Demonstration

Rutherford’s scattering experiment was an ingenious piece of design and interpretation. Whilst it is not possible to reproduce the experiment in a school laboratory, it is well worth demonstrating how it was carried out using photographs, pictures and analogies.

Apparatus and Materials

• Pictures of Rutherford scattering (for example the two further down the page)

Health & Safety and Technical Notes

Read our standard health & safety guidance

Originally the scintillations were counted by eye: trained observers counted for a short time in a darkened room. Rutherford is reputed to have sung Onward Christian Soldiers as he waited for the next flash of light! Today, modern detectors, such as photomuliplier tubes connected to a data logger, would be used.

Much later, a similar method (deep inelastic scattering of electrons) was used to probe inside neutrons and protons and determine their structure: they are made of three smaller particles called quarks.

Procedure

1. It is helpful to show students a video of the alpha scattering experiment and to emphasize that this is not just one more measurement in atomic physics but rather one of the great turning points in physics. It changed scientists' picture of atoms permanently. (You may be able to get hold of a second-hand copy of the Nuffield A-Level version.)
2. Show students a picture of the layout of a scattering experiment showing alpha particles being fired at a ‘solid’ gold foil.

3. Most of the alpha particles go straight through the gold but a few bounce back. From this Rutherford deduced that the atom could not be solid (neither uniform nor a plum pudding but is mainly hollow with a tiny nucleus. See guidance note

   Developing a model of the atom: the nuclear atom

Teaching Notes

• 99.99% of alpha particles are undeflected. This implies that the atom is mainly hollow.
• Some alpha particles bounce back. This implies that there is a single structure in the atom which is more massive than the alpha particle and (probably) repels it.
• More careful studies carried out by Geiger and Marsden provided results that were consistent with a single nucleus carrying a positive charge +Ze where Z is the atomic number of the scattering atom.

• Students need help with these ideas. Analogies such as the three mentioned below will help.
• A haystack analogy: Suppose you wished to investigate the shape and size of a concealed object. Pretend you have a large mound or truss of hay and you suspect that there are some small but massive iron cannon balls hidden in it. Suppose you are not allowed to pull the hay aside. You might still investigate its secret store by firing a stream of machine-gun bullets into it. Let us make some predictions.

• If the hay is only a thin covering on a solid mound of cannon balls then all the bullets will bounce back or perhaps stop and never reappear.
• If there is only hay, and no cannon balls, then the bullets will go completely through the bale of hay, moving almost as fast as they went in.
• However if the mound was mostly hay with a few dense cannon balls scattered through it, spaced well apart, then many of the bullets will go straight through it and a few will bounce back. The proportion bouncing back indicates the spacing of the 'nuclei' in the hay. The more that bounce back, the closer together are the canon balls. To realistically model the nuclei in gold foil, 10 cm canon balls would need a distance of 10 km between them. This illustrates how tiny a nucleus is and how hollow an atom is.
• Marbles analogy: Another model might include marbles rolling down a slightly sloping table with a few spikes sticking out such as in a pin-ball machine. What would happen to the marbles?
• Experimental analogies: You can demonstrate magnetic, electrostatic and gravitational models in the experiments listed below. Rutherford himself used the magnetic model and analogy to explain his theory.
• How science works extension: This experiment provides an excellent opportunity to discuss how scientific theories and principles develop over time and the issues that can arise that may prevent them from being accepted instantly because they contradicted existing views. See the case study:

  Rutherford's alpha scattering experiment

• See also the guidance note:

  The great scattering experiments

  ...This can help students understand how a nuclear model of the atom came to be. The data and analysis may be too complicated for some students, but there is great value in using ‘real’ results in terms of the narrative of scientific discovery.
• There is supplementary information in the guidance note:

  Developing a model of the atom: a nuclear atom

This experiment was safety-checked in December 2006

Demonstration

This demonstration forms a part of the discussion about the scattering experiment performed by Geiger and Marsden for Rutherford. It uses the repulsive forces between magnets to represent the forces between nuclei and alpha particles. A swinging magnet models how an alpha particle is deflected by the repulsive force of the nucleus.

Rutherford himself used this model in explanations and lectures with obvious delight.

Apparatus and Materials

• Bar magnets, 3
• Cylindrical magnets, 4
• Thin-walled rubber tubing, 15 cm length
• Retort stand bases, 2
• Retort stand rods, 3
• G-clamps, 2
• Light rod
• Alpha particle tracks including a collision with a massive nucleus (e.g. nitrogen or oxygen)

• Alpha particle tracks including a collision with a helium nucleus

• Alpha particle tracks including a collision with a hydrogen nucleus

Health & Safety and Technical Notes

Read our standard health & safety guidance

The light rod should be about 1 metre long, either wood or aluminium tube, and about 1 cm in diameter.

The cylindrical magnets should be 3 cm long and 1 cm in diameter. They should be fairly light but strong enough to be repelled from the stationary magnet.

The bar magnets should be at least 6 cm x 1.5 cm x 0.5 cm.

The ideal (but impossible arrangement) would be a very long pendulum with its bob consisting of an isolated north pole so that it swings just above a stationary isolated north pole. Although this is impossible in a real model, it is important to make each magnet long so that its south pole is less important and less strong. The following paragraph explains why for the brave.

The inverse-square repulsion between the two north poles would make the bob follow a hyperbolic path, except for the effect of gravity on the bob. With a very long pendulum, the restoring force due to gravity might be so small compared with the magnetic repulsion that the orbit closely matched the alpha particle’s hyperbola. However, with real magnets there is always a pair of poles. If the magnets are short, the repulsive force between the pendulum magnet and the fixed magnet will be nearer to inverse-fourth power force. The restoring force due to gravity, which increases with displacement, will dominate the motion, except at very small approaches.

It is probably best to start with a collision which is almost head-on, with smaller deflections, before continuing with wider and wider collisions. To minimize gravity effects, limit the pendulum to fairly small amplitudes, but start it with a push. By doing this, the initial and final parts of the path will look almost straight, with the bend showing only during close approach, as with alpha particles.

Procedure

Setting up...

1. Use about 3 cm of the rubber tubing to secure one of the cylindrical magnets to the end of the light rod. Attach a second cylindrical magnet to the first one, using their mutual attraction.
2. Suspend the light rod by a short loop of flexible thread (a 2 cm to 5 cm loop is enough) from a bar held out from a retort stand. The light rod should be able to swing freely as a pendulum with the magnet at the lower end. It is best to clamp the base of the retort stand. This represents the alpha particle.
3. Secure the three bar magnets in a clamp so that similar poles are together. This represents the nucleus.
4. Put the clamp into a retort stand and boss directly beneath, and very slightly below, the suspended cylindrical magnets. Arrange the bar magnets so that they are facing the cylindrical magnets with similar poles. This represents a nucleus.
Carrying out the demonstration...
5. Draw the light rod to one side and let it swing towards the fixed magnets. You should be able to get it to bounce back.
6. Slide the wire loop of the light rod along the retort stand, so that the cylindrical magnets are hanging slightly to one side of the fixed magnets.
7. Repeat step 5 and show that the cylindrical magnets are deflected but don’t bounce back.
8. Repeat steps 6 and 7 until the cylindrical magnets are no longer deflected.
9. Replace the fixed bar magnets with a cylindrical magnet placed on the floor or a flat surface. It should be free to move. This represents an electron in an atom.
10. Draw the light rod to one side and let it swing over the loose magnet. The swinging magnet should knock the loose magnet over without being deflected itself.

Teaching Notes

• You can refer to cloud chamber photographs that show very rare large deflections of alpha particle tracks. Use this demonstration to show that these photographs imply that there must be something massive with which the alpha particles are colliding. The rarity of the collisions shows that most of the atom is hollow.
• By moving the line of the ‘alpha particle’ magnets attached to the light rod, you can show that they are not noticeably deflected if their path is more than about 5 cm away from the ‘nucleus’ of magnets clamped to the stand. In this model, the target is therefore about 10 cm across (5 cm either side of the nucleus). In Rutherford’s experiments, fewer than 1 in 10,000 was noticeably deflected. That means, in this model, the gap between nuclei would be about 1 km.
• By using the small cylindrical magnets as a target, you can discuss how the alpha particle can pass through the electron cloud without being deflected. It can also ionise atoms (by removing electrons) without being deflected. Refer back to the straight tracks in the cloud chamber.

Demonstration

This is another model for the scattering of alpha particles; this time using the electrostatic repulsion between the dome of a Van de Graaff generator and a table tennis ball.

Apparatus and Materials

• Van de Graaff generator

• Table-tennis (ping-pong) ball, coated with Aquadag
• Fine nylon thread
• Sellotape

Health & Safety and Technical Notes

If the table-tennis ball suspension is attached to the ceiling, ensure that an adult is available to hold the step-ladder while another adult works at a height.

Read our standard health & safety guidance

This electrostatic model gives a fairer illustration of the path of an alpha particle under nuclear repulsion. The magnetic model is the one that Rutherford used in lectures.

Magnetic model of alpha particle scattering

Procedure

1. The table tennis ball is coated with Aquadag to make it conducting.
2. Attach a long nylon thread to the ball with Sellotape. Suspend the thread so that the suspension is as long as possible - preferably from the ceiling.
3. Set up the Van de Graaff generator below the suspension so that the ball can swing freely near the sphere and at the same height.
4. With the ball touching the sphere, start the machine so that the two become charged.
5. Pull the charged ball to one side with an insulating rod. Let it fall back towards the sphere of the generator and watch its motion.
6. Move the suspension (or the Van de Graaff generator) so that the ball passes by the dome and is deflected only a small amount.

Teaching Notes

• The suspended ball represents the alpha particle which is repelled by the Van de Graaff sphere when both have charges of the same sign.

This experiment was safety-tested in April 2006

• A video showing how to use a Van de Graaff generator:

Demonstration

This model of alpha particle scattering uses ball bearings to represent alpha particles and a plastic hill to represent the force from a nucleus. The deflections are very clear and this can lead to some useful discussions.

Apparatus and Materials

• Ball bearings
• Flat board or tray

• Alpha particles scattering analogue (plastic hill and ramp)

Health & Safety and Technical Notes

To prevent ball bearings being scattered over the floor, this experiment can be done in a large tray. A framed glass plate as used in puck experiments is ideal.

Read our standard health & safety guidance

The plastic hill is a 1/ r shape, where r is the distance from the centre. Because it is in a uniform gravitational field in the laboratory, the ball bearings gain gravitational potential energy in proportion to 1/ r. This means that the force on them varies as 1/r ² . The Coulomb repulsion between a nucleus and an alpha particle varies in a similar way. The electrical potential energy is proportional to 1/ r and the electrostatic repulsive force is proportional to 1/ r ².

To avoid bounce at the lip of the hill, it is best to put the ramp against the edge of the hill.

Procedure

Setting up...
1. Roll the ball directly along a radius of the hill (i.e. aim it at the centre of the hill). Find a height on the ramp that gives the ball a moderate speed and clearly shows it being deflected straight back. Use this as the starting height for all your rolls.
Carrying out...
2. Let a ball roll onto the hill and show that it is deflected.
3. Move the ramp sideways without turning it. For each roll, the line of the ball’s initial path should be parallel to the first roll. Roll the ball again and note what happens.
4. Repeat step 3 a number of times. Show that the deflection depends on how close the ball’s path is to a head-on collision.
5. With more advanced students, you could show that a ball turns through a bigger angle if it is running more slowly.

Teaching Notes

• Explain to students that the shape of the hill represents the shape of the electric field around a nucleus. This means that the ball experiences a similar variation of force as an alpha particle does as it approaches a nucleus.
• This model allows you to study the path of a single ball approaching a single target ‘nucleus’. You can choose the line of the ball's approach. Explain that Geiger and Marsden had no such control. They could not study individual alpha particles. Instead, they allowed a hail of alpha particles to fall on the many atoms in a foil and observed how many were detected at various angles to the incident beam.
• Make the point that the hill represents the contents of just one atom in the solid. There would be millions of atoms and they are in a very tiny target (the gold foil). The narrow beam of alpha particles will be spread across billions of atoms. The gold foil target is much smaller than the apparatus. This means that the beam is as good as parallel, and the alpha particles which are scattered at a given angle will end up at the same place, regardless of where they passed through the target.

• You could explain it in a thought-experiment extension.
To represent the nuclei of a number of atoms in the gold foil, we could set up 20 of these plastic hills across the middle of the sports hall (5 across and 4 deep). We set up a ramp using a large board (about 2 metres across) and roll hundreds of ball bearings towards the target in the middle of the hall. Each ball bearing will be set off in the same direction, but we won’t be able to aim them at any particular hill. Afterwards, we can go round the edge of the hall and collect up the ball bearings, making a note of where they ended up. We would then count up how many went straight on, how many went to the side, and so on.
• You may need to make some assumptions about the sports hall floor – that it is perfectly flat and doesn’t slow down the ball bearings. Make the point that the ‘beam’ of alpha particles is about 2 metres wide. The reason that you need to use the space of the sports hall is so that the target is small compared with the size of the apparatus.
• Ask students how many ball bearings they think will pass through this set-up without being deflected. The answer is not very many. You can ask them how they could modify the model to allow more through without being deflected. The answer is to spread the hills out more. This will need more space, so you might have to suggest moving to the playground. However, even this would cause too many ball bearings to be deflected. In order to get 99.99% of the ball bearings passing through undeflected, the hills would have to be about 10 km apart. You would have to flatten an area the size of Wales to do the experiment. You would need a million or so ball bearings and thousands of helpers.

This experiment was safety-tested in April 2006

Demonstration

This demonstration shows students that light has a particle property: it packages its energy in small packets or quanta.

Apparatus and Materials

• Gold leaf electroscope

• Zinc-plate attachment
• EHT power supply with large series safety resistor
• Wire mesh
• Fine emery cloth, 1 piece
• Ultraviolet lamp (a blacklight UV lamp will not do - use one with a clear quartz envelope)
• Connecting leads
• Flexicam or webcam linked to a projector (OPTIONAL)
• Lamp, 12 V, 24 W and power supply (OPTIONAL) [Not a modern tungsten-halogen compact lamp which emits some UV]

Health & Safety and Technical Notes

The ultraviolet lamp should have a shield with a fairly small aperture (1 or 2 cm in diameter) so that neither you nor your students can see into the light source. Do not look into the ultraviolet lamp, or expose skin to the UV radiation.

Read our standard health & safety guidance

To help students see the gold leaf, you could use a flexicam or webcam connected through a computer to a projector, or you could use the lamp to cast a shadow of the gold leaf. (Remove the back plate of the electroscope and place the lamp below the leaf to cast a higher shadow.)

It may help if pupils have seen photocells at work in electric or electronic circuits, where light releases a horde of electrons from a sensitive surface in a vacuum and the horde acts as a current to do jobs for us. That might be called the ‘wholesale photoelectric effect’.

The EHT supply has a floating earth. You can use this to earth the case of the electroscope. Then, to charge the plate negatively, connect the EHT supply’s positive terminal to its earth, and use its negative terminal to charge the plate. To charge the plate positively, connect the EHT supply’s negative terminal to its earth, and use its positive terminal to charge the plate.

Procedure

1. Set up the gold leaf electroscope so that the pupils have a clear view of the leaf.
2. Thoroughly clean the zinc plate with the emery cloth and attach it to the electroscope.
3. Support the wire mesh a few centimetres away from the zinc plate. This mesh is connected to the case of the electroscope, which is earthed.
4. Use the EHT supply to charge the plate on the electroscope negatively.
5. Switch on the ultraviolet lamp so that it illuminates the plate. Observe the effect on the gold leaf.
6. Repeat the experiment with the plate and electroscope charged positively.
7. Finally, repeat the experiment with the plate negatively charged. When the charge is clearly seen to be leaking away, put a sheet of glass between the light source and the charged plate.

Teaching Notes

• The negatively charged zinc plate illuminated by ultraviolet radiation loses charge, suggesting that the radiation is ejecting electrons from its surface.
• It only loses charge when it is negatively charged. This suggests that it is negative charges that are ejected by the ultraviolet radiation. They are helped by an electric field which is negative at the plate, but they are held back by an electric field which is positive at the plate. You can tell students that more complex experiments can show that the particles ejected are electrons.
• The piece of glass absorbs ultraviolet radiation. When it reduces the ultraviolet radiation, the discharge slows. This shows that it is the ultraviolet radiation that ejects the electrons from the zinc.
• Normal, visible, light does not release electrons – however long it is left and whatever its intensity. You can show this using a lamp or by referring to the ambient light.
• When the ultraviolet lamp is first turned on there is no delay in the production of electrons. If the discharge were relying on a continuous stream of light, there would need to be a delay to build up enough energy in the metal to eject each electron. The fact that there is no delay is evidence that the energy arrives in quanta.
• More complex experiments can show that the radiation (whether visible or ultraviolet) arrives in quanta. You can say that these are called photons.
• Refer students to the clicks they hear when gamma radiation is detected by a Geiger-Müller tube. The radiation is part of the electromagnetic spectrum but is clearly arriving at the Geiger-Müller tube in quanta.
• The experiment shows that it is the wavelength of the radiation that is important rather than the intensity. You can tell students that more complex experiments can show that the energy of a quantum is given by E = hf.

This experiment was safety-tested in April 2006

Class practical

Some students may have looked at a line source of light through an ordinary grating. Here they look at a point source of light through two identical gratings. They can try crossed gratings or rotating gratings, to get an idea of the pattern that they produce.

Apparatus and Materials

For each student or group of students

• Coarse diffraction gratings, 2
• Finely woven cloth, 2 pieces
• Rotating devices, 1 (if available)
• Sheet of plastic grating replica (if available)
• Compact light source and power supply

Health & Safety and Technical Notes

The compact light source is now known to be a source of UV radiation. Do not allow students to approach nearer than 1.5 m. If this is a possibility, set up a 6 mm-thick sheet of glass as a UV filter.

Read our standard health & safety guidance

The microscope slide of pieces of grating is a model of a crystal with grains in various directions. You can show pictures of what happens when X-rays fall onto a single crystal of potassium alum and powdered potassium alum. These pictures are evidence for the diffraction of X-rays by planes of atoms in a crystal.

If you can get a sheet of plastic grating replica, you can make a composite grating on a microscopic slide. This is an analogue of a crystal. Cut the grating replica into small pieces, a few millimetres across. Stick these onto a 5 cm glass slide, jigsaw fashion, with double sided sellotape so that the rulings are in random directions. Put a second slide over the top to cover the pieces.

Procedure

1. Set up the compact light source at one end of the laboratory; put it fairly high up so that everyone can see it. From a distance, it should behave like a point source of light.
2. Students hold a grating near to one eye and look through it at the distant light source.
3. They then look at the same source holding a tightly stretched piece of finely woven cloth near their eye. A piece of silk or fine cotton should work. This acts as a two-dimensional grating.
4. They can try placing a second grating on top of the first one so that the two sets of slits are at right angles.
5. Ask the students what they would see if the woven cloth were rotated. They can try the special rotating device if it is available.
6. Put the composite grating in the beam of light and note the diffraction pattern on a screen.

Teaching Notes

• Looking through a single grating at a point source produces multiple images of that source; they are coloured if the source is white. The result from two crossed gratings is surprising: rather than two sets of diffraction patterns at right angles, there are more ‘spots’ to be seen. Altering the angle between the gratings changes the pattern.
• Discuss the shape of a diffraction pattern from a single grating. (Multiple images of the light source; coloured if the source is white.) Ask students to predict what they expect to see from crossed gratings.
• Bring out the fact that instead of two diffraction patterns at right angles, the crossed gratings produce a more complex pattern with more spots than the two single gratings.
• The crossed gratings produce a pattern similar to the piece of cloth, which is like a two-dimensional grating.
• The composite grating has multiple, randomly placed pieces of grating. This is like a crystal – with randomly oriented domains. The result is a circular diffraction pattern. Discuss how this is produced by the addition of the diffraction patterns in each direction. They are overlaid on each other.
• If a crossed grating is rotated in a holder, than an image of concentric circles is produced (by persistence of vision), modelling powder photographs of crystals or looking at street lights through steamed up windows.
• This is useful preparation for seeing the diffraction pattern from a crystal – as with the Electron diffraction experiment...

  Electron diffraction

This experiment was safety-tested in May 2006

Demonstration

Visible diffraction rings on a screen show the wave behaviour of electrons.

Apparatus and Materials

• Electron diffraction tube
• Power supply, 0 - 5 kV (Extra High Tension, EHT)

Health & Safety and Technical Notes

For use with a diffraction tube, the 50 MΩ. safety resistor can be left in the circuit. This will reduce the maximum shock current to less than 0.1 mA..

Leads used MUST have shrouded connectors and insulation capable of withstanding 5 kV.

Make all connections with the power supply turned off. Do not adjust connections while the EHT is switched on.

Electron beam tubes are fragile. Because they are evacuated, they will implode if they break. The tubes are also expensive, so handle them with great care. Use the purpose-designed holders during practical work.

Note that when switching the EHT supply off, it can take a little while for the voltage output to fall to zero. Allow sufficient time before disconnecting.

Read our standard health & safety guidance

The electron beam strikes a target of a thin deposit of graphitized carbon on a metal grid situated in the exit aperture of the anode. It is the wave nature of electrons passing through the carbon lattice that produces the diffraction pattern.

The cathode is indirectly heated, so it may take a few moments to warm up.

The wavelength, λ, of the electrons is given by De Broglie’s equation λ=h/ p where h is Planck's constant and p is the momentum of an electron.

Procedure

Setting up...

1. Connect the heater supply of 6.3 volts to the filament.
2. Connect the filament to the negative terminal of the EHT supply. Earth this terminal.
3. Connect the positive terminal of the EHT supply to the anode of the diffraction tube. Set the accelerating voltage to about 4,500 volts.
Carrying out...
4. Switch on the heater supply and the accelerating voltage. Rings should appear on the screen.
5. Bring a strong magnet close to the tube. Show that the rings are distorted.
6. Show how the rings change as the voltage is varied between 3,500 and 5,000 volts.

Teaching Notes

• The diffraction rings are caused by the electrons diffracting and interfering as they pass through the regular crystal structure of the graphite. They are behaving like waves and the graphite’s crystal structure acts as a grating. As the crystals are arranged at any angle, each crystal produces a diffraction pattern, and their diffraction patterns combine around 360° to form rings. This is the same as the microscope slide made from the cut up pieces of a plastic diffraction grating in the

  Two-dimenstional diffraction grating experiment


• Deflecting the pattern with a magnet shows that the pattern is being produced by moving charged particles, rather than light or some other form of radiation. It introduces the dual nature of the electrons: they behave like particles when they are accelerated, like waves as they pass through the graphite foil, and like particles again as they are deflected in the magnetic field. This is an example of complementarity. See guidance note...

  Electrons behaving like waves

• The diameter of the rings will change as the accelerating voltage changes. It seems that the more energy the electrons have, the shorter their wavelength.
• The pattern resulting from the passing of a beam of electrons through graphite is very similar to a beam of X-rays passing through the powdered potassium alum crystal. It suggests that electrons undergo diffraction, and will therefore interfere in the same way as X-rays and other waves.

This experiment was safety-tested in March 2008

Related Guidance

A video showing how to use an electron diffraction tube: