# Gravitational model of alpha particle scattering

##### 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

#### 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.

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/r2. 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/r2

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
a
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
b Let a ball roll onto the hill and show that it is deflected.

c 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.

d Repeat step c a number of times. Show that the deflection depends on how close the ball’s path is to a head-on collision.

e With more advanced students, you could show that a ball turns through a bigger angle if it is running more slowly.

#### Teaching notes

1 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.

2 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.

3 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.

4 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.

5 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