OCR Specification focus:
‘Explain β⁻ and β⁺ decay using quark transformations; balance charge in decay equations.’
Beta decay links changes inside nuclei to transformations of their constituent quarks, allowing unstable nuclides to become more stable. Understanding quark-level changes clarifies how β⁻ and β⁺ emission conserves charge and particle number.
Understanding Beta Decay in Terms of Quarks
Beta decay processes arise from the weak nuclear interaction, the only fundamental force capable of changing one type of quark into another. Because protons and neutrons are made of up (u) and down (d) quarks, a transformation between these quark types causes one nucleon to change into the other. This change is accompanied by the emission of a beta particle and the appropriate neutrino.
Weak interaction: The fundamental force responsible for processes that change quark flavour, enabling beta decays in atomic nuclei.
Beta decay occurs when a nucleus has an imbalance of protons and neutrons relative to its most stable configuration. The quark-level approach helps validate how charge is conserved in every reaction and why each type of beta decay emits specific leptons.
Beta Minus (β⁻) Decay
In β⁻ decay, a neutron (udd) inside an unstable nucleus transforms into a proton (uud). This requires a down quark to change into an up quark, increasing the proton number of the nucleus by one.
A neutron converts into a proton through emission of a W⁻ boson, which decays into an electron and an electron antineutrino. The diagram shows the charge flow and particle paths that characterise β⁻ decay, supporting understanding of weak-interaction mediation. Source.
Quark-Level Change in β⁻ Decay
A d-quark → u-quark conversion occurs via the weak force.
This increases the charge of the nucleon from 0 to +1.
The process emits:
a β⁻ particle (electron) to balance the positive charge gained,
an electron antineutrino, ensuring lepton number conservation.
Lepton number: A conserved quantity assigning +1 to leptons, −1 to antileptons, and ensuring balance in weak interactions such as beta decay.
Between quark conversion and emission of particles, the weak force mediates the interaction using a W⁻ boson, which is momentarily produced during the quark transformation. The W⁻ then decays rapidly into the electron and antineutrino.
Key Features of β⁻ Decay
Nucleon number (A) remains unchanged.
Proton number (Z) increases by 1.
The emitted β⁻ particle is a high-energy electron.
Antineutrinos carry away energy and momentum, ensuring conservation laws are satisfied.
EQUATION
—-----------------------------------------------------------------
β⁻ Decay (Nuclear):
A_Z X → A_(Z+1) Y + β⁻ + ν̄_e
A = Nucleon number (no unit)
Z = Proton number (no unit)
β⁻ = Electron with charge −1 e
ν̄_e = Electron antineutrino (neutral lepton)
—-----------------------------------------------------------------
The quark model makes it clear why β⁻ decay increases the charge of the nucleus: replacing a −1/3 charge d-quark with a +2/3 charge u-quark increases the nucleon charge by +1.
Beta Plus (β⁺) Decay
In β⁺ decay, a proton (uud) converts into a neutron (udd), decreasing the proton number of the nucleus by one. The reverse quark transformation occurs here: an up quark changes into a down quark, reducing the charge of the nucleon.
Quark-Level Change in β⁺ Decay
An u-quark → d-quark transformation occurs through the weak interaction.
This reduces the charge of the nucleon from +1 to 0.
Emission includes:
a β⁺ particle (positron),
an electron neutrino.
Because creating a positron requires energy, β⁺ decay occurs only when the mass difference between the parent and daughter nuclide is sufficient to provide this energy.
Positron: The antiparticle of the electron, carrying charge +1 e and produced in β⁺ decay.
After the quark changes flavour, a W⁺ boson is produced and rapidly decays into the positron and neutrino, mirroring the mechanism of β⁻ decay but with opposite charges.
A proton transforms into a neutron while emitting a W⁺ boson that decays into a positron and an electron neutrino. The reversed charge flow compared with β⁻ decay is clearly illustrated, supporting understanding of why proton number decreases by one. Source.
Key Features of β⁺ Decay
Nucleon number is conserved.
Proton number decreases by 1.
The emitted β⁺ particle has the same mass as an electron but opposite charge.
Neutrinos help maintain conservation of energy, momentum, and lepton number.
EQUATION
—-----------------------------------------------------------------
β⁺ Decay (Nuclear):
A_Z X → A_(Z−1) Y + β⁺ + ν_e
A = Nucleon number (no unit)
Z = Proton number (no unit)
β⁺ = Positron with charge +1 e
ν_e = Electron neutrino (neutral lepton)
—-----------------------------------------------------------------
For OCR students, the important emphasis is that charge must balance on both sides of any decay equation. The quark model does this automatically, providing a foundation for understanding why specific leptons appear in each decay.
Conservation Laws in Beta Decay
Beta decay processes obey strict conservation principles. These guide the structure of decay equations and ensure that quark transformations are physically valid.
Essential Conservation Rules
Charge conservation
β⁻ decay: neutron (0) → proton (+1) + electron (−1) + antineutrino (0)
β⁺ decay: proton (+1) → neutron (0) + positron (+1) + neutrino (0)
Nucleon number conservation
Nucleons convert type but are neither created nor destroyed.
Lepton number conservation
β⁻ decay: electron (+1) is balanced by antineutrino (−1).
β⁺ decay: positron (−1) balanced by neutrino (+1).
Energy and momentum conservation
Neutrinos carry away missing energy and account for continuous beta spectra.
Understanding beta decay through quark changes ensures a deeper grasp of how nuclei achieve stability and why specific particles appear in each decay pathway.
FAQ
The weak interaction allows quarks to change flavour by emitting or absorbing W bosons. These bosons carry charge and energy away from the transforming quark.
During beta minus decay, a down quark emits a W− boson and becomes an up quark.
In beta plus decay, an up quark emits a W+ boson and becomes a down quark.
The weak force’s ability to couple differently to quark types is what makes these transitions possible.
The energy released in beta decay is shared between three products: the daughter nucleus, the beta particle, and the neutrino.
Because the nucleus is very massive, the beta particle and neutrino effectively share the energy.
This sharing can vary continuously, giving the neutrino any energy up to a maximum determined by the decay.
The range of energies reflects the probabilistic nature of the weak interaction.
Beta plus decay requires the nucleus to expend energy to create a positron, which has the same mass as an electron but positive charge.
For the process to occur, the parent nucleus must have a mass greater than the daughter nucleus plus the mass equivalent of the positron.
Many unstable nuclides do not have enough mass-energy to satisfy this condition, so beta minus decay is often the energetically favoured route.
Both processes convert a proton to a neutron, but electron capture is chosen when there is insufficient energy to emit a positron.
Electron capture requires only a bound inner electron and does not need to create a new particle.
If the mass difference between the parent and daughter nuclides cannot provide the positron’s mass, electron capture becomes the dominant process.
The choice depends entirely on the energy balance of the nuclear transition.
W bosons are very massive—about 80 times the mass of a proton—so creating them requires significant energy.
In beta decay, they appear only as virtual particles, meaning they exist for a brief interval permitted by quantum uncertainty.
Their rapid decay into leptons ensures they do not violate conservation laws.
Their short lifetime is a direct consequence of their mass and the rules governing virtual particles.
Practice Questions
Question 1 (2 marks)
A neutron inside an unstable nucleus undergoes beta minus decay.
(a) State the quark change that occurs in this process.
(b) Name the two leptons emitted.
Question 1 (2 marks)
(a) Down quark changes into an up quark. (1 mark)
(b) Electron (beta minus particle) and electron antineutrino. (1 mark)
Question 2 (5 marks)
Beta plus decay and beta minus decay both involve the weak interaction.
Explain, in terms of quark transformations and conservation laws, how each process changes the composition and charge of the nucleus. Your answer should refer to:
• the quark flavour change
• the emitted particles
• charge conservation
• lepton number conservation.
Question 2 (5 marks)
Award marks for any of the following, up to 5 marks total:
• Beta minus decay: a down quark in the neutron changes into an up quark, turning the neutron into a proton. (1 mark)
• The process emits an electron and an electron antineutrino. (1 mark)
• Beta plus decay: an up quark in the proton changes into a down quark, turning the proton into a neutron. (1 mark)
• The process emits a positron and an electron neutrino. (1 mark)
• Charge conservation: beta minus increases nuclear charge by +1, beta plus decreases nuclear charge by 1; emitted leptons balance the charge change. (1 mark)
• Lepton number conservation: electron is balanced by antineutrino in beta minus; positron is balanced by neutrino in beta plus. (1 mark)
