Answers · The particle model

Brownian motion — answer key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. PQ13 · Practice

Model answer. Row A. The clay particles show Brownian motion. Each one is hit from all sides by water molecules, far too small to see, and at each moment the hits do not quite balance, so it is pushed in a random direction: its path is a random zig-zag. Neighbouring clay particles are hit by different molecules, at random, so each moves in its own way. The water molecules never stop moving, so the clay particles are still jiggling after 20 minutes, and would be after a day.

A full answer includes

I chose row A.
I identified that each clay particle moves in a random zig-zag.
I identified that neighbouring clay particles each move in their own way.
I identified that the clay particles are still jiggling after 20 minutes.
I did not choose row B: particles that move the same way together are carried by a current.

Also accept

A: a random zig-zag; each clay particle moves in its own way; still jiggling after 20 minutes.

Watch for

“Row B: neighbouring clay particles all move the same way together.” — Particles that move together are being carried by a current. In a sealed, still drop, each clay particle is hit by different molecules, so each moves in its own way.
“Row C: the clay drifts smoothly, then stops once the water has settled.” — Brownian motion never dies away. The water molecules keep moving, so the hits never stop, and each clay particle keeps jiggling in a random zig-zag.
“Row D: the clay particles move back and forth in a regular way, all together.” — There is no pattern. Each push comes from a random side, so the path is a random zig-zag, different for every particle.

2. PQ14 · Practice

Model answer. Water molecules hit each speck unevenly, at random. They hit it from all sides, all the time, and at each moment the hits on one side do not quite balance the hits on the other, so the speck is pushed one way, then another. Each observation rules out one of the other explanations. Neighbouring specks jump in different directions, so a current is not the cause: it would carry them along together. The specks jiggle in water that was boiled, which kills anything living, and chalk is not alive, so they are not swimming. A speck with no other specks near it jiggles just as much, so the specks are not bumping into each other. And the jiggling has not died away by the next day, because the water molecules never stop moving.

A full answer includes

I chose: water molecules hit each speck unevenly, at random.
I gave one observation and the explanation it rules out (for example, neighbouring specks jumping in different directions rule out a current).
I did not choose that the specks bump into each other: a speck with no other specks near it jiggles too.

Also accept

c; for example, neighbours jump different ways, so it is not a current; boiled water still works, so they are not alive; a lone speck jiggles, so they are not bumping each other.

Watch for

“Currents in the water carry the specks along with them.” — A current would carry neighbouring specks along together, the same way. Here neighbours jump in different directions, each on its own.
“The specks are tiny living things that swim about.” — Chalk is not alive, and boiling the water would kill anything living in it. The specks still jiggle in boiled, cooled water.
“The specks keep bumping into and pushing each other.” — A speck with no other specks near it jiggles just as much. What hits each speck is far smaller: the water molecules.

3. PQ15 · Practice

Model answer. Each droplet jiggles at random, independently of its neighbours. In a smooth air with no particles, nothing would push a droplet first one way and then another: it could only drift with the air or fall. If the air is made of particles that are always moving, they hit each droplet unevenly, from all sides, so each droplet jiggles in its own random way. That is Brownian motion, and it is evidence for the kinetic particle model. The other three observations would be just the same in a smooth air: the droplets would still scatter light, still be too small to see without a microscope, and still be pulled slowly down by gravity.

A full answer includes

I chose: each droplet jiggles at random, independently of its neighbours.
I did not choose that the droplets settle: they would fall through a smooth air too.
I did not choose that the droplets scatter light, or that they need a microscope: both would be true whatever the air is made of.

Also accept

a: a random jiggle of each droplet on its own needs moving particles that hit it unevenly; a smooth air could not cause it.

Watch for

“The droplets scatter light, so they shine on a dark background.” — They would scatter light whatever the air is made of. It tells you about the droplets, not about the air.
“The droplets are too small to see without using a microscope.” — That is true in any air. The size of the droplets says nothing about whether the air is made of particles.
“The droplets slowly settle towards the bottom of the jar.” — Gravity pulls the droplets down through any air, smooth or not. Only a random jiggle, each droplet on its own, needs moving particles to explain it.

4. PQ16 · Practice

Model answer. More, shorter jumps, making a more jagged zig-zag. The straight lines between marks are not the speck’s real path. The speck is hit by air molecules all the time, and the side that gets more hits keeps changing at random, so between two marks made 10 s apart it changed direction many times. Marking it every 1 s catches more of those changes: there are ten times as many marks, the lines between them are shorter, and the path looks more jagged. However often it is marked, the path between two marks would still be a smaller zig-zag.

A full answer includes

I chose: more, shorter jumps, making a more jagged zig-zag.
I wrote that the speck is hit unevenly all the time, so it changes direction many times between two marks made 10 s apart.
I wrote that marking every 1 s shows more of these changes of direction.
I did not choose a smooth curve: the speck never moves smoothly, however often it is marked.

Also accept

a: more, shorter jumps; the speck changes direction many times between the 10 s marks, so marking more often shows a more jagged path.

Watch for

“The same lines, with extra marks dotted along them.” — The speck does not travel along the straight lines between the 10 s marks. Between two marks it changed direction many times, so the new marks will not lie on the old lines.
“A smooth curve, as the marks are much closer in time.” — The speck never moves smoothly. Each moment, the uneven hits push it in a new random direction, so closer marks show a more jagged path, not a smoother one.
“Fewer jumps, each one ten times longer than before.” — Marking every 1 s gives ten times as many marks in the same time, so there are more jumps, and each one is shorter.

5. PQ17 · Practice

Options as numbered on the pupil sheet: 1 — atom or molecule; 2 — microscopic particle; 3 — living cell that swims by itself.

Model answer. An argon atom, a carbon dioxide molecule and a methane molecule are atoms or molecules: far too small to see with any light microscope. A grain of potato starch, a speck of rust and a water droplet in a cloud are microscopic particles: big enough to see through a microscope, each made of a vast number of atoms or molecules. A cloud droplet is made of water molecules, but it is not one molecule: it holds billions of them. None of the six is a living cell: a starch grain is a store of food made by a plant, and it jiggles in water because water molecules hit it, not because it swims.

A full answer includes

I sorted the grain of potato starch as a microscopic particle.
I sorted the speck of rust as a microscopic particle.
I sorted the water droplet in a cloud as a microscopic particle.
I sorted the argon atom as an atom or molecule.
I sorted the carbon dioxide molecule as an atom or molecule.
I sorted the methane molecule as an atom or molecule.
I did not sort the grain of starch as a living cell.

Also accept

Atoms or molecules: argon, carbon dioxide, methane; microscopic particles: starch grain, rust speck, cloud droplet.

Watch for

“A grain of potato starch is a living cell that swims.” — A starch grain is a store of food made inside a plant cell. It is not alive: it jiggles in water because water molecules hit it.
“A water droplet in a cloud is a water molecule.” — A cloud droplet is made of water molecules, billions of them. It is a microscopic particle, and one water molecule is far too small to see.
“A speck of rust is a molecule of rust.” — A speck you can see through a microscope is made of a vast number of atoms. It is a microscopic particle, not a molecule.

6. PQ18 · Practice

Model answer. Change the sphere’s width to nanometres: 0.7 μm = 0.7 × 1000 nm = 700 nm. Then divide: 700 nm ÷ 0.28 nm = 2500. The sphere is about 2500 times wider than a water molecule, and it is made of a vast number of atoms, so it is far heavier. One hit by one water molecule barely moves it. The sphere jiggles only because it is hit an enormous number of times each second, and the hits on its sides never quite balance.

Checked automatically

Width of the sphere ÷ width of a water molecule: 2500 (within ±5%)
- Common wrong answer 2.5 : You divided 0.7 by 0.28 without changing units. 0.7 μm is 700 nm: 700 ÷ 0.28.
- Common wrong answer 0.0004 : You divided the molecule by the sphere. The sphere is the bigger one: 700 nm ÷ 0.28 nm.
- Common wrong answer 250 : 1 μm is 1000 nm, not 100 nm. So 0.7 μm is 700 nm: 700 ÷ 0.28.
- Common wrong answer 196 : You multiplied. To find how many times wider, divide: 700 nm ÷ 0.28 nm.

A full answer includes

I changed the sphere’s width to nanometres: 0.7 μm = 700 nm.
I divided: 700 nm ÷ 0.28 nm.
I wrote about 2500 times.
I wrote that one water molecule is tiny and very light compared with the sphere, so one hit barely moves it.
I did not divide 0.7 by 0.28 without changing the units.

Also accept

About 2500 times (700 nm ÷ 0.28 nm).

Watch for

“The sphere is about 2.5 times wider.” — You divided 0.7 by 0.28 without changing the units. 0.7 μm is 700 nm, so divide 700 nm by 0.28 nm.
“The molecule and the sphere are about the same size, because both are particles.” — Both are particles, but of very different kinds. The sphere is a microscopic particle, made of a vast number of atoms; a water molecule is thousands of times narrower.

7. PQ19 · Practice

Model answer. Each water molecule is light, but it moves very fast, at hundreds of metres per second, and the droplet is hit by an enormous number of them every second, from all sides. At each moment, just by chance, the hits on one side do not quite balance the hits on the other. The uneven part of all those hits is enough to push the droplet a little way. A moment later a different side gets more hits, so it is pushed another way, and the droplet jiggles in a random zig-zag that can be seen.

A full answer includes

I wrote that the droplet is hit an enormous number of times every second.
I wrote that the water molecules are light but move very fast.
I wrote that the hits come from all sides, but never quite balance.
I wrote that the uneven part pushes the droplet, and which side gets more hits changes at random.
I did not write that some of the water molecules are as big as the droplet.

Also accept

An enormous number of hits each second by light, fast molecules from all sides; they never quite balance, and the uneven part pushes the droplet, in a random direction each time.

Watch for

“Some of the water molecules are as big as the droplet.” — Every water molecule is thousands of times narrower than the droplet. It is the vast number of hits, slightly uneven, that moves it.
“All the molecules hit the droplet from the same side at once.” — They hit it from all sides all the time. Only a small difference between the sides, at each moment, pushes it.

8. PQ20 · Practice

Model answer. Evidence: graphite specks jiggling at random in a still drop of water, and talc specks in a sealed cell of air each jiggling on its own. In each, a microscopic particle is hit unevenly by molecules too small to see, so it moves in a random zig-zag on its own, as the kinetic particle model predicts. Not evidence: the flakes in a snow globe are carried round together by the swirling water, a current; a tadpole is alive and swims, using its own energy; grains of rice are far too big to be moved visibly by molecules, so they simply sink and lie still.

A full answer includes

I chose: graphite specks jiggling at random in a still drop of water.
I chose: talc specks in a sealed cell of air jiggling, each on its own.
I did not choose the snow globe: the flakes are carried round together by the moving water.
I did not choose the tadpole: it is alive and swims by itself.
I did not choose the grains of rice: they sink because gravity pulls them, and then they lie still.
My explanation says that the specks are hit unevenly by molecules too small to see.

Also accept

a and c: random jiggling of microscopic specks, each on its own, caused by uneven hits from molecules.

Watch for

“Flakes in a shaken snow globe swirl round together, then settle.” — The flakes are carried by a current of water: they move together, the same way, and they stop when the water stops. Brownian motion is a jiggle of each speck on its own, and it never stops.
“A tadpole darts about in a jar of pond water, then stops still.” — A tadpole is alive and swims by itself. Evidence for the particle model comes from specks that are not alive.
“Grains of rice dropped in water sink and lie still on the bottom.” — Grains that big are hit by so many molecules that the hits balance out, so they do not jiggle. They sink because gravity pulls them down.

9. PQ21 · Practice

Model answer. Hana is incorrect because the speck is not pushed once, like the football. It is hit all the time, from all sides, by water molecules, and the water molecules never stop moving: they are always moving fast in random directions. At each moment the hits on its sides do not quite balance, so the speck gets a new uneven push, in a new random direction, again and again. Each jump slows down quickly, but the next push comes straight away, so the jiggling goes on for as long as the drop is watched.

A full answer includes

I wrote that the speck is hit all the time, not once.
I wrote that the water molecules never stop moving, so the hits never stop.
I wrote that the hits never quite balance, so new uneven pushes keep coming, in random directions.
I did not write that the speck is alive, or that it has energy of its own.

Also accept

The speck is hit all the time, not once; the water molecules never stop moving, so new uneven pushes keep coming.

Watch for

“The speck keeps jiggling because it is alive.” — Brick dust is not alive. It keeps jiggling because the water molecules keep hitting it.
“The water molecules slow down and stop after a while.” — The molecules of the water never stop moving while it stays at the same temperature. So the hits, and the jiggling, never stop either.

10. PT2 · Apply

Model answer. (a) The ball stands for the speck, the microscopic particle being pushed about; the hands of the crowd stand for the molecules that hit it. (b) In real Brownian motion the molecules are thousands of times smaller and far lighter than the speck, but the people are not much smaller than the ball; molecules move at random, but people push on purpose; a speck is hit an enormous number of times each second, the ball only a few times; and molecules fly about fast, while the crowd stands still. (c) The small ball jiggles about more. It is lighter, so each push moves it further, and fewer hands push it at the same time, so at each moment the pushes on its sides balance less well. In the same way, a smaller speck jiggles more than a bigger one. (d) On a still night, nothing else could push the ball first one way and then another. Its uneven, changing motion shows that unseen people are under it, pushing it unevenly. Brownian motion is the same argument: the molecules are far too small to see, but the random jiggle of a speck, with no current and nothing alive, shows that the air or water is made of particles in constant random motion.

A full answer includes

(a) I identified the ball as standing for the speck.
(a) I identified the people’s hands as standing for the molecules.
(b) I stated one difference: for example, the people are not thousands of times smaller than the ball.
(b) I stated a second difference: for example, the people push on purpose, not at random, or there are far fewer pushes each second.
(c) I predicted that the small ball jiggles more.
(c) I wrote that it is lighter, so each push moves it more.
(c) I wrote that fewer hands push it at once, so the pushes on its sides balance less well.
(c) I did not predict that the huge ball jiggles more because more people push it.
(d) I wrote that the ball moves one way, then another, with no wind, so something unseen must be pushing it unevenly.
(d) I wrote that in the same way the molecules cannot be seen, but the random jiggle of a speck shows that they are there and moving.

Also accept

(a) ball = speck, hands = molecules; (b) people are not tiny, not random, too few pushes; (c) the small ball more: lighter, pushes balance less well; (d) the unseen people are shown by the ball’s uneven, changing motion, just as unseen molecules are shown by a speck’s random jiggle.

Watch for

“(a) The ball stands for an air molecule.” — The ball is the big thing being pushed about, so it stands for the speck. The many pushers stand for the molecules.
“(c) The huge ball jiggles more, because more people push it.” — More pushes from all sides cancel out more closely, and the huge ball is heavier. The small ball, with fewer pushes, is pushed about more.
“(d) The ball is moved by the wind, not by the people.” — The night is still, and the wind would carry the ball steadily one way. A push one way and then another, at random, can only come from the unseen crowd.