Summary

Composition and size: a nucleus $^{A}_{Z}X$ contains $Z$ protons and $N=A-Z$ neutrons (together, nucleons); nuclear radius $R=R_0A^{1/3}$, $R_0\approx1.2\ \text{fm}$, so nuclear volume $\propto A$ and nuclear density is nearly the same ($\approx2.3\times10^{17}\ \text{kg/m}^3$) for every nucleus. Atomic mass unit: $1\ \text{u}=1.660539\times10^{-27}\ \text{kg} = 931.5\ \text{MeV}$. Isotopes = same $Z$, different $A$; isobars = same $A$, different $Z$; isotones = same $N=A-Z$, different $Z$. Radioactivity: alpha ($^4_2$He nucleus, $A{-}4,Z{-}2$, lowest penetrating/highest ionizing power), beta (fast electron/positron, $A$ same, $Z\pm1$, moderate penetrating/ionizing power), gamma (EM photon, $A,Z$ unchanged, highest penetrating/lowest ionizing power). Decay law: $dN/dt=-\lambda N \Rightarrow N(t)=N_0e^{-\lambda t}$; half-life $T_{1/2}=0.693/\lambda$; mean life $\tau=1/\lambda=T_{1/2}/0.693$; activity $\mathcal{A}=\lambda N$, SI unit becquerel (Bq), $1\ \text{Ci}=3.7\times10^{10}\ \text{Bq}$. Mass-energy relation: $E=mc^2$; mass defect $\Delta m=[Zm_H+(A-Z)m_n]-M$ is the mass 'missing' from a bound nucleus versus its free nucleons. Binding energy $BE=\Delta m\,c^2$; binding energy per nucleon $BE/A$ measures nuclear stability, rising steeply for light nuclei, peaking $\approx8.8\ \text{MeV}$ near $A\approx56$ (iron), then falling slowly for heavy nuclei ($\approx7.6\ \text{MeV}$ at $A=238$). Nuclear fission: a heavy nucleus (e.g. $^{235}_{92}$U) splits into two medium nuclei on neutron absorption, releasing $\approx200\ \text{MeV}$ and further neutrons that can sustain a chain reaction, controlled in a reactor or uncontrolled in a weapon. Nuclear fusion: two light nuclei combine into a heavier one, releasing energy but requiring extremely high temperature ($\sim10^7$ …