Nuclear force and its properties
A new force, the nuclear force, holds nucleons together. It is very strong but short range, the same for p-p, n-n and n-p pairs, and acts only between neighbours.
Why a new force is needed
Protons in a nucleus are only about 10⁻¹⁵ m apart, so they repel each other very strongly. Gravity between them is far too weak to hold them together. If only these forces acted, the nucleus would fly apart. So there must be a much stronger attractive force between nucleons. This is the nuclear force. Nothing like it appears in everyday physics.
Properties of the nuclear force
- It is the strongest force known: much stronger than the electric force, and gravity is about 10⁻³⁹ times weaker.
- It is short range: it acts only up to about 10⁻¹⁵ m (a few fermi) and is almost zero beyond.
- It is charge independent: the force between p-p, n-n and n-p pairs is about the same.
- It shows saturation: each nucleon attracts only its nearest neighbours, not every nucleon in the nucleus.
- It is attractive at normal spacing but turns repulsive if nucleons come very close (a fraction of a fermi). This keeps them from collapsing together.
- Unlike gravity and the electric force, it does not follow an inverse square law.
Worked example: how strong is the repulsion?
Two protons are 1 fm apart. Find the electrostatic force and the gravitational force between them. (1/4πε₀ = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C, G = 6.67 × 10⁻¹¹ N m² kg⁻², mₚ = 1.67 × 10⁻²⁷ kg)
- Electrostatic force: F = (1/4πε₀)e²/r² = 9 × 10⁹ × (1.6 × 10⁻¹⁹)² ÷ (10⁻¹⁵)².
- F = 9 × 10⁹ × 2.56 × 10⁻³⁸ ÷ 10⁻³⁰ = 230 N (repulsive).
- Gravitational force: F = Gmₚ²/r² = 6.67 × 10⁻¹¹ × (1.67 × 10⁻²⁷)² ÷ 10⁻³⁰.
- F = 6.67 × 10⁻¹¹ × 2.79 × 10⁻⁵⁴ ÷ 10⁻³⁰ ≈ 1.9 × 10⁻³⁴ N (attractive).
- The electric push is about 10³⁶ times the gravitational pull, so only a much stronger force can hold the nucleus.
Electrostatic ≈ 230 N; gravitational ≈ 1.9 × 10⁻³⁴ N
How to draw the graph of nuclear force against distance
- Draw the x-axis for distance between two nucleons (fm), from 0 to about 5 fm. The axis itself means zero force.
- Mark repulsion above the axis and attraction below it.
- Near r = 0, draw the curve high above the axis: strong repulsion at very small distances.
- Let it cross the axis at a fraction of a fermi and dip to a deep attraction around 1 fm.
- Then let it rise back to zero within a few fermi: no force beyond that.
Three forces inside a nucleus
| Force | Acts between | Range | Size for two protons 1 fm apart |
|---|---|---|---|
| Nuclear | All nucleons | A few fm | Strongest; attractive at about 1 fm |
| Electrostatic | Protons only (repulsion) | Long (falls as 1/r²) | About 230 N |
| Gravitational | All masses | Long (falls as 1/r²) | About 10⁻³⁴ N, negligible |
The nuclear force holds together the nucleus of every atom in your body, from the carbon in rice to the calcium in your bones. It wins even though the protons push each other apart with forces of hundreds of newtons.
2 marks: “State any two properties of the nuclear force.” It is the strongest force but short range (about 10⁻¹⁵ m); it is charge independent (same for p-p, n-n and n-p); it saturates (acts only between neighbours). Any two.
2 marks: “Why can neither gravity nor the electric force hold the nucleons of a nucleus together?” The electric force between protons is repulsive; gravity is attractive but about 10⁻³⁹ times too weak. So a new, strong, attractive nuclear force is needed.
1 marks: “What is meant by saying that the nuclear force is charge independent?” It is about the same between two protons, two neutrons, or a proton and a neutron.
Strong, Short, Same, Saturated: strongest force, about 10⁻¹⁵ m range, same for all pairs, only between neighbours.