Atomic structure and alpha scatteringEdexcel International A Level Physics: Revision notes

An atom has a tiny central nucleus made of protons and neutrons, together called nucleons, surrounded by electrons.

• Proton number $Z$ (atomic number): the number of protons in the nucleus. It identifies the element.
• Nucleon number $A$ (mass number): the total number of protons and neutrons.
• Neutron number $N = A - Z$.

A nuclide is written $^{A}_{Z}\mathrm{X}$. For example $^{238}_{92}\mathrm{U}$ has $Z = 92$ protons, $A = 238$ nucleons and $238 - 92 = 146$ neutrons. A neutral atom has $Z$ electrons.

Nuclei with the same $Z$ but different $A$ are isotopes. They have the same chemistry but different masses.

After J. J. Thomson discovered the electron in 1897, he proposed the plum pudding model: a sphere of positive charge with negative electrons embedded in it. The atom is neutral overall. In this model the positive charge, and so the mass, is spread evenly through the whole atom.

In 1909 Geiger and Marsden, working with Rutherford, fired a narrow beam of alpha particles at a very thin gold foil in an evacuated chamber (air would absorb or scatter the alpha particles). A detector counted the particles scattered at different angles.

• Most alpha particles pass straight through: most of the atom is empty space
• A few are deflected through large angles: a small region of positive charge repels the alpha particles
• About 1 in 8000 is deflected back through more than 90°: the nucleus contains most of the mass and is very small

The plum pudding model predicts only small deflections, so the experiment disproved it. The nuclear radius is about $10^{-15}$ m, compared with about $10^{-10}$ m for the atom.

Our picture of the atom has changed as new evidence appeared:

• Thomson (1897 to 1904): plum pudding, after discovering the electron
• Rutherford (1911): nuclear atom, from the alpha scattering results
• Bohr (1913): electrons in fixed orbits with discrete energy levels, explaining line spectra
• Chadwick (1932): discovery of the neutron, explaining why nuclear masses are larger than the proton masses alone
• later scattering experiments showed that protons and neutrons contain smaller particles called quarks

A model is kept only while it explains the evidence. When an experiment contradicts it, the model is revised.

Question. In an alpha scattering experiment $3.2 \times 10^{5}$ alpha particles hit a gold foil and 1 in 8000 is scattered through more than 90°. How many are scattered through more than 90°?

$3.2 \times 10^{5} \div 8000 = 40$

Such a small fraction shows that the nucleus takes up only a tiny proportion of the atom's volume.

Question. How many neutrons are in $^{197}_{79}\mathrm{Au}$? $197 - 79 = 118$.