The alpha-particle scattering experiment, the nuclear model of the atom, the proton and neutron, nuclide notation, and estimating nuclear radius and density.

What this dot point is asking

Edexcel wants you to describe the alpha-particle scattering experiment and the nuclear model it established, identify the proton and neutron, use nuclide notation, and estimate nuclear radius (through $R = r_0 A^{1/3}$) and the very high density of nuclear matter.

The answer

The alpha-particle scattering experiment

The Geiger-Marsden experiment, interpreted by Rutherford, fired alpha particles at a thin gold foil and recorded where they went. Most passed straight through, a small fraction were deflected through large angles, and about one in $8000$ bounced almost straight back. The "mostly straight through" result shows the atom is largely empty space; the rare large-angle and back-scattering events show that the positive charge and nearly all the mass are concentrated in a tiny central nucleus that strongly repels an incoming positive alpha particle.

Protons, neutrons and nuclide notation

A nuclide is written with $A$ as a superscript and $Z$ as a subscript before the element symbol. Isotopes of an element have the same $Z$ but different $A$ (different numbers of neutrons), so they share chemical behaviour but differ in mass and nuclear stability.

Nuclear radius and density

Electron-diffraction and scattering experiments show that nuclear radius depends on nucleon number through a simple law:

The cube-root law means the nucleus behaves like a drop of incompressible fluid: doubling the number of nucleons doubles the volume, not the radius. The resulting density, around $10^{17}$ kg per cubic metre, is fantastically larger than everyday matter and matches the density of a neutron star.

Examples in context

The nuclear model underpins all of nuclear physics and chemistry, explaining the periodic table through proton number. Electron-scattering measurements of nuclear radius confirm the $A^{1/3}$ law and feed into models of nuclear stability. The extreme nuclear density reappears in astrophysics: a neutron star is essentially nuclear matter on a stellar scale, where gravity has crushed protons and electrons together. Isotope identification by mass spectrometry relies on the proton-neutron picture established here.

Try this

Q1. State what the back-scattering of a few alpha particles told Rutherford. [1 mark]

• Cue. That the atom has a tiny, dense, positively charged nucleus containing most of its mass.

Q2. A nucleus has nucleon number $A = 27$ and $r_0 = 1.2 \times 10^{-15}$ m. Find its radius. [2 marks]

• Cue. $R = r_0 A^{1/3} = 1.2 \times 10^{-15} \times 27^{1/3} = 1.2 \times 10^{-15} \times 3.0 = 3.6 \times 10^{-15}$ m.

Q3. Explain why all nuclei have approximately the same density. [2 marks]

• Cue. Volume is proportional to $A$ (since $R \propto A^{1/3}$ so $R^3 \propto A$), and mass is also proportional to $A$, so mass per unit volume stays roughly constant.