The strong nuclear force

The strong nuclear force is the force that holds protons and neutrons together in the nucleus. It is the strongest of the four fundamental forces, strong enough to overcome the electrostatic repulsion between protons, but it only acts over a very short range: AQA describes it as attractive up to about 3 femtometres (3 × 10⁻¹⁵ m) and repulsive at separations below about 0.5 fm.

Why the nucleus needs a strong force

A nucleus contains positively charged protons packed extremely close together. Like charges repel, and the electrostatic (Coulomb) force between them is long range. On its own, it would blow the nucleus apart. Gravity between nucleons is far too weak to help. Something else must hold the nucleus together: a short-range force that makes all nucleons, protons and neutrons, attract one another. That is the strong nuclear force, also called the strong interaction.

Properties of the strong nuclear force

The strong nuclear force graph

The graph shows how the strong force between two nucleons changes with their separation r:

• Below about 0.5 fm the force is repulsive. This stops nucleons being squeezed into each other.
• From about 0.5 fm to about 3 fm it is attractive. Nucleons sit at the separation where the force holds them together.
• Beyond about 3 fm it falls to almost zero, which is why a nucleon only attracts its nearest neighbours.

The electrostatic repulsion between two protons, by contrast, falls off with 1/r² but never reaches zero. That difference matters for big nuclei, as the next section shows.

The strong force and nuclear stability

In a small nucleus, every nucleon is close to most of the others, so the strong force easily wins. In a large nucleus, each nucleon still only feels the strong force from its neighbours, but every proton repels every other proton. Extra neutrons help: they add strong attraction without adding any electrostatic repulsion, which is why heavier stable nuclei have more neutrons than protons. Nuclei that cannot balance the two forces are unstable and decay, for example by alpha or beta decay; see alpha, beta and gamma decay.

Exchange particles: pions and gluons

In particle physics, forces are explained by exchange particles passing between the particles that interact. CERN lists the carriers: the photon for the electromagnetic force, the W and Z bosons for the weak force, and the gluon for the strong force.

• Between nucleons (AQA A-level): the strong nuclear force is modelled as the exchange of pions, a type of meson.
• Between quarks: at the deepest level the strong force acts between quarks and is carried by gluons. AQA states that knowledge of the gluon will not be tested, but other courses use it.

Match each force to its carrier in this question from the Particles course.

The four fundamental forces compared

CERN describes the strong force as the strongest of the four, the weak force as the weakest of the other three, and gravity as the weakest of all but with infinite range. The weak and strong forces only dominate at the level of subatomic particles.

Worked examples

Example 1: how big is the repulsion it beats?

Find the electrostatic and gravitational forces between two protons 1.0 fm apart. Use k = 8.99 × 10⁹ N m² C⁻², e = 1.60 × 10⁻¹⁹ C, G = 6.67 × 10⁻¹¹ N m² kg⁻² and m = 1.67 × 10⁻²⁷ kg.

1. Electrostatic: F = ke² ÷ r² = 8.99 × 10⁹ × (1.60 × 10⁻¹⁹)² ÷ (1.0 × 10⁻¹⁵)² = 230 N, repulsive.
2. Gravitational: F = Gm² ÷ r² = 6.67 × 10⁻¹¹ × (1.67 × 10⁻²⁷)² ÷ (1.0 × 10⁻¹⁵)² = 1.9 × 10⁻³⁴ N, attractive.
3. Gravity is about 10³⁶ times too weak to hold the protons together. The strong force at this separation must be attractive and larger than 230 N.

Check the electrostatic part with the Electric Force Calculator; the Coulomb's law guide explains the formula.

Example 2: attract, repel or nothing?

Using AQA's figures, describe the strong force between two neutrons at separations of 0.3 fm, 1.5 fm and 6 fm.

• 0.3 fm: below 0.5 fm, so the force is repulsive.
• 1.5 fm: between 0.5 fm and 3 fm, so the force is attractive.
• 6 fm: beyond the range of about 3 fm, so the strong force is negligible.

Common mistakes

• Saying the strong force acts only between protons. It acts between all nucleons, including neutrons.
• Saying it is always attractive. Below about 0.5 fm it is repulsive.
• Giving it a long range. It is negligible beyond about 3 fm.
• Saying electrons feel it. Only hadrons do; electrons are leptons.
• Naming the gluon in an AQA answer about nucleons. AQA expects the pion as the exchange particle of the strong nuclear force.

Practise with a short timed paper

The strong nuclear force is in the first year of AQA A-level Physics (3.2.1). The daily A-level Physics: Year 1 paper is a short timed paper of 8 questions, with a new one every day. For drawing interactions, see Feynman diagrams.

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