Early in the $20th$ century, many physicists were investigating the recently discovered phenomenon of radioactivity, the process whereby unstable nuclei emit radiation. One kind of radiation they found consisted of what they called α-particles (alpha-particles).
These $\alpha  - $particles were known to have a similar mass to the smaller atoms (such as hydrogen, helium and lithium) and had relatively high kinetic energies. Hence, they were useful in experiments designed to discover the composition of atoms.

In 1906, while experimenting with the passage of $\alpha  - $particles through a thin mica sheet, Ernest Rutherford (Figure 15.2) noticed that most of the $\alpha  - $particles passed straight through. (Mica is a natural mineral that can be split into very thin sheets.) This suggested to him that there might be a large amount of empty space in the atom, and by 1909 he had developed what we now call the nuclear model of the atom.
In 1911, Rutherford carried out a further series of experiments with Hans Geiger and Ernest Marsden at the University of Manchester using gold foil in place of the mica. They directed parallel beams of $\alpha  - $particles at a piece of gold foil only ${10^{ - 6}}\,m$ thick. Most of the α-particles went straight through. Some were deflected slightly, but about 1 in 20000 were deflected through an angle of more than ${90^ \circ }$, so that they appeared to bounce back off the foil. This helped to confirm Rutherford in his thinking about the atom – that it was mostly empty space, with most of the mass and all of the positive charge concentrated in a tiny region at the centre. This central nucleus only affected the $\alpha  - $particles when they came close to it.
Later, Rutherford wrote: ‘It was quite the most incredible event that has happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.’
In fact, he was not quite as surprised as this suggests, because the results confirmed ideas he had used in designing the experiment.

Figure 15.3 shows the apparatus used in the α-scattering experiment. Notice the following points:
The α-particle source was encased in metal with a small aperture, allowing a fine beam of $\alpha  - $particles to emerge.
Air in the apparatus was pumped out to leave a vacuum; $\alpha  - $radiation is absorbed by a few centimetres of air.
One reason for choosing gold was that it can be made into a very thin sheet or foil. Rutherford’s foil was only a few hundreds of atoms thick.
The $\alpha  - $particles were detected when they struck a solid ‘scintillating’ material. Each $\alpha  - $particle gave a tiny flash of light and these were counted by the experimenters (Geiger and Marsden).
The detector could be moved round to detect α-particles scattered through different angles.
Geiger and Marsden had the difficult task of observing and counting the tiny flashes of light produced by individual α-particles striking the scintillation screen. They had to spend several minutes in the darkened laboratory to allow the pupils of their eyes to become dilated so that they could see the faint flashes. Each experimenter could only stare into the detector for about a minute before the strain was too much and they had to change places.

Explaining $\alpha  - $scattering

How can we explain the back-scattering of $\alpha  - $particles by the gold atoms?
If the atom was as Thomson pictured it, with negatively charged electrons scattered through a ‘pudding’ of positive charge, an individual α-particle would pass through it like a bullet, hardly being deflected at all. This is because the α-particles are more massive than electrons–they might push an electron out of the atom, but their own path would be scarcely affected.
However, if the mass and positive charge of the atom were concentrated at one point in the atom, as Rutherford suggested, an $\alpha  - $particle striking this part would be striking something more massive than itself and with a greater charge. A head-on collision would send the α-particle backwards.
The paths of an α-particle near a nucleus are shown in Figure 15.4.

Rutherford reasoned that the large deflection of the α-particle must be due to a very small charged nucleus. From his experiments he calculated that the diameter of the gold nucleus was about ${10^{ - 14}}\,m$. It has since been shown that the very large deflection of the $\alpha  - $particle is due to the electrostatic repulsion between the positive charge of the $\alpha  - $particle and the positive charge of the nucleus of the atom. The closer the path of the $\alpha  - $particle gets to the nucleus, the greater will be this repulsion. An $\alpha  - $particle making a ‘head-on’ collision with a nucleus is back-scattered through ${360^ \circ }$. The $\alpha  - $particle and nucleus both experience an equal but opposite repulsive electrostatic force F. This force has a much greater effect on the motion of the α-particle than on the massive nucleus of gold.

PRACTICAL ACTIVITY 15.1

 

An analogy for Rutherford scattering

Roll a ball-bearing down a slope towards a cymbal. It may be deflected but, even if you roll it directly at the cymbal’s centre, it will not come back – it will roll over the centre and carry on to the other side. 
However, if you roll the ball-bearing towards a ‘tin hat’ shape (with a much narrower but higher central bulge) any ball-bearings that you roll close to the centre will deflect a lot, and any ball-bearings that you roll directly towards the centre will roll straight back. This is a very simple analogy (or model) of Rutherford’s experiment.

The shape of the cymbal represents the shape of the electric field of an atom in the ‘plum pudding’ model: low central intensity and spread out. The ‘tin hat’ represents the shape of the electric field for the nuclear model: high central intensity and concentrated.
From the $\alpha  - $particle scattering experiment, Rutherford deduced the following.
- An $\alpha  - $particle is deviated due to the repulsive force between the α-particle and the positive charge in the atom.
- Most $\alpha  - $particles have little or no deviation–so most of an atom is empty space.
- A very few $\alpha  - $particles are deviated more than ${90^ \circ }$ – so most of the mass of an atom is concentrated in a small space (the nucleus) and most of the atom is empty space.