OCR · A-Level · Physics

    Course version: H556 · Version from Sept 2015

    (i) β⁻ decay in terms of a quark model; d → u + ⁰₋₁e + ν̄

    Full specification wording

    Fundamental particles: (i) β⁻ decay in terms of a quark model; d → u + ⁰₋₁e + ν̄

    Beta-minus decay happens when a neutron-rich nucleus converts a neutron into a proton.

    Checked against the OCR H556 specification (opens in a new tab) on .

    • Point 9 of 12
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    Beta-minus decay happens when a neutron-rich nucleus converts a neutron into a proton. In the quark model the neutron is udd and the proton is uud, so one down quark must change into an up quark. The transformation is d → u + ⁰₋₁e + ν̄, where ⁰₋₁e is the beta-minus particle (an electron) and ν̄ is the electron antineutrino. Charge must balance: the down quark has charge −1⁄3, while the up quark (+2⁄3), the electron (−1) and the antineutrino (0) sum to −1⁄3. Lepton number also balances because the electron has lepton number +1 and the antineutrino has −1. The emitted electron and antineutrino are not quarks; they are leptons produced by the weak interaction. A useful check is to write the quark content of the parent and daughter nucleon and confirm that only one quark flavour changes.

    What earns the marks

    • Identifies that in β⁻ decay a down quark transforms into an up quark, changing a neutron into a proton.
    • States the transformation d → u + ⁰₋₁e + ν̄ with the electron and electron antineutrino as products.
    • Confirms charge conservation: −1⁄3 = +2⁄3 + (−1) + 0.
    • Recognises that the emitted electron and antineutrino are leptons, not quarks, and that the weak interaction mediates the change.
    • Distinguishes β⁻ decay from β⁺ decay by the direction of quark flavour change and the particle emitted.

    Common mistakes and how to put them right

    • Writing the antineutrino as a neutrino.

      Put it right: The β⁻ product is the electron antineutrino ν̄, which balances lepton number against the electron.

    • Treating the electron as a quark or as part of the nucleon.

      Put it right: It is a lepton emitted from the nucleus, not a constituent of the neutron.

    • Balancing charge incorrectly by ignoring the down quark's negative charge.

      Put it right: The down quark charge is −1⁄3, not +1⁄3 or zero.

    Exam tips

    • Write the quark-level equation and then check charge on both sides before selecting an answer.
    • Check lepton number as well as charge; a correct-looking charge balance can still have the wrong neutrino type.
    • Remember that the nucleon changes because its quark content changes, not because a proton is added from outside.

    Try the lesson

    The start of the Fundamental particles: (i) β⁻ decay in terms of a quark model; d → u + ⁰₋₁e + ν̄ lesson, made from checked teaching notes for this specification point.

    Listen

    Beta-minus decay happens when a neutron-rich nucleus converts a neutron into a proton. In the quark model the neutron is udd and the proton is uud, so one down quark must change into an up quark. The transformation is d → u + ⁰₋₁e + ν̄, where ⁰₋₁e is the beta-minus particle (an electron) and ν̄ is the electron antineutrino. Charge must balance: the down quark has charge −1⁄3, while the up quark (+2⁄3), the electron (−1) and the antineutrino (0) sum to −1⁄3. Lepton number also balances because the electron has lepton number +1 and the antineutrino has −1. The emitted electron and antineutrino are not quarks; they are leptons produced by the weak interaction. A useful check is to write the quark content of the parent and daughter nucleon and confirm that only one quark flavour changes. A strong answer earns marks for these points. Identifies that in β⁻ decay a down quark transforms into an up quark, changing a neutron into a proton. States the transformation d → u + ⁰₋₁e + ν̄ with the electron and electron antineutrino as products. Confirms charge conservation: −1⁄3 = +2⁄3 + (−1) + 0. Recognises that the emitted electron and antineutrino are leptons, not quarks, and that the weak interaction mediates the change. Exam tip: Write the quark-level equation and then check charge on both sides before selecting an answer.

    See it

    A top-down flowchart. At the top is a node labelled Neutron udd, which leads down to a node labelled Down quark d. From the down quark node, one arrow leads to a node labelled Up quark u, which leads on to a node labelled Proton uud. Two further arrows from the down quark node lead to a node labelled Electron ⁰₋₁e and a node labelled Electron antineutrino ν̄. A separate node labelled Weak interaction has an arrow pointing into the down quark node.
    Shows how a down quark in a neutron changes into an up quark, producing a proton, an electron and an electron antineutrino in β⁻ decay.

    Key words

    Say what each word means before you turn the card.

    Quark model of nucleons

    Try answering aloud or in your head before turning the card.

    Conservation of charge

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    Conservation of lepton number

    Try answering aloud or in your head before turning the card.

    Weak interaction and particle decay

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    See every definition
    Quark model of nucleons
    In this model the neutron is udd and the proton is uud, so in β⁻ decay one down quark must change into an up quark.
    Conservation of charge
    Charge must balance: the down quark has charge −1⁄3, while the up quark (+2⁄3), the electron (−1) and the antineutrino (0) sum to −1⁄3.
    Conservation of lepton number
    Lepton number balances because the electron has lepton number +1 and the antineutrino has −1.
    Weak interaction and particle decay
    The emitted electron and antineutrino are not quarks; they are leptons produced by the weak interaction.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. At the top is a node labelled Neutron udd, which leads down to a node labelled Down quark d. From the down quark node, one arrow leads to a node labelled Up quark u, which leads on to a node labelled Proton uud. Two further arrows from the down quark node lead to a node labelled Electron ⁰₋₁e and a node labelled Electron antineutrino ν̄. A separate node labelled Weak interaction has an arrow pointing into the down quark node.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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