Bohr Model
Quantum and Nuclear

Model of the atom

for 14-16

At the beginning of the twentieth century, there were still some sceptics who were not convinced of the existence of atoms. Since the discovery of radioactivity, physicists have been probing and smashing atoms. They have devised and developed theories to try to describe their structure and explain their behaviour.

In this collection, you can give students a glimpse of some of the groundbreaking experiments that have changed the way that physicists have thought about atoms and the particles inside them. If you follow the experiments in the order below, students will be taken from Rutherford’s first suggestion of a nucleus through to a model based on the wave behaviour of electrons.

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Alpha particle scattering

Bohr Model
Quantum and Nuclear

Alpha particle scattering

Practical Activity for 14-16

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

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Magnetic model of alpha particle scattering

Bohr Model
Quantum and Nuclear

Magnetic model of alpha particle scattering

Practical Activity for 14-16

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.
  5. Carrying out the demonstration...
  6. 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.
  7. 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.
  8. Repeat step 5 and show that the cylindrical magnets are deflected but don’t bounce back.
  9. Repeat steps 6 and 7 until the cylindrical magnets are no longer deflected.
  10. 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.
  11. 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.

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Electrostatic model of alpha particle scattering

Bohr Model
Quantum and Nuclear

Electrostatic model of alpha particle scattering

Practical Activity for 14-16

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

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:

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Gravitational model of alpha particle scattering

Bohr Model
Quantum and Nuclear

Gravitational model of alpha particle scattering

Practical Activity for 14-16

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

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.
  2. Carrying out...
  3. Let a ball roll onto the hill and show that it is deflected.
  4. 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.
  5. 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.
  6. 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

Up next

‘Wholesale’ photoelectric effect

Bohr Model
Quantum and Nuclear

‘Wholesale’ photoelectric effect

Practical Activity for 14-16

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

  • A video showing how to use an oscilloscope:

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Two-dimensional diffraction grating

Bohr Model
Quantum and Nuclear

Two-dimensional diffraction grating

Practical Activity for 14-16

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

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Electron diffraction

Bohr Model
Quantum and Nuclear

Electron diffraction

Practical Activity for 14-16

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.
  4. Carrying out...
  5. Switch on the heater supply and the accelerating voltage. Rings should appear on the screen.
  6. Bring a strong magnet close to the tube. Show that the rings are distorted.
  7. 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:

Up next

Developing a model: the nuclear atom

Ionising Radiation
Quantum and Nuclear

Developing a model of the atom: the nuclear atom

Teaching Guidance for 14-16

Students will have seen signs of electrons and positive ions (perhaps carrying a current through ionized neon or helium). On this evidence, Thomson proposed his ‘plum pudding’ model, in which the negative electrons sit in the positive nucleus like currents in a bun.

However, students may well have been exposed to images, stories, films and textbooks which incorporate a version of a planetary model. They may find it strange that you even mention the plum pudding model. It is not difficult to persuade them that this model has been superseded. What is more challenging is to take them beyond the simple pictures that they may have seen and to give them some idea of the size of atoms and nuclei – i.e. that the atom is not just hollow but extremely hollow (too hollow to represent in simple images).

The Rutherford-Bohr model

Rutherford proposed the idea of a central nucleus in an atom in around 1908. The nucleus contains the atom’s positive charge whilst the electrons are outside. From back scattering experiments, he showed that the radius of the nucleus was 100,000 times smaller than the radius of an atom. This is equivalent to the head of a pin (the nucleus) in the middle of a large stadium (the atom). Consequently, the relative sizes of the atom and its nucleus cannot be shown in simple diagrams.

back scattering experiments


Given that the electrons were easily removed, Rutherford assumed that they were on the edge of the atom. There emerged a picture of orbiting electrons that mirrored the planets orbiting the Sun.

Problems with the planetary model

However, whilst the existence of the hollow atom is well accepted, there have always been serious objections to a classical planetary model. The main objection is that the orbiting electrons are moving charges and should radiate electromagnetic waves, losing energy. This loss of energy would cause them to spiral into the nucleus. In other words, there was no way of explaining why an atom with orbiting electrons is stable.

The Bohr model

This issue of instability was addressed by Niels Bohr in 1913. He combined Rutherford’s model with the quantum ideas put forward by Max Planck at the turn of the century. Bohr no longer referred to orbits but only to ‘stationary states’. Atoms could exist in a stationary state and be stable. Spectral lines were a result of transitions between these stationary states. Bohr’s model was the first step towards an atom that is described by quantum mechanics. It no longer followed classical laws – particularly those of electrodynamics. The reason for this was straightforward: classical electrodynamics could not explain how the electron could be bound to the nucleus and be stable.

In the late 1920s, the quantum mechanics of Schrödinger and Heisenberg offered two further developments to Bohr’s model.

The atom: a quantum mechanical model


These models become ever more difficult to represent in simple images. Perhaps because of this, the simple planetary picture has endured as one of the icons of twentieth century atomic physics, even though it was superseded within a few years of being proposed.

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Alpha particles as tools

Bohr Model
Quantum and Nuclear

Alpha particles as tools

Teaching Guidance for 14-16

When Geiger and Marsden carried out the gold foil experiment in 1909, a lot was already known about alpha particles. Although the rare back scattering was a surprise to Rutherford, he knew that the bullets he was firing were helium nuclei.

Rutherford had been working on alpha particles for a number of years. This was before the development of the cloud chamber and mainly relied on recording alpha particles with photographic plates. Between 1903 and 1908, he had:

  • deflected alpha particles in electric and magnetic fields and determined their charge to mass ratio (half the value for a hydrogen ion). This meant that they were probably either He2+or singly ionised hydrogen molecules; Rutherford favoured the former.
  • with Frederick Soddy, published a paper in which they estimated the mass, energy and speed of alpha particles.
  • noticed small deflections of alpha particles by air and mica (by firing them through the target at a photographic plate).
  • tried to count and collect alpha particles to measure their charge; he later measured their charge (as +2e).

It was whilst trying to get a reliable counter that he and Geiger noticed the amount of scattering. At first, the scattering was a frustration. But once Geiger had noticed some large angles, they turned it into the famous investigation that began in 1908.

In 1909, Rutherford and Royds collected the gas that was formed when alpha particles were trapped in a tube and showed that it was helium. So they were now sure that alpha particles were doubly-ionised helium atoms, He2+.

However, because Rutherford still thought of atoms as plum puddings, he was still astonished when some of them were back scattered in the Geiger and Marsden experiment. It was sometime in 1910 that Rutherford put forward his idea of a nuclear atom and so the alpha particle itself could be referred to publicly as a helium nucleus.

Up next

The great scattering experiments

Bohr Model
Quantum and Nuclear

The great scattering experiments

Teaching Guidance for 14-16

Hans Geiger was one of Rutherford’s students at Manchester University. He had been trying to make a workable detector to count alpha particles. During his investigations, he found that the alpha particles were deflected when they passed through a mica film. He told Rutherford of this effect.

Rutherford encouraged Geiger and Ernest Marsden, an undergraduate student, to investigate the deflections. They counted scattered alpha particles by the faint scintillations they make on a screen.

Only a few bounced back. Rutherford is widely quoted presenting this as an amazing result, saying 'it was as if you fired a 15" shell at a piece of tissue paper and it came back to hit you'. From Geiger and Marsden's results, Rutherford devised his new model of the atom: a very small massive nucleus with electrons so far out, and so light, that the alpha particles which were seriously deflected met the full force of a bare nucleus. He assumed that the nucleus carried a charge of +Ze, where Z is the serial number in the periodic table. Using this theory, the force between the alpha particle, itself a helium nucleus, and a gold nucleus is the inverse-square law Coulomb force of electrostatic repulsion.

Geiger and Marsden went on to make a great series of measurements of the deflections of a narrow beam of alpha particles that hits gold leaf in a vacuum. Their measurements served to test his new model.

Alpha particles making a very close approach to another nucleus are deflected through a large angle. Those missing the target widely are deflected through a small angle. Measurements over a big range of angles serve to investigate the field of force inside the scattering atoms over a large range of distances from the centre.

Rutherford assumed an inverse-square law of repulsion between the big electric charge on the massive nucleus of the gold atom and the smaller charge on the alpha particle flying past it. That is equivalent to Newton’s assumption of an inverse-square law attraction between the massive Sun and a planet. Instead of the simple circular orbits which serve approximately for planets, the change to a repulsive force predicts a different shape: hyperbolas. The alpha particle sails in, bends around, and sails out again on another almost straight track in a new direction. The simple calculation with circular orbits that predicts Kepler III becomes more complicated.

Instead of measuring the orbits of a few planets, Rutherford had to use hordes of little alpha particles to give him a statistical test. He made his theory predict the number of particles that an observer would count on a receiving screen in various directions, in some standard time. In calculating that prediction he simply used an inverse-square law of repulsive force and Newton’s laws of motion.

The table of actual measurements of scattered alpha particles for various angles (taken from Geiger and Marsden’s original paper) shows how the numbers counted fit the predictions for an inverse-square law of force.

Geiger and Marsden's table of results compared with predictions using Rutherford's model.

* Of path of alpha-particles. † Number of scintillations seen, for deflection A°, in a standard time.

Note:

In the actual experiments Geiger and Marsden made one set of measurements for the larger angles of deflection, and another set, with a much smaller radioactive source, for the smaller angles. To make one complete set in the table above, the numbers for smaller angles have been multiplied up to fit the set for larger angles. The multiplying factor was provided by experiment because counting was done for 30° in both data sets.

Finding the charge on the nucleus

Rutherford’s theory also predicted the way the count on a fixed screen would depend on the speed of the alpha particles:

N ∝ 1/ v 4 and on the electric charge of the scattering nucleus:

N ∝ (Ze)2 Chadwick used this to measure the charge on the nuclei of a number of elements. He used thin sheets of copper, silver and platinum instead of gold and measured the scattering of alpha particles from each. From his counts, with Rutherford’s theory, he calculated the charge on the nucleus of each of those nuclei.

His results were: copper 29.3 electron charges, silver 46.3 electron charges, platinum 77.4 electron charges, with expected errors of about 1%. The serial numbers of those elements, arranged in order of atomic weights and placed in the period table are: 29, 47, 78. Chadwick’s measurements showed that the nuclear charge is the atomic number.

Nowadays the charge of a nucleus is understood in terms of the proton number, and its value is measured in electron charges. Originally, from Geiger and Marsden's scattering experiments, it was deduced that the nucleus had a charge of about half the atomic weight multiplied by the electron charge.

Back-scattering to measure the size of the nucleus

From the known mass and speed of the alpha particles, Rutherford could calculate the distance of closest approach to a nucleus. This is the distance from a gold atom’s centre at which an alpha particle making a rare head-on collision would come to rest momentarily and bounce straight back.

Rutherford tried different energy alpha particles, and found some for which the measured number deviated from the predicted number. He suggested that, at this energy, the alpha particles were reaching the nucleus and being assimilated into it. This, he said, gave an indication of the radius of the nucleus. That radius turned out to be 10,000 times smaller than the radius of the atom.

Thanks to David Baum for pointing out an error on this page, now corrected. Editor

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Light behaving like a particle

Photoelectric Effect
Quantum and Nuclear

Light behaving like a particle

Teaching Guidance for 14-16

No sooner do students see that light has a wave property (and have measured its wavelength) then this story is upset with further demonstrations that light has a particle property; it packages its energy in small quanta. The idea that radiation packages its energy in quanta proportional to frequency first arose in Planck’s mind when trying to fit the theoretical prediction for the energy distribution in the spectrum of a perfect radiator with the experimental results. The variation of the specific heat of materials with temperature also appeared to require a quantum rule. The photoelectric effect appeared to be pointing in the same direction when Einstein applied his clear vision to it in 1905 and was awarded the Nobel Prize for his efforts.

It is assumed that 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’. In this, light ‘flicks’ electrons out of a metal, ultra-violet light tearing them out with the crack of a whip and X-rays hurling them out. This strange interchange between radiation and electrons throws much ‘light’ on the micro-physical world.

A Geiger-Müller tube responding to gamma rays is demonstrating the photoelectric effect of those very energetic photons. However, the random counting is due to the random instability of the parent radioactive nuclei, not the effect of photons arriving at random from a steady stream of radiation. But if you shine a steady stream of ultra-violet light or light from a match onto a Geiger-Müller tube, with a thin mica window, then the Geiger-Müller tube will show random counts. A sheet of glass placed between the light source and the Geiger-Müller tube will show that it is not the visible light which is the active agent.

Further experiments

This experiment suggests some of the photo-electric effect story, but it does not show that the negative electricity is coming out in particles: electrons. It also does not show that light is arriving in bundles of energy: quanta. It only suggests that there is some connection between the wavelength of the light and its efficacy in ejecting negative charge.

More complex experiments, or perhaps a film, are needed to show:

  • photons arriving one by one
  • that the particles ejected are electrons with the usual value of e / m
  • that the electrons emerge with a given illumination, with a variety of speeds, the slower ones having probably lost energy by travelling through the outer layers of the metal
  • that with light of a given frequency, all the electrons ejected have the same maximum energy. This is the basis of Einstein’s equation, Eelectrons = hflight − Φ, where Φ is the ‘work function’ and h is the Planck constant.
  • that the maximum energy of the ejected electrons is determined by the frequency of the light used and not by its intensity. Brighter light only produces more electrons and not faster ones
  • that when the light is first turned on there is no delay in the production of electrons as one would expect if a continuous stream of light had to build up enough energy in the metal to eject each electron in turn. This is especially an impressive story with weak light. Sometimes an electron is ejected early, sometimes it may be later and so we are forced to conclude that the arrival of quanta is random in time.

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Electrons behaving as waves

Bohr Model
Quantum and Nuclear

Electrons behaving as waves

Teaching Guidance for 14-16

Students will know that electrons carry energy and momentum when they are moving. Yet these moving electrons seem to be guided to an interference pattern just like waves of light; or just like photons of light in the micro-physical world.

In the macro-physical world, large particles such as tennis balls and people do not display wave behaviour; wavelengths associated with such particles, at usual speeds, are so extremely minute that it won’t be possible to observe the diffraction or interference pattern associated with them. Nevertheless the behaviours of waves and particles in the micro-physical world are not entirely separate. Moving particles do follow wave directions, and it is the wave which predicts a probability of where to find the particle. The particles are guided by ‘matter waves’. Wave-particle duality was first suggested by Louis de Broglie about a century ago.

This raises the question of whether electrons (and other tiny particles) are particles or waves. Many observations in atomic physics can be treated using the particle model on its own. Others require the wave model. Both models prove to be useful and, despite their contradictory nature, must both be used for a full description. The two aspects of the electron both contradict and complement one another: both aspects are needed for a complete description. Niel’s Bohr’s solution was the principle of complementarity.

The Complementarity Principle says that sometimes electrons have the properties of particles and sometimes the properties of waves, but never both together. Their two types of behaviour complement each other but never coexist. The type of behaviour that is shown usually depends on the measurement technique being used. To put it another way, ask a wave-type question and you will get a wave’s answer. Ask a particle-type question and you will get a particle’s reply.

Bohr’s interpretation was that the two irreconcilable descriptions should be applied in turn but cannot be applied simultaneously. They are never in direct conflict, because it is impossible to determine at the same time all the information required to make the two images precise.

This relates to Heisenberg’s Uncertainty Principle . The more precise the observations of one picture, the less precise the other becomes. Define the wavelength of an electron sharply enough and the attempt to apply the particle model will surely fail. Localize the electron definitely enough and the wave model fails.

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The atom – a quantum mechanical model

Bohr Model
Quantum and Nuclear

The atom – a quantum mechanical model

Teaching Guidance for 14-16

The Bohr planetary model of the atom is often what sticks in students’ minds. It provides a neat and familiar picture of electrons orbiting a central nucleus like planets around the Sun. Because of this, it can be challenging to replace this picture with one that more accurately represents the quantum-mechanical model used by modern physicists: an atom with a tiny nucleus with probability waves instead of sharp orbits to describe the distribution of electrons, which have fuzzy positions but definite energy levels. Nevertheless, students should get a glimpse of this more modern model.

The locations and motions of the electrons are described by their matter waves. These wave patterns, which are written as equations when they are too difficult to sketch, predict the probability of finding an electron in a given region of the atom. They provide the betting odds, never the certainty. Yet the betting is useful: it predicts definite energy levels; it explains chemical bonding by electrons; and, when applied to particles in the nucleus, they not only explain the known random laws of radioactivity but also predict new nuclear particles.

Although this picture dispenses with electrons in neat, sharply defined orbits, it still gives them fixed energy levels. Electrons in the higher energy levels are more likely to be found in the outer regions of an atom, some distance out from the nucleus.

Where did this model come from?

Bohr’s planetary model had begun the process of introducing quantum theory to the structure of the atom.

Developing a model of the atom: radioactive atoms


Bohr introduced the idea of stationary states in which the atom was stable. Transitions between these states explained the existence of spectral lines. In the case of hydrogen, he was able to derive energy levels: transitions between his predicted energy levels matched the lines in the hydrogen spectrum. However, his model could not predict energy levels for any other atoms (though those of the hydrogen-like alkali metals could be approximated}.

It took the work of Heisenberg and Schrödinger to separately come up with ways of describing more fully the quantized energy levels of atoms. Heisenberg used matrices and Schrödinger developed a wave equation. It is solutions of Schrödinger‘s equation that provide pictures of electrons’ probability densities around the nucleus of an atom.

Thanks to Nathan Rasmussen for pointing out an error on this page, now corrected. Editor

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Evidence for the hollow atom

Ionising Radiation
Quantum and Nuclear | Forces and Motion

Evidence for the hollow atom

Teaching Guidance for 14-16

The main and first evidence for the hollow atom came from...

Rutherford's alpha scattering experiment


However, the first evidence students see for a hollow-atom often comes from cloud-chamber photographs. Although this may be historically back to front, it is reasonable to use the cloud chamber photographs as the first indication that atoms are mainly empty.

Chronology of evidence

Rutherford had devised his model of a nuclear atom by 1910, before alpha particle tracks were photographed in cloud chambers (c1911). However, Rutherford and Wilson worked in the same laboratory so it is likely that Rutherford had seen tracks in cloud chambers.

The evidence provided by cloud chamber photographs and the inferences that can be made are extremely useful whether you present them as preparation for the Rutherford model or follow-up support for it.

Evidence from cloud chambers

Most of the time there is just a straight track produced when an alpha particle passes through the cloud-chamber, producing ions. Mostly, these ions are produced by inelastic collisions with electrons in neutral particles. An alpha particle will have around 100,000 inelastic collisions before it no longer has energy stored kinetically. The number of collisions shows that electrons are easily removed.

The straightness of the tracks shows that:

  • an electron has a mass that is much smaller than the mass of an alpha particle (now known to be about 7000 times smaller).
  • the atom is hollow: each straight track represents about 100,000 collisions without any noticeable deviation. All of these collisions missed anything with significant mass. During a session, the class might observe 1000 tracks between them – all of which are straight.

Therefore, in all of these 100 million collisions with atoms, the alpha particles never hit anything with significant mass. So most of the atom is empty.

However, students will see photographs that show large deflections of alpha particles. These are rare events (requiring thousands of photographs to be taken). They show that:

  • there is something in an atom that has a mass that is similar to the mass of an alpha particle; only a target with a comparable mass could cause a large deviation.
  • this mass is very concentrated; the rareness of the forked tracks shows that most alpha particles miss this massive target.

Evidence from alpha particle scattering

The hollowness of the atom is treated more quantitatively in the Rutherford scattering experiment. In this, 99.99% of the alpha particles are undeflected. This gives an indication of how tightly the positive charge of the nucleus is packed together.

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