Atoms and Nuclei — Easy Practice (Set 2)

Quick Recap — The Nucleus

• Composition: $Z$ protons and $A$ nucleons; isotopes (same $Z$), isobars (same $A$), isotones (same neutron number).
• Size: $R = R_0 A^{1/3}$ (with $R_0 \approx 1.2$ fm); the nuclear density is nearly the same for all nuclei.
• Binding energy: $BE = \Delta m\,c^2$; $1\ \text{u} = 931.5$ MeV; the binding-energy-per-nucleon curve peaks near $A \approx 56$.
• Radioactivity: alpha (a helium nucleus), beta (an electron), gamma (a photon); decay law $N = N_0 e^{-\lambda t}$, half-life $T_{1/2} = \dfrac{0.693}{\lambda}$, activity $A = \lambda N$.
• Fission splits heavy nuclei and fusion joins light nuclei — both release energy and power the stars.