Quarks and leptons, antiparticles, baryons and mesons, conservation laws of charge, baryon and lepton number, and beta decay at the quark level.

What this dot point is asking

WJEC wants you to describe quarks and leptons and their antiparticles, classify hadrons as baryons or mesons, apply conservation laws to test whether a reaction is allowed, and explain beta-minus and beta-plus decay in terms of quarks. The standard model of particle physics looks intimidating, but at AS level it reduces to a small set of building blocks and three bookkeeping rules that the examiners test again and again.

The answer

Quarks and leptons

The antiparticle of the up quark is the anti-up with charge $-\frac{2}{3}e$, and the antiparticle of the electron is the positron with charge $+e$. When a particle meets its antiparticle they can annihilate, converting their rest mass into energy (typically gamma photons) in line with $E = mc^2$.

Baryons and mesons

Particles made of quarks are hadrons. A baryon is made of three quarks: a proton is uud (charge $+e$) and a neutron is udd (charge $0$). A meson is a quark and an antiquark, for example a pion. Because mesons contain one quark and one antiquark, their baryon number is zero, which matters when you apply the conservation rules below.

Conservation laws

Baryon number is $+1$ for a baryon, $-1$ for an antibaryon and $0$ for a meson or lepton. Lepton number is $+1$ for a lepton, $-1$ for an antilepton, and $0$ for a hadron. Checking a proposed reaction is then a matter of adding these numbers up on each side, as in the worked example below.

Beta decay at the quark level

In beta-minus decay, a down quark changes into an up quark, so a neutron (udd) becomes a proton (uud), emitting an electron and an electron-antineutrino. In beta-plus decay, an up quark changes into a down quark, so a proton becomes a neutron, emitting a positron and an electron-neutrino. Both are mediated by the weak interaction.

Examples in context

Example 1. Carbon-14 dating. A carbon-14 nucleus is unstable because it has too many neutrons. One neutron undergoes beta-minus decay, $n \rightarrow p + e^- + \bar{\nu}_e$, turning the nucleus into nitrogen-14. At the quark level a single down quark inside that neutron flips to an up quark. The steady rate of this decay is what makes radiocarbon dating possible.

Example 2. The PET scanner. Positron emission tomography uses a beta-plus emitter such as fluorine-18. A proton becomes a neutron, $p \rightarrow n + e^+ + \nu_e$, emitting a positron. The positron travels a few millimetres, meets an electron, and they annihilate into two gamma photons that fly off in opposite directions. Detecting these back-to-back photons lets the scanner reconstruct where the tracer is concentrated.

Try this

Q1. Write the quark composition of a proton and a neutron. [2 marks]

• Cue. Proton uud; neutron udd.

Q2. Explain, in terms of quarks, what happens in beta-minus decay. [2 marks]

• Cue. A down quark changes to an up quark, so a neutron becomes a proton, emitting an electron and an antineutrino.