The Nuclear Atom

At the start of the twentieth century, the atom was imagined as a diffuse sphere of positive charge with electrons embedded throughout — the so-called "plum pudding" model proposed by J. J. Thomson. It was a reasonable guess given the evidence available, but it was about to be demolished by one of the most important experiments in physics.

The Rutherford Scattering Experiment

In 1909, Hans Geiger and Ernest Marsden, working under the direction of Ernest Rutherford at the University of Manchester, fired alpha particles at a thin gold foil and observed where they went. Alpha particles are helium-4 nuclei — positively charged, relatively massive, and fast-moving.

If Thomson's model were correct, the alpha particles should have passed through the gold atoms with only slight deflections. The positive charge was supposed to be spread thinly across the whole atom, so there would be nothing dense enough to cause a large deflection.

What They Observed

Most alpha particles passed straight through the foil with little or no deflection. This confirmed that atoms are mostly empty space.
A small fraction were deflected through large angles, some greater than 90°.
A very tiny number (roughly 1 in 8,000) bounced almost straight back towards the source.

Rutherford famously said it was "almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

The Nuclear Model

Rutherford concluded that the atom must contain a tiny, dense, positively charged centre — the nucleus. The key features of the nuclear model are:

The nucleus contains almost all the mass of the atom
The nucleus is positively charged (due to protons)
The nucleus is extremely small compared to the atom (nuclear radius ~ 10⁻¹⁵ m, atomic radius ~ 10⁻¹⁰ m)
Electrons orbit the nucleus at relatively large distances
Most of the atom is empty space

Nuclear Radius

Experiments using electron diffraction (high-energy electrons scattered off nuclei) have shown that the nuclear radius R depends on the nucleon number A according to the empirical formula:

R = R₀ A^(1/3)

where R₀ ≈ 1.2 – 1.4 fm (femtometres, 10⁻¹⁵ m).

This tells us something remarkable: nuclear volume is proportional to A (since V = 4/3 πR³ ∝ A), which means that every nucleon occupies roughly the same volume regardless of the size of the nucleus. This leads directly to the conclusion that nuclear density is approximately constant.

Calculating Nuclear Density

Using R₀ = 1.4 fm:

Volume of a nucleon ≈ 4/3 π (1.4 × 10⁻¹⁵)³ ≈ 1.15 × 10⁻⁴⁴ m³
Mass of a nucleon ≈ 1.67 × 10⁻²⁷ kg
Nuclear density ≈ 1.67 × 10⁻²⁷ / 1.15 × 10⁻⁴⁴ ≈ 1.45 × 10¹⁷ kg m⁻³

This is extraordinarily dense — about 10¹⁴ times denser than water. A teaspoon of nuclear matter would have a mass of roughly 5 billion tonnes. Neutron stars, which are essentially giant nuclei, have densities in this range.

Proton Number, Nucleon Number, and Isotopes

Every nucleus is characterised by two numbers:

Proton number (Z): the number of protons in the nucleus. This determines the element and its chemical properties.
Nucleon number (A): the total number of nucleons (protons + neutrons). A = Z + N, where N is the number of neutrons.

The standard notation for a nuclide is:

ᴬ_Z X

For example, carbon-12 is ¹²₆C — it has 6 protons and 6 neutrons.

Isotopes

Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A). For example:

Isotope	Protons	Neutrons	Nucleon Number
¹²₆C	6	6	12
¹³₆C	6	7	13
¹⁴₆C	6	8	14

All three are carbon (Z = 6), so they have the same electron configuration and almost identical chemical properties. However, they have different masses and different nuclear stability — ¹⁴C is radioactive and is the basis of carbon dating.

The Strong Nuclear Force

If the nucleus contains multiple protons packed into a tiny space, why doesn't the electrostatic repulsion between them blow the nucleus apart? The answer is the strong nuclear force — one of the four fundamental forces of nature.

Properties of the Strong Nuclear Force

Property	Detail
Nature	Attractive between all nucleons (proton–proton, proton–neutron, neutron–neutron)
Range	Very short range — acts only up to about 3 fm; negligible beyond this
At very short range (< 0.5 fm)	Becomes repulsive, preventing nucleons from being squeezed into each other
Strength	Much stronger than the electromagnetic force at nuclear distances
Charge independence	Acts equally between all pairs of nucleons regardless of charge

The balance between the attractive strong force and the repulsive electromagnetic force explains nuclear stability:

Small nuclei (low Z): the strong force easily overcomes electromagnetic repulsion, so these nuclei are stable with roughly equal numbers of protons and neutrons.
Large nuclei (high Z): the electromagnetic force has infinite range while the strong force does not. As the nucleus grows, each proton repels every other proton, but the strong force only acts on nearest neighbours. This is why heavy nuclei need a greater proportion of neutrons (which contribute strong force attraction without adding electromagnetic repulsion) to remain stable. Eventually, above Z = 83 (bismuth), no stable nuclei exist at all.

Summary

The nuclear atom model, established by Rutherford's scattering experiment, revealed that atoms consist of a tiny, dense, positively charged nucleus surrounded by orbiting electrons. The nucleus has a radius given by R = R₀A^(1/3), leading to a remarkably constant nuclear density of approximately 10¹⁷ kg m⁻³. Nuclei are characterised by their proton number Z and nucleon number A, with isotopes being atoms of the same element with different neutron counts. The strong nuclear force holds nuclei together against electromagnetic repulsion, but its short range means that very large nuclei become unstable.