving particle has somewhere to go, and it works its way across the room without any draught.
Pack the space solid and nothing can move anywhere. A smell would never cross a still room, and it does.
Think again
“You stopped cutting because the knife was not sharp enough. A better knife would keep going.”
This is the sensible objection, and it is worth taking seriously before you answer it. Commit.
A sharper knife does not help, because past this point you are not cutting any more. Splitting a sugar particle takes it apart into different substances altogether — that is a chemical change, not a smaller slice. Cutting has a floor, and this is it: what is impossible is a smaller piece that is still sugar.
That is what the model claims, and it is a much stronger claim than "things are small". It says matter comes in units with a floor, and below that floor the substance stops existing. Everything you meet in this unit — melting, pressure, diffusion — is that floor doing work.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
What does the particle model say is between the particles of a gas?
Rung 2 · The one that catches people
A student halves a sugar cube twenty-four times, each cut leaving a piece half as wide, and reaches one particle. Why can they not make the twenty-fifth cut?
Rung 3 · Explain
Explain, using the particle model, why 50 ml of water added to 50 ml of alcohol gives 97 ml and not 100 ml.
Rung 4 · Take it somewhere new
A student says the gaps between particles in a gas must contain air, "because otherwise it would be a vacuum in there, and you cannot have a vacuum in the middle of a room." Reply to them.
Key note
Matter is made of particles with a floor you cannot cut past, nothing at all between them, and constant motion. Three claims. You have tested two of them in this lesson and the third is the next five lessons.
Going further
The Greeks got here by argument alone, around 400 BC — Democritus reasoned that cutting must stop somewhere and called the last piece atomos, uncuttable. He had no evidence, and for two thousand years his idea sat next to the equally reasonable one that matter is continuous, with nothing to choose between them. What broke the tie was not a better argument but a measurement: gases combining in fixed whole-number ratios, mass balancing exactly through a reaction, and eventually the water-and-alcohol arithmetic you did at the top of this page. An idea does not become science when someone thinks of it. It becomes science when a number forces it.
Before this lesson
- Nothing — this is where the unit starts
Next in this unit
At GCSE this becomes
Where to next
Ask Mr Badmus AI
Still think something must be in the gap?
Lesson content © MrBadmusAI.