The Nuclear Atom

A narrow beam of alpha particles from a radioactive source was directed at a very thin gold foil in a vacuum. A movable detector — originally a zinc sulfide screen viewed through a microscope — counted scintillations at different angles.

The vacuum matters: alpha particles are strongly ionising and would be stopped within a few centimetres of air. The foil must be thin so that each alpha particle is scattered by at most one nucleus.

The observations were: most alpha particles passed straight through with little or no deflection; a small fraction were deflected through large angles; and a very small number, roughly 1 in 8000, were scattered back through more than $90^{\circ}$.

$\textbf{Most passed straight through}$: the atom is mostly empty space.

$\textbf{Some deflected through large angles}$: there is a concentration of positive charge that repels the positive alpha particles strongly.

$\textbf{A very few bounced back}$: that charge, and most of the atom’s mass, is concentrated in a very small volume. Only a massive, compact centre could reverse an alpha particle’s motion, and the rarity of back-scattering shows how small a target it presents.

In the plum-pudding model, positive charge was spread thinly through the atom. Its field would be far too weak anywhere to deflect a fast alpha particle through a large angle, so the model could not explain the results.

For an alpha particle heading straight at a nucleus, it slows as it approaches, stops momentarily, and is pushed back. At that turning point all its initial kinetic energy has become electric potential energy.

Setting $E_{k} = \dfrac{kQ_{\alpha}Q_{N}}{r}$ gives the distance of closest approach. The nucleus must be smaller than this, so it gives an upper limit on nuclear radius.

The charge of a nucleus with proton number $Z$ is $Ze$, and an alpha particle carries $2e$.

A nucleus is written $^{A}_{Z}\mathrm{X}$, where $Z$ is the proton number and $A$ is the nucleon number (protons plus neutrons). The number of neutrons is $A - Z$.

$\textbf{Isotopes}$ are nuclei of the same element — same $Z$ — with different numbers of neutrons. Carbon-12 and carbon-14 are both carbon, with 6 and 8 neutrons.

Alpha particles are limited as probes: they are affected by the strong nuclear force if they get close enough, and they cannot reach heavy nuclei at typical source energies. High-energy $\textbf{electrons}$ are better — they are not affected by the strong force, and at high energy their de Broglie wavelength $\lambda = h/p$ is comparable to nuclear dimensions, so they diffract around nuclei and reveal their size.

The same approach, at still higher energies, showed that electrons scatter from three point-like charges inside each proton — the first evidence for quarks.