Magnetic model of alpha particle scattering

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.