Final answer:
The equations are associated with nuclear physics, particularly the calculation of binding energy in atomic nuclei and nuclear decay processes such as β+ decay and electron capture.
Step-by-step explanation:
The provided equations relate to the physics of nuclear reactions and energy calculations in atomic nuclei. Specifically, the equation BE = {[2m(¹H)+2mn]_m(He)} c² represents the binding energy (BE) of a helium nucleus, calculated using the masses of hydrogen (¹H), neutron (mn), and helium (He) in unified atomic mass units (u). This equation takes into account the energy equivalent (E = mc²) and allows for the calculation of binding energy, which is the energy required to split a nucleus into its component nucleons.
The provided decay equations deal with nuclear decay processes, such as β+ decay (positron emission) and electron capture. The β+ decay equation AZ-1 AXN YN+1 + B+ +ve indicates a nucleus X transforming into a nucleus Y with the emission of a positron (B+) and an electron neutrino (ve). Electron capture is represented by AXN + e YN+1 +ve, where a nucleus X absorbs an electron (e) to become nucleus Y and emits an electron neutrino (Ve). The conservation of electron family number and total nucleons is emphasized in these nuclear reactions.