Quark Character Changes in Beta Decay Revision Notes | A Level AQA Physics

1. Why Quarks Matter in Beta Decay

At GCSE, beta decay looks like a nucleus spitting out an electron. At A Level, you go one layer deeper: the electron does not come from the electron cloud — it is created inside the nucleus when a quark changes its identity. That single quark transformation is the entire story of beta decay.

Understanding quark character changes lets you write decay equations at the most fundamental level, justify conservation laws, and answer the higher-mark 'explain' questions that separate A-grade responses from C-grade ones.

2. Quark Composition of the Proton and Neutron

Before you can track what changes in beta decay, you need to know the starting point. Both the proton and the neutron are baryons, meaning they are each made of three quarks. The two quark flavours you need here are the up quark (symbol $u$, charge $+\frac{2}{3}e$) and the down quark (symbol $d$, charge $-\frac{1}{3}e$).

Notice the pattern: the proton has two up quarks and one down quark, while the neutron has one up quark and two down quarks. The only difference between them is the swap of one quark flavour — and that is precisely what beta decay exploits.

3. Beta-Minus Decay: The Down-to-Up Transformation

In beta-minus ($\beta^-$) decay, a neutron inside the nucleus transforms into a proton. At the nuclear level you see the proton number increase by one and the nucleon number stay the same. At the quark level, the mechanism is this: one down quark inside the neutron changes into an up quark.

The neutron's quark composition changes from $udd$ to $uud$ — which is exactly the proton. The transformation creates a $W^-$ boson (the exchange particle of the weak interaction), which then decays into an electron ($e^-$) and an electron antineutrino ($\bar{ u}_e$).

Worked example: Writing the Beta-Minus Decay Equation at the Quark Level

Show the quark character change in $\beta^-$ decay and verify that charge is conserved.

1. Neutron: $u\, d\, d$ — The neutron is the particle undergoing the decay. Its three quarks are one up and two down.
2. One $d$ quark $\rightarrow$ one $u$ quark — This is the defining quark character change in $\beta^-$ decay. The weak interaction mediates this transformation via a $W^-$ boson.
3. $u\, d\, d \rightarrow u\, u\, d$ — The new combination $uud$ is the quark composition of a proton.
4. $n \rightarrow p + e^- + \bar{ u}_e$ — The electron and antineutrino are produced when the $W^-$ boson decays. Both are needed to conserve lepton number.
5. Left: $0$. Right: $+1 + (-1) + 0 = 0$. ✓ — Charge is conserved across the decay. The quark charge change from $d$ ($-\frac{1}{3}e$) to $u$ ($+\frac{2}{3}e$) accounts for the $+1e$ gained by the proton, balanced by the $-1e$ of the emitted electron.

Answer: In $\beta^-$ decay: $d \rightarrow u$. The neutron ($udd$) becomes a proton ($uud$). Charge is conserved: $0 = +1 - 1 + 0$.

4. Beta-Plus Decay: The Up-to-Down Transformation

Beta-plus ($\beta^+$) decay is the mirror image of $\beta^-$ decay. Here, a proton inside the nucleus transforms into a neutron. The proton number decreases by one and the nucleon number stays the same. At the quark level, one up quark inside the proton changes into a down quark.

The proton's quark composition changes from $uud$ to $udd$ — which is the neutron. This time the exchange particle is a $W^+$ boson, which decays into a positron ($e^+$) and an electron neutrino ($ u_e$).

Worked example: Writing the Beta-Plus Decay Equation at the Quark Level

Show the quark character change in $\beta^+$ decay and verify that charge is conserved.

1. Proton: $u\, u\, d$ — The proton is the particle undergoing the decay. Its three quarks are two up and one down.
2. One $u$ quark $\rightarrow$ one $d$ quark — This is the defining quark character change in $\beta^+$ decay. The weak interaction mediates this via a $W^+$ boson.
3. $u\, u\, d \rightarrow u\, d\, d$ — The new combination $udd$ is the quark composition of a neutron.
4. $p \rightarrow n + e^+ + u_e$ — The positron and electron neutrino are produced when the $W^+$ boson decays. Both are needed to conserve lepton number.
5. Left: $+1$. Right: $0 + (+1) + 0 = +1$. ✓ — Charge is conserved. The quark charge change from $u$ ($+\frac{2}{3}e$) to $d$ ($-\frac{1}{3}e$) accounts for the $-1e$ lost by the proton, balanced by the $+1e$ of the emitted positron.

Answer: In $\beta^+$ decay: $u \rightarrow d$. The proton ($uud$) becomes a neutron ($udd$). Charge is conserved: $+1 = 0 + 1 + 0$.

5. Comparing Beta-Minus and Beta-Plus: The Full Picture

Now that both decay types are established, it is worth placing them side by side. The two processes are genuinely opposite in their quark transformation, their emitted particles, and the direction of charge change — but they share the same conservation laws and the same weak interaction mechanism.

One pattern worth locking in: the charge of the emitted lepton always matches the charge change of the quark. In $\beta^-$ decay, the quark gains $+1e$ (d to u), so the emitted electron carries $-1e$ to balance. In $\beta^+$ decay, the quark loses $+1e$ (u to d), so the emitted positron carries $+1e$ to balance.

6. Conservation Laws at the Quark Level

Every beta decay must satisfy four conservation laws simultaneously: charge, baryon number, lepton number, and energy-momentum. The quark character change is the engine that drives the charge change, but the other laws constrain which particles must accompany it.

Baryon number is conserved because the total number of quarks does not change — one quark changes flavour. Each quark carries baryon number $+\frac{1}{3}$, so three quarks always give baryon number $+1$. The neutron and proton both have baryon number $+1$, and the emitted electron or positron has baryon number $0$, so the total is unchanged.

Lepton number conservation is why the neutrino or antineutrino must be emitted. Before the decay, lepton number is $0$. An electron ($L = +1$) must be accompanied by an antineutrino ($L = -1$) to keep the total at zero. A positron ($L = -1$) must be accompanied by a neutrino ($L = +1$) for the same reason.

7. Exam Technique and Common Mistakes

Questions on quark character changes tend to appear as 'explain' or 'describe' questions worth 2–4 marks. The mark scheme rewards specific quark-level language, not just the nuclear-level description you learned at GCSE. Saying 'a neutron becomes a proton' alone will not score the quark-level marks.

When a question asks you to 'explain' beta decay in terms of quarks, structure your answer in three beats: name the quark that changes, state what it changes into, and state the resulting nucleon. For example: 'A down quark changes into an up quark, so the neutron ($udd$) becomes a proton ($uud$).' That is a complete, mark-winning explanation at the quark level.

The quark character changes in $\beta^-$ and $\beta^+$ decay are the fundamental mechanism behind all beta decay processes: $d \rightarrow u$ for $\beta^-$ and $u \rightarrow d$ for $\beta^+$, each mediated by the weak interaction and each satisfying charge, baryon number, and lepton number conservation simultaneously.