How the ideas connect
A good science page should make the connection visible, not just list definitions.
Radioactivity
Radioactivity comes from unstable atomic nuclei that transform spontaneously and emit radiation. It is a nuclear phenomenon, distinct from ordinary chemical reactions involving electrons.
The same phenomenon helps us understand nuclei, date materials and build important medical techniques.
Half-life
Half-life is the time required for the expected number of undecayed nuclei, or equivalently the activity of a large sample, to fall to one half of its initial value.
Successive half-lives produce halves, quarters, eighths and so on; the process is exponential rather than linear.
Alpha decay
Alpha decay is a nuclear transformation in which an unstable nucleus emits an alpha particle, a helium-4 nucleus containing two protons and two neutrons.
The parent loses two units of atomic number and four units of mass number, giving a simple conservation check for nuclear equations.
Beta decay
Beta decay changes the proton-neutron balance of a nucleus through the weak interaction. In beta-minus decay a neutron becomes a proton while an electron and an antineutrino are emitted.
Beta processes explain why a nucleus can change element without losing four nucleons as in alpha decay.
Gamma radiation
Gamma radiation consists of high-energy photons emitted when a nucleus moves from a higher-energy state to a lower-energy state.
Gamma emission changes nuclear energy without changing proton or neutron numbers, although it often follows another nuclear transformation.
What to notice
A good science page should make the connection visible, not just list definitions.
Sources
IUPAC Gold Book · NIST · BIPM