Experiments you can run yourself.
A nucleus's mass is smaller than the sum of its nucleon masses — this mass defect corresponds to the binding energy E=Δm·c². The most stable nuclei have a mass around that of iron (maximum binding energy per nucleon).
Energy is released when the products lie closer to the peak of the binding-energy curve: fusion joins light nuclei (stars), fission splits heavy ones (power plants).
In a nuclear reaction the mass number A and the atomic number Z are conserved. α decay changes (A−4, Z−2), β⁻ (A, Z+1). Penetrating power increases: α < β < γ.
N=N₀(½)^(t/T½); after each T½ half of the nuclei are gone.
Paper stops α, aluminium stops β, and only thick lead stops γ.
A few alpha particles bounce back at large angles — the atom has a small, massive nucleus (Nobel 1908).
Neutrinos change "flavour" in flight — possible only if they have mass (Nobel 2015).
Atoms of the same element with different numbers of neutrons are isotopes (Nobel Prize in Physics 1935).
When an electron meets a positron, they annihilate, converting all their mass into pure energy (Nobel Prize in Physics 1936).
A neutrino beam that has crossed the entire Earth barely changes (Nobel Prize in Physics 1995).