Explain the change of quark character associated with the beta-plus decay and deduce the equation.

First, we can deduce the equation for beta-plus decay in terms of the nucleons. We know a positron, ß⁺ (antilepton), is produced, so to conserve lepton number an electron neutrino, v_e (lepton), must also be produced. As we know this is a nuclear reaction (occurring in the nucleus) it must involve either proton or neutron decay. We can then work out that, to conserve charge, it must be a proton decaying into a neutron as the positron on the right-hand side is positively charged:

p → n + ß⁺ +v_e

Now we consider the quark composition of the proton and neutron. As baryons both must contain 3 quarks. As the up quark has charge +2/3 and the down has charge -1/3 we can use our knowledge of the charge of the proton and neutron to figure out their compositions; uud and udd respectively. Finally, we can see the actual change occurring is an up quark decaying into a down quark:

u → d + ß⁺ +v_e