Atomic Models – Rutherford Scattering

In order to understand atomic spectra, we need to start with the structure of an atom. Already at the beginning of the 20th century, it was known that atoms were made up of smaller particles with a positive and a negative charge. However, it was not yet clear how an atom looked on the inside. Were negative and positive particles distributed evenly? Or, maybe, negative particles were on the outside, and positive ones inside? If so, how far apart were they?

You could ponder over these questions as much as you want, but the only way to really find out is by performing an experiment.

The ingenious experiment of Rutherford was essential for finding the answer. Radioactivity had just been discovered, and Rutherford could use an alpha emitter, that is, fast atomic nuclei of helium, which are emitted by radioactive radium.

Rutherford chose a gold foil as a target for fast alpha particles. The foil was extremely thin, and had only a few atomic layers. To measure how alpha particles were deflected in the gold foil, Rutherford used scintillation screens. The experiment was performed in complete darkness. The screens gave off tiny flashes of light when struck by alpha particles.

Detecting the alpha particles, which were scattered at all angles, helped to figure out the structure of a gold atom. It turned out that most alpha particles passed straight through the gold foil. Unexpectedly, only a few alpha particles were deflected by the foil. Some of them, however, were bounced back with a considerable force. What did that mean?

Electrons are very light, and do not present a significant obstacle for alpha particles. An alpha particle will move onwards practically undisturbed. Only heavy, positively charged atomic nuclei can deflect alpha particles. It appears that atomic nuclei must be astonishingly small; otherwise, many more alpha particles would be deflected.

Deflected particles with positive charge follow hyperbolic paths. Those paths are more sharply curved when the alpha particles are nearer to the nucleus.

Any distance between an alpha-particle and the nucleus is equally likely. In other words, alpha particles passing close to the nucleus, which are scattered through large angles, occur as often as those that are slightly less close and are less scattered, or those that are further away still and are even less scattered, and so on. The hyperbolic paths have already demonstrated that particles were much less likely to be scattered through large angles than through smaller ones.

Most alpha particles pass far away from the tiny nucleus. Their hyperbolic paths are hardly deflected, and they come straight through the gold foil. This is true as long as the nucleus only acts on the particles through its force of repulsion, that is, the Coulomb force.

The closer an alpha particle comes to the nucleus, the larger the scattering angle. The particle deflects from its hyperbolic path only when a new force, that is, the nuclear force, comes into play. Rutherford was able to specify a limit at which such deflections occur. He also inferred the size of the atomic nucleus from the respective scattering angle. That size is 10^-15m. This is how we know that most of the atom is empty. The electron shell is almost a hundred thousand times larger than the nucleus. It is thus clear that the binding energy of the nuclear force must be over a hundred thousand times that of the Coulomb energy; otherwise, the positively charged nucleus would come apart.

If an atom were as big as a football stadium, we would find its electron orbits in the spectator stands. The nucleus would be roughly the size of a pin.