# Episode 521: Rutherford’s experiment

Lesson for 16-19

- Activity time 110 minutes
- Level Advanced

In this episode, students look in detail at Rutherford’s experiment and relate it to a mechanical analogue.

Lesson Summary

- Discussion: Recollecting the significance of Rutherford’s experiment (10 minutes)
- Discussion: Rutherford’s experiment (20 minutes)
- Demonstration: Collisions and momentum (10 minutes)
- Discussion: Rutherford scattering and Coulomb’s law (10 minutes)
- Student experiment or demonstration: The Gravitational model (30 minutes)
- Student questions: Rutherford experiment and atomic structure (optional) (20 minutes)
- Question: Rutherford’s results (optional)
- Discussion: Models in physics (10 minutes)

## Discussion: Recollecting the significance of Rutherford’s experiment

As a preparatory task, ask your students to revise what they have previously learned about Rutherford’s α-scattering experiment. What idea of the atom did it suggest? (The nuclear model.) What model of the atom did this replace? (Thomson’s plum pudding

model, in which atoms are seen as essentially small balls composed of a mixture of positive and negative electric charge, with no concentration of charge at any particular position.)

Is plum pudding

a good name for the model? (Yes, if you see the negative electrons dispersed throughout a spherical lump of continuous positive charge, not so good if the volume of the atom has both positive and negative particles continuously distributed through it – students may well be recalling different pictures from different sources.)

## Discussion: Rutherford’s experiment

Now you can present a more advanced exposition of the experiment. Why did Rutherford ask for the experiment to be done? Experiments on the absorption of β particles had also shown that sometimes the β particles were back scattered

. Rutherford suggested that Geiger and Marsden should try looking for similar behaviour with α particles. Rutherford thought it was highly unlikely; because α particles are relatively massive compared with electrons, it was predicted that the αs would simply suffer a series of small deflections. They were expected to travel more or less straight through the absorber.However, Rutherford’s main concern was to give Geiger and Marsden something to do that would occupy them and get them some useful hands-on experience, rather than expecting them to get any very exciting results.

Show a diagram of the apparatus. The absorber was a thin gold metal foil. Why use gold? (Thin gold foils, typically 250 atoms thick, were easy to make and readily available.) Why thin? (as are easily absorbed.)

As expected , *virtually all* the αs went straight through, but about 1:8000 were turned through large angles (reflected or back-scattered). An 8 kBq a source gives one large-angle scattering per second.

The chance of a series of small *deflections* resulting in a *reflection* is far too small to account for what was observed.

Rutherford was astonished at the result: It was quite the most incredible event that ever happened to me in my life. It was as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you!

(You may find other versions of this quote, because Rutherford described his experience on many different occasions.)

Episode 521-1: Rutherford scattering (Word, 27 KB)

Episode 521-2: Alpha particle scattering experiment (Word, 48 KB)

## Demonstration: Collisions and momentum

Use colliding balls to show what happens to a projectile particle hitting a target particle; as the target ball mass gets bigger, the follow through by the projectile gets less. Use a selection of ball bearings, marbles etc on some curtain track, or trolleys loaded with different weights. When the target mass is small relative to the projectile mass, the missile follows through. For equal masses the projectile stops and the target sets off with the speed of the projectile. If the target mass is large, the projectile rebounds. (If your students have already studied momentum, they should be able to predict the outcome of each of these demonstrations.)

The back scattering of αs through large angles implies (i) all the positive charge is concentrated together, and (ii) the mass of the concentrated positive charge must be quite a bit larger than of an α particle.

## Discussion: Rutherford scattering and Coulomb’s Law

Rutherford assumed that (i) Coulomb’s Law was obeyed down to very small distances, and that (ii) most of the mass of the nucleus was concentrated into a very small volume – the nuclear atom that resembles a miniature solar system. (Because the analysis works, we can take this as proof

that Coulomb’s Law *is* valid down to distances about the size of a nucleus.)

Show a diagram to explain how the terms impact parameter p and scattering angle f are defined. Ask: how would you expect the number of αs scattered through angle f to depend upon (i) the impact parameter p, (ii) the charge on the target nucleus Z, and (iii) the energy of the α particles? (As *p* increases f decreases (force weaker); as Z increases f increases (greater repulsive force); as energy increases, f decreases (less interaction

time).)

Episode 521-3: Rutherford’s picture of alpha particle scattering (Word, 298 KB)

## Student experiment or demonstration: The Gravitational model

The gravitational model

analogue provides a practical way for students to get a feel for the physics of alpha-scattering. Roll a marble past the model to see it deflected. You can change the speed and impact parameter. Students can change these parameters systematically and observe the effects.

The model is designed so that, as the slope of the model

gets steeper, the component of gravity parallel to the slope opposing the motion of the ball also gets larger. The actual shape is such that at any position on the slope a distance *r* from the centre of the hill

, the component of a particle’s weight parallel to the slope ~ 1*r*^{ 2}. (Revision of the relationship between 1*r* potential and 1*r*^{ 2} force can be done here if desired.)

If possible, it’s worth getting several gravitational models so that students can work with them in small groups. (The model

can also be used when studying gravity. Turn it upside down to become a potential well

so that you can demonstrate orbits, and discuss the difference between bound and unbound particles

.)

Episode 521-4: The 1/r hill: Slope and force

Episode 521-5: A model for Rutherford scattering (Word, 37 KB)

A good simulation of alpha particle scattering could be used if desired.

## Student questions (optional): Rutherford experiment and atomic structure

Episode 521-6: Rutherford experiment and atomic structure (Word, 28 KB)

## Question: Rutherford’s results (optional)

Some actual results are given. Students may plot a graph to test Rutherford’s relation for α -scattering

Episode 521-7: Rutherford scattering data (Word, 41 KB)

## Discussion: Models in physics

If time permits, you might have a discussion on the role of models (physical and mathematical) in physics. In what ways is the gravitational model similar to Rutherford scattering? In what ways does it differ? In which ways is the solar system a good model for the nuclear atom? What other models do your students know?