Rutherford Scattering
Properties of Matter

Finding the size of atoms

for 14-16

The fact that matter is made of particles is perhaps the most powerful idea in science. Understanding the scale of the particles is important. This collection shows how students can estimate the size of molecules and atoms for themselves. 
 
In a classic experiment, first performed by Lord Rayleigh, a small drop of oil spreads out to form a circular patch on the surface of water. Simple measurements lead to the length of the oil molecule, from which the diameter of carbon atoms can be deduced.

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Change in volume from a liquid to a gas for nitrogen

Rutherford Scattering
Properties of Matter

Change in volume from a liquid to a gas for nitrogen

Practical Activity for 14-16

Demonstration

Apparatus and Materials

    Method 1
  • A supply of liquid air (or liquid nitrogen)
  • Measuring flask, 100 ml
  • Chemical balance
  • Method 2
  • Trough
  • Water
  • Measuring cylinder (must have a volume 750 times greater than that of the test tube)
  • Rubber tubing
  • Small test tubes, similar, 2
  • A supply of liquid air and liquid nitrogen

Health & Safety and Technical Notes

Liquid nitrogen presents the following particular risks:

  • asphyxiation in oxygen-deficient atmospheres
  • fire in oxygen-enriched atmospheres
  • cold burns, frost bite & hypothermia from the intense cold
  • over-pressurisation from the large volume expansion of the liquid
  • manual-handling accidents if using 25 l volumes.

A full risk assessment for using solid CO2 and nitrogen is available (to subscribers) from: CLEAPSS.

Read our standard health & safety guidance


Procedure

Method 1

  1. Pour liquid air or nitrogen quickly into the 100 ml measuring flask of known mass.
  2. Once the jar has been cooled sufficiently, the violent bubbling will cease. Add more liquid to top the level up to the 100 ml mark so that the volume is known.
  3. Weigh the whole on the balance and find the mass of liquid.
  4. Calculate the density of liquid nitrogen.
  5. Measure the density of air (Air is 80% nitrogen. Oxygen and nitrogen have a similar density).

Method 2: To measure the volume change when liquid nitrogen turns into a gas directly.

  1. Fill the trough and measuring cylinder with water. Invert the measuring cylinder in the trough.
  2. Find the volume of the test tube by filling it with water and measuring the volume of water.
  3. Pour liquid nitrogen into the second, dry test tube and when the liquid has stopped bubbling, top up the test tube and quickly fit the rubber tubing.
  4. Insert the rubber tube into the open end of the measuring cylinder and collect the nitrogen gas.
  5. Compare the ratio of the volume of nitrogen gas to the volume of liquid nitrogen of the same mass.

Teaching Notes

  • The density of liquid air/nitrogen is about 90 g/100 ml, which is 900 kg /m 3 .
  • The density of air/nitrogen is about 1.2 kg /m 3 .
  • Hence the volume change when liquid nitrogen becomes gaseous nitrogen is 900/1.2 = 750.
  • If there is no liquid air/nitrogen available, then solid carbon dioxide can be allowed to sublime. A small solid lump of carbon dioxide can be put into a measuring tube filled with water, and the volume of the gas measured. It is better to get the carbon dioxide from a solid block because that produced by a cylinder is not compacted enough.

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Simple molecular model of different states of matter

Rutherford Scattering
Properties of Matter

Simple molecular model of different states of matter

Practical Activity for 14-16

Demonstration

Using models to support a discussion of the mean-free-path of molecules in a gas, and, perhaps, to lead to a value for the size of a molecule.

Apparatus and Materials

Coins, 20 to 30

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Scatter coins upon the table, spaced so that they are well apart from one another. Discuss the possible mean-free path.
  2. Use a ruler to sweep them closer together and, again, discuss the possible mean-free paths.

Teaching Notes

  • A typical discussion might be as follows.
  • "Let's pretend that the coins represent air molecules. If they are close together we must have liquid air. If you can guess how crowded the molecules would look in that liquid, you will be able to find the size of a single molecule. This is where you will have to make a guess."
  • "Imagine the molecules are round balls – not true but it will get us going. Experiments show that the volume change from gaseous air to liquid air is about 750 to 1\. Imagine that compression has pushed the molecules together until they are touching."
  • "Do you think the molecules could be that close? Could molecules arranged like that behave as a liquid which can be poured easily? No; this would be a solid. In a liquid which can be poured and move around easily, the molecules are probably a little further apart than that."
  • "If we give the molecules twice as much space, does that look like a liquid?"
  • "It might, but the spaces do look large. It looks as if a molecule could move quite a long way among its neighbours. Diffusion would be fairly fast, but actually diffusion is fairly slow in liquids. (Try putting copper sulphate crystals at the bottom of a tall jar of water, wait, and see how slowly the blue solution diffuses.) Molecules with this spacing would be a gas."
  • "Think of a crowd of people when it is behaving as a liquid; a crowd that can flow through streets to a railway station or a football match but is too dense to allow individual people to move far among their neighbours. An intermediate guess somewhere between the extremes of no distance between molecules, which would lock them tight like a solid, and spaces as big as one whole diameter which would make them behave as a cool gas."
  • "Look at one molecule and guess its mean-free-path. Draw an arrow to show how far it can move in any direction. Start the arrow at the surface of the molecule and continue it until you meet the surface of another molecule."
  • "Do that in many different directions, measure the length of the arrows and find the average. (This is only a 2-dimensional plot but we will use it to make guesses in 3-dimensions.) The average length is about 1/3 of a diameter, its mean-free-path."
  • (If students do this as well, the range of their guesses is likely to be from 1/10 to 9/10 of a diameter. This whole range covers only one order of magnitude; an uncertainty of half an order of magnitude is not a problem. Accept whatever they come up with otherwise you might as well tell them the answer!)
  • "All right, we agree on 1/3 of a diameter for the mean-free-path at liquid crowding. Then, we have squeezed the mean-free-path down by 750 from that in ordinary air until it is only 1/3 of a diameter, d/3."
  • "Therefore, the mean-free-path in the gas, 10 -7 m, is squeezed down to 10 -7 /750 m = d/3\. So, d = 4 x 10 -10 m and we have found the ‘diameter’ of a single molecule of air! (An atom, or diatomic molecule, is probably half that size.) It is a rough guess but it is a good estimate; it is the right order of magnitude. We have made an atomic measurement."
  • The difference between a solid and liquid is not just the change in molecular separation. Intermolecular forces and kinetic energies also differ.

This experiment was safety-tested in July 2006.

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Introducing the oil film experiment

Rutherford Scattering
Properties of Matter

Introducing the oil film experiment

Practical Activity for 14-16

Class practical

Experiments to help a class understand this experiment:

Estimating the size of a molecule using an oil film


Apparatus and Materials

    For each student pair
  • Crystallizing dish
  • Eye dropper
  • Beaker, 400 ml
  • Splint
  • Iron wire, 20 cm of 16 swg
  • Bunsen burner
  • Heat resistant mat
  • For the class
  • Lycopodium powder dispensers, several (or talcum powder)
  • Olive oil in a bottle
  • Alcohol in a bottle
  • Crumbs of camphor
  • Detergent for cleaning dishes (for technician use)
  • Paper towels, large pack

Health & Safety and Technical Notes

Remember that lycopodium powder is dried pollen. See CLEAPSS guide L77 for advice on use of pollen. Any students who suffer badly from hay fever might try talcum powder instead. It is not quite as good but would do. Indeed, any student wanting to repeat these experiments at home could use talcum powder. Check school records for asthma sufferers.

When ethanol is in use, remember to have no naked flames in the laboratory.

Read our standard health & safety guidance


Cleanliness is essential. As the dishes become dirty quickly, it is advisable to have spares. Before the lesson begins, the dishes must be cleaned carefully. They should be cleaned with a non-foaming and soda-free detergent and then carefully washed to remove all detergent.

In storing apparatus, it is essential to keep the lycopodium far away from any oil or camphor.

Procedure

  1. Fill each dish to overflowing with clean water. Hold it with fingers outside, well away from the rim and tip it sharply to pour out half the water. (Students must be very careful not to let their fingers touch the water or the inside of the dishes.)
  2. Dust the water surface with lycopodium powder – very lightly.
  3. Allow a drop of alcohol to fall on the surface.
  4. With a new lot of water and another light dusting of powder, try a very small quantity of olive oil. A matchstick dipped in oil and then wiped clean should provide enough.
  5. With a very clean dish, dip what you think is a clean finger in a dusted surface and see the ‘grease ring’ that forms.
  6. With a fresh, clean dish, try placing crumbs of camphor on a clean water surface.
  7. With a fresh, clean dish filled with water and dusted with lycopodium powder, bring a red-hot iron wire near to the surface.

Teaching Notes

  • The secret of these experiments is cleanliness. If the expected behaviour is not observed, it is almost certainly due to the presence of unwanted oil. The dish must be cleaned again or replaced. A monomolecular layer of oil (about 25 micrograms) can spoil the experiment. A finger touched to a hair on one’s head can spoil it. It is also undesirable to put too much lycopodium powder on the water surface – a common student failing.
  • After steps 1 to 3, the students should observe a clean patch appearing as the powder moves away towards the edges. The powder returns as the alcohol dissolves in the water or evaporates.
  • After procedure 4, the powder is again seen to be pushed aside, this time by the oil. Now the powder does not return as it did with the alcohol.
  • After procedure 6, if the camphor seems lazy in its movement it is a sure sign that the water surface is oily. A full recleaning is necessary.
  • Here is a test for cleanliness before the dish is released for use. Fill the dish with water. Then put a drop of alcohol on the water surface with a very little powder on it. If the powder rushes to the edge and back again quickly, it is clean enough.
  • Step 7 could be done as a demonstration by the teacher. The powdered surface rushes away from the iron wire. The rise in temperature weakens the surface skin.

This experiment was safety-tested in July 2006

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Illustration of oil spreading

Rutherford Scattering
Properties of Matter

Illustration of oil spreading

Practical Activity for 14-16

Demonstration

This helps students to remember that olive oil molecules stick up out of water like grass on a lawn.

Apparatus and Materials

  • Transparent trough
  • Drinking straws
  • Plasticine

Health & Safety and Technical Notes

Read our standard health & safety guidance


The drinking straws are cut into similar lengths of about 2.5 cm. Roll a plug of Plasticine and force it into one end of each of the small lengths, closing that end and making a loaded cylinder. The amount of Plasticine used determines whether the straws float or sink. Once you find the right amount, the straws will float upright and bob up and down in the water if disturbed.

Procedure

  1. Drop a handful of about fifty of the loaded straws into water, from about 10 cm above the water surface. Observe the behaviour.

Photo courtesy of Mike Vetterlein

Teaching Notes

  • The straws should float upright and congregate together just like an oil film.
  • The patch is one straw deep - that is significant.
  • Olive oil has a long molecule. One end attaches to water and the other end is inert.

This experiment was safety-tested in July 2006

Up next

Estimating the size of a molecule using an oil film

Rutherford Scattering
Properties of Matter

Estimating the size of a molecule using an oil film

Practical Activity for 14-16

Demonstration

Finding the thickness of an oil film enables an estimate of the size of atoms to be made.

Apparatus and Materials

  • Oil film kit
  • Olive oil in a bottle, and some small dishes
  • Lycopodium powder and dispenser
  • Paintbrush, soft, 5 cm
  • Vegetable black, 250 g
  • Paraffin wax, white, 3 kg
  • Tin can
  • Bucket
  • Metre rule
  • Camphor in a bottle
  • Retort stand
  • Hand lens
  • Paper towels, large pack

Health & Safety and Technical Notes

Almost every class will contain several asthmatics. Lycopodium powder is dried pollen. See CLEAPPS guide L77 for advice on use of pollen.

Read our standard health & safety guidance


To empty a tray, put a bucket under the hole and release the bung. The trays should be washed carefully in a detergent solution and then flushed with cold tap water for a considerable time before storing with, for example, some card separating tray from tray.

Store the lycopodium away from the olive oil.

Procedure

  1. Place the tray on the bench, with the corner that has the drain hole hanging over the bench edge. Close the hole with the rubber bung from below. Partially fill the tray with clean tap water and then level it by careful use of the wedges. Fill the tray to over-brimming with further levelling. Finally, clean the water surface by slowly moving the metal booms from the middle to the two ends of the tray. Leave them there. The advantage of this arrangement is that it makes it easy to clean the water surface.
  2. Take the loop of very thin wire and dip it into the olive oil to catch a small drop.
  3. Image courtesy of Mike Vetterlein
  4. Hold the loop in the special holders at eye level in a clamp stand. Adjust the position of the loop so that the drop can be clearly seen against the 0.5 mm graticule through the magnifying glass. Using a second loop of wire which has also been dipped in oil, tease the original drop or run several drops together until it is 0.5 mm in diameter.
  5. If there is an excess of oil on the loop, it can be wiped with filter paper.
  6. Lightly dust the clean water surface with the powder and touch the 0.5 mm drop of oil onto the water.
  7. Image courtesy of Mike Vetterlein
  8. Use a rule to measure the maximum diameter of the patch of oil. (With some water supplies, the patch contracts to a smaller size soon after it has formed. This is probably due to water-softening agents attacking the oil, though this is not certain. Whatever the cause of the contraction, the proper measurement to take is the initial maximum diameter.)
  9. Place the booms, touching together, in a part of the water surface free from oil and then move them slowly apart to produce a fresh clean surface. Another student can then try the experiment.

Teaching Notes

  • It is important that each student has an opportunity to do their own experiment.
  • Students need to realize that if the oil has spread out to produce a patch that does not reach the edges of the tray, the film on the surface is likely to be one molecule deep. Furthermore, these chain molecules have one end in the water and the other in the air. They also need to realize that the volume of the oil film is the same as the volume of the initial drop.
  • From the 0.5 mm width ( d ) of the drop, its volume can be found, even if it is taken as a cube by students not capable of dealing with the volume of a sphere. From the diameter ( D ), the area of the oil film and its thickness can then be calculated. If the drop was treated as a cube, the area should be taken as a square. (Approximating to a cube and a square only involves a factor of 2/3 less than the more accurate result.)
  • Typical results:
  • d 3 = D 2 x length of the molecule
  • 0.5 x 0.5 x 0.5 = 250 x 250 x length of molecule
  • So the length of the molecule = 2 x 10 -9 m
  • There are approximately 12 atoms in the olive oil chain so the size of an atom is approximately 1.7 x 10 -10 m.

This experiment was safety-tested in August 2007

Up next

Dependence of size on method of measurement

Rutherford Scattering
Properties of Matter

Dependence of size on method of measurement

Practical Activity for 14-16

Demonstration

This introduces students to the idea that the value of a measurement depends on the nature of that measurement.

Apparatus and Materials

  • Rope or belt, 1.5 m
  • Metre rule

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Use the rope or belt as a tape measure, putting it around a student's waist.
  2. Remove the rope. Lay it straight and, with the aid of the metre rule, find the circumference of the waist.
  3. Invite students to calculate the diameter.
  4. As a thought experiment only, ask what the diameter would be if a wire were used instead of the rope ' particularly if the wire were pulled tight like that used to cut cheese!

Teaching Notes

  • Though students may think this experiment trivial, it starts an important idea. The idea that a measured result may depend on the way it was obtained is fundamental to operational physics. Neither atoms nor students' waists are hard: their size will depend on the energy involved in making the measurement.
  • The estimates for molecules or atoms lying side by side, or loosely attached to other atoms, or making mild collisions like those between air molecules, are approximations to reality.
  • With sufficiently violent collisions, one atom moves right through the electron structure of another. Scientists lose track of the lightweight electrons and see a collision in which there seems to be only a nucleus with a diameter 10 000 times smaller. Nuclear collisions are not restricted to alpha particles or other charged projectiles. Neutral atoms endowed with the same large energy will make the same kind of nuclear collisions. (Though it is difficult to accelerate uncharged particles and produce violent collisions between them.)

Thanks to Leon Firth for suggesting improvements to the teaching notes.

This experiment was safety-tested in December 2006

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