Nuclei

The chapter that goes inside Rutherford's dot — short, numerical-friendly and dependably worth 4-6 Board marks plus 1-2 questions in JEE/NEET. It opens with the bookkeeping of nuclear matter: the atomic mass unit (1 u = $1.66 \times 10^{-27}$ kg = 931.5 MeV/$c^2$), isotopes-isobars-isotones, the proton, and Chadwick's 1932 neutron ($m_n \approx m_p$, free mean life ~1000 s). Electron-scattering gives the size rule $R = R_0A^{1/3}$ ($R_0$ = 1.2 fm), whose stunning corollary is a constant nuclear density ~$2.3 \times 10^{17}$ kg/m³ — every nucleus is a droplet of the same liquid. Einstein's $E = mc^2$ then unlocks the chapter's engine: the mass defect $\Delta M = [Zm_p + (A-Z)m_n] - M$ and binding energy $E_b = \Delta Mc^2$, plotted per nucleon against A to give physics' most consequential curve — flat at ~8 MeV for 30 < A < 170, peaking near 8.75 MeV at A = 56, drooping at both ends. The droop explains everything: heavy nuclei release ~200 MeV by fission ($^{235}$U + n → Ba + Kr + 3n, the reactor and bomb reaction), light nuclei release energy by fusion (the p-p cycle burning four protons into helium + 26.7 MeV — the Sun's furnace, needing ~$10^7$-$10^9$ K to beat the ~400 keV Coulomb barrier). The short-range, charge-blind nuclear force (strongest of all, saturating, repulsive below ~0.8 fm) holds it together, and radioactivity (alpha, beta, gamma — with the decay law, half-life and activity covered as JEE/NEET essentials) marks the nuclei that fail. Every formula, curve-reading and exam trap is covered.