E.1.1 Historical models and experimental evidence Notes

The Geiger–Marsden Experiment and the Discovery of the Nucleus

Why Does Matter Behave the Way It Does?

1. Consider you're playing a game of billiards, and one ball suddenly ricochets sharply backward after hitting another, as if it struck a hidden, rock-solid object.
2. This unexpected behavior mirrors what Hans Geiger and Ernest Marsden observed during their groundbreaking experiment under the guidance of Ernest Rutherford.

Their findings not only challenged the prevailing atomic model but also revealed the existence of the nucleus, a discovery that transformed our understanding of matter.

The Geiger–Marsden Experiment: Scattering Alpha Particles

The Setup

1. In 1911, Geiger and Marsden conducted an experiment to investigate the structure of the atom.
2. They directed a beam of alpha particles (positively charged helium nuclei) at an extremely thin sheet of gold foil.
3. Surrounding the foil was a screen coated with zinc sulfide, which produced tiny flashes of light whenever an alpha particle struck it.

Observations

The results of their experiment were astonishing:

1. Most alpha particles passed straight through the foil with little to no deflection.
2. A small number of particles were deflected at large angles, with some even rebounding toward the source.

Rutherford’s Interpretation

1. Rutherford concluded that the large-angle deflections could only occur if the atom’s positive charge was concentrated in a tiny, dense region.
2. He proposed a new model of the atom:
   1. The atom contains a compact, massive, positively charged nucleus at its center.
   2. Electrons orbit this nucleus, similar to how planets orbit the Sun.

This became known as the nuclear model of the atom.

Why the Plum Pudding Model Failed

The plum pudding model failed because it could not account for the large-angle scattering observed in the Geiger–Marsden experiment.

1. Small Deflections:
   1. These could be explained by the weak, spread-out positive charge in the plum pudding model. However...
2. Large Deflections:
   1. For an alpha particle to deflect at a large angle, it must encounter a very strong repulsive force.
   2. This is only possible if the positive charge is concentrated in a small, dense region contradicting the plum pudding model’s assumptions.

Rutherford’s nuclear model resolved this issue by proposing that nearly all the atom’s mass and positive charge are concentrated in the nucleus, which is about $10^{-15},\text{m}$ in diameter.

Nuclear Notation: Representing Atoms

1. To describe nuclei concisely, we use nuclear notation, which specifies the number of protons and nucleons in an atom.
2. Each nucleus is represented as: $$
   ^{A}_{Z}X
   $$
3. $X$: the chemical symbol of the element.
4. $Z$: the proton number (also called the atomic number).
5. $A$: the nucleon number (total number of protons + neutrons).

Implications of the Nuclear Model

The nuclear model reshaped our understanding of the atom. Here are three key insights:

1. Atoms are mostly empty space:
   1. The fact that most alpha particles passed through the foil unimpeded shows that the nucleus occupies only a tiny fraction of the atom’s volume.
2. The nucleus Is dense and massive:
   1. The large-angle deflections indicate that the nucleus contains almost all the atom’s mass.
3. Positive charge Is concentrated:
   1. The repulsion between alpha particles and the nucleus confirms that the nucleus is positively charged.