= Solution
The original chart has $Z$ vertically and $N$ horizontally. Thus its region (a) is proton-rich relative to the beta-stable band, whereas (b) is neutron-rich.
* In (a), <beta-plus decay> changes a <proton> into a <neutron>:
$$
(Z,N)\longrightarrow(Z-1,N+1)+e^++\nu_e.
$$
<Electron capture>, $e^-+(Z,N)\to(Z-1,N+1)+\nu_e$, is the other proton-to-neutron weak process; it remains possible for some neutral atoms whose <beta-plus decay> lacks the $2m_e$ atomic-mass threshold.
* In (b), <beta-minus decay> changes a <neutron> into a <proton>:
$$
(Z,N)\longrightarrow(Z+1,N-1)+e^-+\bar\nu_e.
$$
* In the heavy region (e), <alpha decay> moves the parent down and left:
$$
(Z,N)\longrightarrow(Z-2,N-2)+{}^4_2\mathrm{He}.
$$
The emitted <alpha particle> contains two <protons> and two <neutrons>. Very heavy <nuclei> can also compete through <nuclear fission>; the chart alone does not determine each nuclide's branching fractions.
\Image[/past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2021-beta-quark-diagrams.png]
{title=Quark-level beta-plus, beta-minus, and electron-capture processes}
The quark transitions are $u\to d+W^+$ followed by $W^+\to e^+\nu_e$ in (a), and $d\to u+W^-$ followed by $W^-\to e^-\bar\nu_e$ in (b). The additional panel shows <electron capture> as $u+e^-\to d+\nu_e$ through <W boson> exchange. The remaining quarks in each <nucleon> are spectators.
Regions (c) and (d) lie beyond the proton and neutron binding limits, respectively. In (c), unbound <protons> can be emitted, $(Z,N)\to(Z-1,N)+p$; in (d), unbound <neutrons> can be emitted, $(Z,N)\to(Z,N-1)+n$. These are the <proton drip line> and <neutron drip line> limits, with one- or several-nucleon emission possible according to the <nuclear separation energies>. They are not merely more distant points on a beta-decay trajectory.
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