The nuclear atom and alpha scatteringEdexcel A-Level Physics: Revision notes

The atom has a small, dense, positively charged nucleus containing protons and neutrons (together called nucleons), surrounded by electrons.

• Proton number $Z$: the number of protons in the nucleus. It defines the element.
• Nucleon number $A$: the total number of protons and neutrons.
• Neutron number: $N = A - Z$.

A nuclide is written ${}^{A}_{Z}\text{X}$. For ${}^{63}_{29}\text{Cu}$ there are 29 protons, $63 - 29 = 34$ neutrons and, in a neutral atom, 29 electrons.

Atoms of the same element with different numbers of neutrons (same $Z$, different $A$) are isotopes. Copper-65 has 29 protons and 36 neutrons.

After the discovery of the electron in 1897, J. J. Thomson proposed the plum pudding model: an atom is a sphere of positive charge spread evenly through its volume, with negatively charged electrons embedded in it, so the whole atom is neutral.

In this model the positive charge is spread out, so the electric force on a charged particle passing through is weak everywhere. A fast alpha particle should pass through with at most a small deflection.

In 1909 Geiger and Marsden, working with Rutherford, fired a narrow beam of alpha particles (positively charged) at a very thin gold foil in an evacuated chamber, and counted the scattered particles at different angles.

• The chamber is evacuated because alpha particles have a short range in air and would be absorbed or scattered by air molecules.
• The foil is very thin so that each large deflection is due to one interaction with one nucleus, not several.

Observations:

1. Most alpha particles passed straight through, or with little deflection.
2. A small fraction (about 1 in 8000) was deflected through more than 90°.
3. A few were scattered almost straight back.

Rutherford explained the results with the nuclear model (1911):

• Most alpha particles pass through undeflected, so most of the atom is empty space.
• Some are deflected through large angles, so there is a strong repulsive force, and the nucleus is positively charged (like charges repel).
• Very few are scattered back, so the nucleus is very small compared with the atom, and the charge is concentrated in a tiny region.
• Alpha particles rebounding almost straight back must have hit something far more massive, so most of the mass is in the nucleus.

Electrons are too light to deflect alpha particles significantly.

Models change when new evidence cannot be explained:

• Dalton: atoms as tiny, solid, indivisible spheres.
• Thomson: the electron's discovery showed that atoms have structure, giving the plum pudding model.
• Rutherford: the alpha-scattering results contradicted the plum pudding model, giving the nuclear atom.
• Later refinements: for example the discovery of the neutron explained the mass of the nucleus, and Bohr added energy levels for electrons.

A model is accepted when it explains the evidence and its predictions are tested by repeatable experiments checked by other scientists, and it stays provisional.