6.4.2(h)-(l) - Quarks, beta decay and particle decay

6.4.2(h)-(l) - Quarks, beta decay and particle decay

Beta decay is not just a nucleus changing its proton number; in the quark model, it is one quark inside a particle changing type. In this lesson you will use the u\mathrm{u}, d\mathrm{d} and s\mathrm{s} quark charges to write beta-minus and beta-plus decay equations, check charge conservation, and handle simple particle-decay bookkeeping in OCR style.

Weak interactions and spectator quarks

From the previous lesson, retrieve only the pieces we need:

  • an up quark has charge +23e+\frac{2}{3}e
  • a down quark has charge −13e-\frac{1}{3}e
  • a strange quark also has charge −13e-\frac{1}{3}e
  • an antiquark has the opposite charge to its matching quark
  • a proton has quark composition uud\mathrm{uud}
  • a neutron has quark composition udd\mathrm{udd}

The weak interaction changes one quark type in beta decay. The other quarks in the hadron remain unchanged spectators.

Spectator quark

A spectator quark is a quark in the particle that does not change during the decay. It stays in the particle and is carried into the product hadron.

The emitted beta particle is a charged lepton:

  • beta-minus, β−\beta^-, is an electron, often written −10e{}^{0}_{-1}e
  • beta-plus, β+\beta^+, is a positron, often written +10e{}^{0}_{+1}e

The other emitted particle is neutral: an electron antineutrino in beta-minus decay, and an electron neutrino in beta-plus decay. OCR often writes these simply as νˉ\bar{\nu} and ν\nu; the subscript ee in this lesson reminds you that they are the electron-flavour neutrino and antineutrino.

For OCR quark-decay questions, first identify the quark that changes, then check that charge is conserved.

Beta-minus decay

In beta-minus decay, a down quark changes into an up quark. The charge of the quark has increased from −13e-\frac{1}{3}e to +23e+\frac{2}{3}e, an increase of +e+e. To keep total charge conserved, an electron with charge −e-e is emitted, along with an electron antineutrino with charge zero.

Beta-minus quark transformation

d→u+−10e+νˉed \rightarrow u + {}^{0}_{-1}e + \bar{\nu}_e

For a neutron, the full quark picture is:

udd→uud+−10e+νˉeudd \rightarrow uud + {}^{0}_{-1}e + \bar{\nu}_e

That is the quark-model version of a neutron becoming a proton. Only one of the two down quarks changes into an up quark; the original up quark and the other down quark are spectators.

[DIAGRAM: asset_name: 6.4.2(h)-(l) - Quarks, beta decay and particle decay - diagram 1; asset_slug: 6_04_2b_quarks_beta_decay_and_particle_decay__diagram_01; recommended_method: drawn_physics; description: Only one d changes in udd to uud; electron and antineutrino, spectator pair and charge equation all correct.; caption: In beta-minus decay, a down quark becomes an up quark and emits an electron and an electron antineutrino.]
In beta-minus decay, a down quark becomes an up quark and emits an electron and an electron antineutrino.

Worked charge check:

Left-hand side:

d=−13ed = -\frac{1}{3}e

Right-hand side:

u+e−+νˉe=+23e−e+0=−13eu + e^- + \bar{\nu}_e = +\frac{2}{3}e - e + 0 = -\frac{1}{3}e

So the quark equation is balanced in terms of charge.

Beta-plus decay

Beta-plus decay is the opposite quark change. An up quark changes into a down quark. The quark charge decreases from +23e+\frac{2}{3}e to −13e-\frac{1}{3}e, a decrease of ee. A positron with charge +e+e is emitted, with an electron neutrino of charge zero.

Beta-plus quark transformation

u→d++10e+νeu \rightarrow d + {}^{0}_{+1}e + \nu_e

Inside a proton-rich nucleus, the quark model for a proton changing into a neutron is:

uud→udd++10e+νeuud \rightarrow udd + {}^{0}_{+1}e + \nu_e

One up quark becomes a down quark. The other up quark and the original down quark are spectators.

Continue this lesson.

You’re previewing NovaLearn without an account. Create a free account to read the rest.

Create free account