Atoms and Scale

Believing in something nobody could see

Everything around you is made of atoms. You have been told this since primary school, and almost certainly never asked the obvious question: how does anybody know? ⚠️ NOBODY HAS EVER SEEN AN ATOM WITH LIGHT, and it is not a matter of needing a better microscope. An atom is THOUSANDS OF TIMES SMALLER THAN THE WAVE OF LIGHT that would have to bounce off it, and you cannot make out a thing using a wave far larger than the thing itself. So the case for atoms was not built by looking. It was built entirely on THINGS ATOMS DO. A speck of dust jiggles for no visible reason. A drop of ink spreads through still water on its own. A gas squashes into a fraction of its volume while a liquid barely budges. None of those show you a particle. Every one of them is very hard to explain without particles. ⚠️ That gives you a move you will use across this whole paper. WHEN YOU CANNOT OBSERVE A THING DIRECTLY, LOOK FOR SOMETHING IT MUST CAUSE. And the scale is not a separate fact to memorise. THE SCALE IS THE REASON THE EVIDENCE HAD TO BE INDIRECT, which is why this module puts the two together.

Terms for size and for evidence

Six terms. What each one means, with no measurements attached.

Order these by size, smallest first

Five things spanning seven orders of magnitude. Smallest first.

• An atom, about 10^-10 m across
• A virus, about 10^-7 m across
• A bacterium, about 10^-6 m across
• The width of a human hair, about 10^-4 m
• A grain of sand, about 10^-3 m across

Three things atoms do that you can actually watch

Not one of these shows you a particle. Every one of them is difficult to explain without particles, which is what makes them evidence.

Why a better microscope would not help

A student suggests that atoms could be seen with an ordinary light microscope if only the lenses were made powerful enough. Why is that not the problem?

• An atom is thousands of times smaller than the wavelength of visible light, and a wave that much larger than an object cannot resolve it however much the image is magnified
• Lenses good enough have simply not been manufactured yet
• Atoms move too quickly to be photographed
• Atoms are transparent, so light passes straight through them

How to argue from indirect evidence

This whole topic is a worked example of something science does constantly: establishing that a thing exists without ever observing it. The move has three parts, and questions on it reward all three. ⚠️ ONE: state what was OBSERVED. Not what it means. What was actually seen, by anyone who cared to look. TWO: state what it would be hard to explain WITHOUT. This is the load-bearing part. Evidence is not something that merely fits your idea; it is something your idea explains and the alternatives struggle with. THREE: say what the evidence does NOT establish. Watching specks jiggle tells you particles are there and moving. It tells you nothing whatever about what is inside one. ⚠️ And handle the arithmetic carefully, because comparisons of scale are all divisions in standard form. To find how many of a small thing fit across a larger one, divide the large length by the small one and subtract the powers of ten. A millimetre is 1 x 10^-3 m, and across an atom of 2 x 10^-10 m that gives 0.5 x 10^7, which is 5 x 10^6 atoms. Always sanity-check the direction. More of the small thing fits into the large one, so the answer must come out large. If it comes out as a fraction, the division went the wrong way round.

Atoms across a micrometre

An atom is about 2 x 10^-10 m across. A micrometre is 1 x 10^-6 m. Work out how many atoms would fit side by side across one micrometre. Give the number only.

How many times bigger the light wave is

Violet light has a wavelength of about 4 x 10^-7 m. An atom is about 2 x 10^-10 m across. Work out how many times larger that wavelength is than the atom. Give the number only.

The jiggling speck under the microscope

Put a little smoke in a small glass cell, light it from the side, and look at it through a microscope. You will not see smoke. You will see individual specks of light, and every one of them is trembling. They never settle. They drift a little way in one direction, jerk off in another, and keep going for as long as you watch. ⚠️ Nothing visible is touching them. The cell is sealed, the air inside is still, and there is no current. And yet the movement never stops and never runs down. Now run the three-part move. THE OBSERVATION: small specks suspended in air jiggle constantly and at random. WHAT IT WOULD BE HARD TO EXPLAIN WITHOUT: countless particles far too small to see, moving fast, striking each speck from every side at once. At any instant slightly more arrive from one direction than another, and the speck lurches. Notice the detail that makes it convincing rather than merely consistent. ⚠️ The SMALLER the speck, the more violently it moves. A large speck is struck from so many sides at once that the imbalances average out. A small one is not. A theory of invisible particles predicts that. An explanation based on stirring or draughts does not. ⚠️ AND SAY WHAT IT DOES NOT SHOW. It establishes that particles exist and are in motion. It says nothing at all about what one is made of.

Match each observation to what it shows

True about the scale of atoms

Select the TWO statements that are true.

• An atom is smaller than the wavelength of visible light
• Instruments now exist that can show the arrangement of individual atoms
• A light microscope could resolve an atom if its magnification were high enough
• Atoms have never been imaged by any instrument at all

The evidence run

Five questions on how the case for atoms was actually made. Three lives.

Spot the true facts about atomic scale

Tap the TWO statements that are true.

• An atom is thousands of times smaller than the wavelength of visible light
• The case for matter being made of particles was built on indirect evidence
• Enough magnification would let a light microscope resolve an atom
• Brownian motion reveals what is inside an atom

Complete the evidence facts

The spreading of one substance through another with nothing stirring it is called _____, and it is evidence that particles are in constant motion. Very small or very large measurements are written in _____, so that an atom can be given as about 2 x 10^-10 m. A length of one thousand millionth of a metre is called a _____. The smallest separation at which two things can still be told apart is an instrument's _____, and it is not the same thing as its magnification.

Three claims about seeing atoms

Three statements to judge. Each answer has to carry the reasoning, not just the verdict.

• A student writes that atoms cannot be seen "because microscopes are not powerful enough yet". How should that be improved?
• Another student, told that light cannot show atoms, concludes that nobody has ever produced an image of one by any means. Is that right?
• A student uses Brownian motion as evidence, then writes that it "proves atoms have a nucleus with electrons around it". What is wrong?

Explain how we know atoms are there

A classmate accepts that everything is made of atoms but has never been given a reason to. Write them the explanation, including why nobody simply looked.

• Explain how small an atom is, comparing it with something a reader can picture
• Explain why visible light cannot be used to see one, referring to the wavelength
• Describe one observation that is hard to explain without particles, and say clearly what makes it hard
• Explain the general move being used here: what to do when a thing cannot be observed directly
• Finish by saying what this evidence does NOT establish about atoms