Nuclear force
The nuclear force is the strongest force but acts only over a few femtometres. It holds nucleons together and is about the same for p-p, n-n and n-p pairs.
Why a new force is needed
Protons in a nucleus are only about a femtometre apart, so they repel each other very strongly. Gravity between them is far too weak to hold them together. So there must be a much stronger attractive force between nucleons. This is the nuclear force (also called the strong force). It acts between all nucleons: proton-proton, neutron-neutron and proton-neutron.
Properties of the nuclear force
- It is the strongest force known, much stronger than the Coulomb and gravitational forces.
- It is short range: it is strong only up to a few femtometres and is almost zero beyond that.
- Because of the short range, each nucleon attracts only its nearest neighbours. This is called saturation, and it keeps the binding energy per nucleon nearly constant for medium nuclei.
- It is charge independent: the p-p, n-n and n-p nuclear forces are about the same.
- It is attractive when nucleons are more than about 0.8 fm apart and strongly repulsive when they are closer, which stops the nucleus from collapsing.
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 potential energy curve for two nucleons
- Draw the x-axis for the separation r (fm), from 0 to about 3 fm, and the y-axis for potential energy (MeV), with zero in the middle.
- Start the curve very high (positive) near r = 0.
- Bring it down steeply to a deep minimum at r₀ ≈ 0.8 fm, below the axis.
- Then let it rise gently and flatten to zero by about 2 to 3 fm.
- Label the part r < r₀: repulsive and the part r > r₀: attractive.
Three forces inside a nucleus
| Force | Acts between | Range | Size for two protons 1 fm apart |
|---|---|---|---|
| Nuclear | All nucleons | A few fm | Strongest; attractive beyond 0.8 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: “Write any two properties of the nuclear force.” It is the strongest force and short range (a few fm). It is charge independent: p-p, n-n and n-p forces are about equal.
3 marks: “Draw a graph of the potential energy of a pair of nucleons against their separation. Mark the regions where the force is attractive and repulsive.” Curve high at small r, minimum at r₀ ≈ 0.8 fm, rising to zero by a few fm. Repulsive for r < r₀; attractive for r > r₀; negligible beyond a few fm.
1 marks: “Which force holds the protons of a nucleus together in spite of their electric repulsion?” The strong nuclear force.
Strong, Short, Same, Switch: strongest, short range, same for all pairs, switches from attractive to repulsive at 0.8 fm.