Beta-Minus Decay and Quarks

In beta-minus (β⁻) decay a neutron in a neutron-rich nucleus changes into a proton. An electron and an electron antineutrino are emitted:n → p + e⁻ + ν_eThe neutron is udd and the proton is uud, so at quark level one down quark changes into an up quark:d → u + e⁻ + ν_eCharge balances: −1/3 e = +2/3 e + (−1 e) + 0. The two leptons carry away a total charge of −e, which is exactly the change from a d quark to a u quark. A change of quark type like this is caused by the weak interaction.In the nucleus, the nucleon number A stays the same and the proton number Z goes up by 1. A free neutron can also decay this way, because the neutron has a slightly greater mass than the proton.Worked example: carbon-14 decays by β⁻ emission.¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν_eCarbon-14 has 6 protons and 8 neutrons, so it contains 2 × 6 + 8 = 20 up quarks and 6 + 2 × 8 = 22 down quarks. Nitrogen-14 has 7 protons and 7 neutrons: 2 × 7 + 7 = 21 up quarks and 7 + 2 × 7 = 21 down quarks. Exactly one down quark has become an up quark.