Nuclear and Particle Physics: Atomic Structure, Radioactivity, Binding Energy and the Standard Model
Atomic structure and decay
A nuclide is written ^A_Z X, where A is nucleon number and Z is proton number. Isotopes have the same Z but different A. Alpha decay decreases A by 4 and Z by 2; beta-minus decay increases Z by 1 and emits an electron and antineutrino; gamma emission changes energy but not A or Z.
Activity and half-life
Activity A = λN, with λ = ln2/T½. After n half-lives, activity and undecayed nuclei fall by 2^n. Count half-lives, not days. Decay is random and spontaneous; the half-life is unaffected by temperature or chemical state.
Binding energy and particles
Mass defect Δm gives binding energy E = Δm c²; 1 u = 931.5 MeV. Binding energy per nucleon peaks near iron-56, so fusion releases energy for light nuclei and fission for heavy nuclei. The Standard Model has quarks and leptons as fundamental particles; hadrons are baryons (three quarks) or mesons (quark–antiquark). Charge, baryon number, lepton number and energy–momentum are conserved.
Worked example
A source has activity 640 Bq and half-life 8.0 days. After 24 days, n = 24/8.0 = 3 half-lives, so A = 640/2³ = 80 Bq. Alternatively, λ = ln2/(8.0 × 86400) = 1.0 × 10^-6 s^-1, and N = A/λ ≈ 8.0 × 10^7 nuclei.
Traps
Using atomic mass instead of nuclear mass in mass defect; forgetting the antineutrino in beta-minus decay; thinking gamma decay changes the element; using 2n instead of 2^n; ignoring lepton number in decay equations.