The Fundamental Interactions and Exchange Particles – Nature of Particles and Their Interactions (Senior 6 Physics) | Ganzaa

Nature of Particles and Their Interactions

Lessons

Senior 6 · Physics

Nature of Particles and Their Interactions

5 lessons

Lesson 3 of 5

The Fundamental Interactions and Exchange Particles

25 min

Why does a nucleus hold together?

Two protons in a nucleus sit about 2 fm apart. Coulomb's law gives the repulsion between them as $F = \frac{ke^2}{r^2} = \frac{(8.99 \times 10^{9})(1.60 \times 10^{-19})^2}{(2.0 \times 10^{-15})^2} \approx 58\,\mathrm{N}$ : the weight of a 6 kg bag of rice, acting on a particle whose mass is $1.7 \times 10^{-27}$ kg. Gravity is hopelessly weak by comparison. Something far stronger must hold the nucleus together, yet it must act only over very short distances, or every nucleus in the universe would collapse into one. And something else must make a neutron turn into a proton in beta decay. Physics needs four basic interactions to explain everything we observe. This lesson compares them and introduces the modern picture of how a force acts: by the exchange of particles.

The four interactions

Interaction	Acts on	Range	Relative strength (at about 1 fm)	Exchange particle
strong	quarks and gluons (so all hadrons)	about $10^{-15}$ m	1	gluons (8 kinds); between nucleons, effectively pions
electromagnetic	electric charges	infinite ( $\propto \frac{1}{r^2}$ )	about $10^{-2}$	photon $\gamma$
weak	all quarks and leptons, including neutrinos	about $10^{-18}$ m	about $10^{-6}$	$\mathrm{W^+}$ , $\mathrm{W^-}$ , $\mathrm{Z^0}$
gravitational	all mass and energy	infinite ( $\propto \frac{1}{r^2}$ )	about $10^{-38}$	graviton (predicted, never observed)

Relative strengths depend on the distance and energy, so these are only orders of magnitude. Each interaction has its own job: the strong force binds quarks into hadrons and nucleons into nuclei; the electromagnetic force binds electrons to nuclei and atoms into molecules; the weak force changes one kind of quark or lepton into another, as in beta decay and the fusion reactions in the Sun; gravity, the weakest by far, dominates on the scale of planets and galaxies because it is always attractive and acts on everything.

Worked example 1: electric versus gravitational force

Compare the electric and gravitational forces between two protons 2.0 fm apart ( $G = 6.67 \times 10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}$ , $m_p = 1.67 \times 10^{-27}$ kg).

Solution

$F_E = \frac{ke^2}{r^2} = \frac{(8.99 \times 10^{9})(1.60 \times 10^{-19})^2}{(2.0 \times 10^{-15})^2} = 58\,\mathrm{N}$ .

$F_G = \frac{Gm_p^2}{r^2} = \frac{(6.67 \times 10^{-11})(1.67 \times 10^{-27})^2}{(2.0 \times 10^{-15})^2} = 4.7 \times 10^{-35}\,\mathrm{N}$ .

$\frac{F_E}{F_G} = 1.2 \times 10^{36}$ , whatever the distance, since both follow $\frac{1}{r^2}$ . Gravity is irrelevant inside the nucleus; the strong force must beat the electric repulsion.

Forces as the exchange of particles

Imagine two people on skateboards throwing a heavy ball back and forth. Each throw and each catch pushes them apart: the ball carries momentum between them, and they behave as if they repel. In quantum theory every interaction works by the exchange of exchange particles (also called gauge bosons or force carriers). Two electrons repel by exchanging photons; quarks attract by exchanging gluons; the weak interaction uses the W and Z bosons. (The ball picture cannot explain attraction; it is only an analogy for how momentum is carried.)

These exchanged particles are virtual: they exist only briefly and cannot be detected directly. Their mass sets the range of the force. By the energy–time uncertainty principle, energy $\Delta E \approx mc^2$ can be "borrowed" to create a particle of mass $m$ only for a time $\Delta t \approx \frac{\hbar}{\Delta E}$ , where $\hbar = \frac{h}{2\pi}$ . Moving at most at speed $c$ , it can cover a distance

R \approx c\,\Delta t \approx \frac{\hbar c}{mc^2} \qquad (\hbar c = 197.3\,\mathrm{MeV\,fm})

This is an order-of-magnitude estimate. A massless exchange particle (the photon, and the graviton) gives an infinite range; a heavy one (W and Z) a very short range. In 1935 Hideki Yukawa ran the argument backwards: from the short range of the nuclear force, he predicted an exchange particle about 200 times as heavy as the electron (roughly 100 MeV). The pion (140 MeV), found in 1947, fitted.

Definition

An exchange particle (gauge boson) is a virtual boson whose exchange between particles produces a fundamental interaction: the photon (electromagnetic), gluons (strong), $\mathrm{W^\pm}$ and $\mathrm{Z^0}$ (weak). The range of the interaction is roughly $R \approx \frac{\hbar c}{mc^2}$ , where $m$ is the mass of the exchange particle. Example: the W boson (80.36 GeV) gives the weak force a range of about $2.5 \times 10^{-18}$ m.

Worked example 2: the ranges of the nuclear and weak forces

Estimate the range of (a) the force carried by a pion ( $m_\pi c^2 = 139.6\,\mathrm{MeV}$ ), (b) the weak force carried by the W boson ( $m_Wc^2 = 80.36\,\mathrm{GeV}$ , PDG 2026).

Solution

(a) $R \approx \frac{197.3\,\mathrm{MeV\,fm}}{139.6\,\mathrm{MeV}} = 1.4\,\mathrm{fm} = 1.4 \times 10^{-15}\,\mathrm{m}$ : about the distance between neighbouring nucleons, which is why the nuclear force acts only on near neighbours (Unit 5).

(b) $R \approx \frac{197.3\,\mathrm{MeV\,fm}}{80\,360\,\mathrm{MeV}} = 2.5 \times 10^{-3}\,\mathrm{fm} = 2.5 \times 10^{-18}\,\mathrm{m}$ , a thousandth of a proton's size. The weak interaction is weak mainly because it has such a short range, which makes it very unlikely to happen.

Feynman diagrams

Richard Feynman invented a shorthand for particle interactions. In this course, time runs upward (some books draw it left to right).

A straight line with an arrow is a matter particle (fermion). An arrow pointing BACKWARD in time (downward) shows an antiparticle moving forward in time.
A wavy line is a photon, W or Z boson; a gluon is drawn as a curly line.
Lines meet at vertices. At every vertex, charge, baryon number and lepton number are conserved.
Particles coming in at the bottom are the reactants; those leaving at the top are the products. The exchanged boson is virtual.

Figure 3.1: Feynman diagrams for the electromagnetic and weak interactions.

In Figure 3.1(b), check the charge at each vertex. Lower vertex: d $\left(-\frac{1}{3}\right) \rightarrow$ u $\left(+\frac{2}{3}\right) + \mathrm{W^-}\ (-1)$ : $-\frac{1}{3} = \frac{2}{3} - 1$ . Upper vertex: $\mathrm{W^-}\ (-1) \rightarrow \mathrm{e^-}\ (-1) + \bar{\nu}_e\ (0)$ . Beta-minus decay is therefore really the weak decay of a single down quark. Only the weak interaction can change a quark's flavour (d into u) or turn a charged lepton into a neutrino.

Worked example 3: the Feynman diagram for beta-plus decay

In beta-plus decay a proton in a nucleus becomes a neutron: $\mathrm{p} \rightarrow \mathrm{n} + \mathrm{e^+} + \nu_e$ . Describe its Feynman diagram and check the charge at each vertex.

Solution

At quark level, an up quark becomes a down quark: $\mathrm{u} \rightarrow \mathrm{d} + \mathrm{W^+}$ . Charge: $+\frac{2}{3} = -\frac{1}{3} + 1$ . ✓

The $\mathrm{W^+}$ then decays: $\mathrm{W^+} \rightarrow \mathrm{e^+} + \nu_e$ . Charge: $+ 1 = + 1 + 0$ . ✓

So the diagram is Figure 3.1(b) with u at the bottom, d at the top, a $\mathrm{W^+}$ , a positron (drawn as an electron line with its arrow pointing DOWN) and a neutrino (arrow up). The other two quarks (u, d) pass straight through: uud becomes udd.

Two faces of the strong force, and the unification of forces

The strong force acts between quarks through the exchange of gluons, which carry a kind of strong charge called colour. Unlike other forces, it does not weaken as quarks are pulled apart: the energy stored grows until it is enough to create a new quark–antiquark pair, so a single quark can never be pulled free (confinement, Lesson 1). Between whole nucleons, a weaker "left-over" strong force acts, carried effectively by pions: this is the nuclear force of Unit 5.

In the 1960s Sheldon Glashow, Abdus Salam and Steven Weinberg showed that the electromagnetic and weak interactions are two aspects of one electroweak interaction, which predicted the W and Z bosons. Their discovery at CERN in 1983, with the predicted masses, was a triumph of the theory. Combining the strong force as well, and finally gravity, remains unfinished: gravity is not part of the Standard Model.

Warning

Common mistakes. (1) Saying the weak force is weak because it acts at long range: it is VERY short-ranged. (2) Calling the graviton a known particle: it has never been observed. (3) Drawing an antiparticle with its arrow along time: an outgoing antiparticle's arrow points backward (down). (4) Forgetting that the W carries charge, so charge must balance at each vertex, not just overall. (5) Thinking neutrinos feel the electromagnetic or strong force: they feel only the weak force (and gravity).

Tip

For any Feynman diagram, do a vertex check: at each vertex, add up the charge in and the charge out, then the baryon number and the lepton number. If every vertex balances, the diagram is allowed. A W boson always appears when a quark changes flavour or a lepton changes into its neutrino.

Feynman diagrams (Fermilab). Watch how each line and vertex stands for a particle and an interaction, and how a few simple rules describe processes such as electron scattering and beta decay.

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Practice

Name the four fundamental interactions in order of strength, with the exchange particle of each.
Which interaction is responsible for (a) the binding of a nucleus, (b) beta decay, (c) the orbit of the Moon, (d) the shape of a water molecule?
Estimate the range of the interaction carried by the Z boson ( $m_Zc^2 = 91.19\,\mathrm{GeV}$ ).
The range of a hypothetical force is $2.0 \times 10^{-15}$ m. Estimate the rest energy of its exchange particle.
Explain why the photon gives the electromagnetic force an infinite range.
Draw the Feynman diagram for electron–positron annihilation into two photons, and label every line.
In a Feynman diagram a W⁻ boson connects a down quark that becomes an up quark with an electron and an antineutrino. Show that charge is conserved at both vertices.
Mugisha says: "Gravity is the strongest force, because it holds the planets in orbit and keeps us on the ground." Evaluate his statement.

Show answersHide answers

Strong (gluons), electromagnetic (photon), weak (W⁺, W⁻, Z⁰), gravitational (graviton, not yet observed).
(a) strong; (b) weak; (c) gravitational; (d) electromagnetic.
$R \approx \frac{197.3}{91\,190}\,\mathrm{fm} = 2.2 \times 10^{-3}\,\mathrm{fm} = 2.2 \times 10^{-18}\,\mathrm{m}$ .
$mc^2 \approx \frac{\hbar c}{R} = \frac{197.3\,\mathrm{MeV\,fm}}{2.0\,\mathrm{fm}} \approx 99\,\mathrm{MeV}$ , about 100 MeV.
The photon is massless, so no energy has to be borrowed for its rest mass; $\Delta t$ , and so the range $c\,\Delta t$ , are unlimited (the force falls off as $\frac{1}{r^2}$ but never reaches zero).
An electron line (arrow up) and a positron line (arrow down) come in from the bottom and meet; an electron line runs between two vertices; one photon (wavy) leaves from each vertex at the top.
Lower: $-\frac{1}{3} \rightarrow +\frac{2}{3} + (-1)$ , i.e. $-\frac{1}{3} = -\frac{1}{3}$ . Upper: $-1 \rightarrow -1 + 0$ .
Wrong. Gravity is by far the weakest (about $10^{-36}$ of the electric force between two protons). It dominates on astronomical scales only because it is always attractive and acts on all mass, while electric charges in large bodies cancel and the strong and weak forces have tiny ranges.

Key points

Four interactions: strong (gluons), electromagnetic (photon), weak (W⁺, W⁻, Z⁰), gravity (graviton, unobserved).
Forces act by exchange of virtual bosons; range $R \approx \frac{\hbar c}{mc^2}$ : infinite for massless carriers, about $10^{-18}$ m for the W and Z.
Feynman diagrams: time upward, fermion lines with arrows (backward for antiparticles), wavy bosons; conservation at every vertex.
Beta decay is the weak interaction: d → u + W⁻, then W⁻ → e⁻ + $\bar{\nu}_e$ .

Sources and credits

11.6: The Standard Model, from University Physics Volume 3 by Samuel J. Ling, Jeff Sanny and William Moebs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Particle data (W and Z masses): Review of Particle Physics, Summary Tables, Particle Data Group, 2026.
Video: Feynman diagrams, Fermilab, embedded from YouTube.

The Feynman diagrams, the worked examples and the practice exercises are written by Ganzaa.

1Why does a nucleus hold together?

2The four interactions

3Forces as the exchange of particles

4Feynman diagrams

5Two faces of the strong force, and the unification of forces

Why does a nucleus hold together?

The four interactions

Forces as the exchange of particles

Feynman diagrams

Two faces of the strong force, and the unification of forces