Dual Nature of Radiation and Matter

The chapter where light stops being only a wave and matter stops being only a particle — short, formula-light and extremely high-yield: 4-6 Board marks and 1-2 near-guaranteed questions in JEE/NEET. The story opens with the discovery of the electron (cathode rays, Thomson's $e/m = 1.76 \times 10^{11}$ C/kg, Millikan's oil-drop quantisation of charge) and the idea of the work function $\phi_0$ — the minimum energy an electron needs to escape a metal, deliverable by heat, strong fields or light. Hertz, Hallwachs and Lenard's experiments reveal the photoelectric effect's strange rules: current tracks intensity, but the stopping potential $V_0$ (and hence $K_{max} = eV_0$) depends only on frequency, with a sharp threshold $\nu_0$ below which nothing happens no matter how bright the light, and emission is instantaneous even in dim light. The wave theory fails on all counts, and Einstein's photon picture rescues everything with one line: $K_{max} = h\nu - \phi_0$ — a straight $V_0$ vs $\nu$ graph of slope $h/e$ that Millikan verified while trying to disprove it. The photon emerges as a genuine particle with $E = h\nu$ and $p = h/\lambda$, and de Broglie completes the symmetry: every moving particle carries a wavelength $\lambda = h/p$, measurable for electrons, hopelessly tiny for cricket balls. Every graph, law, constant and exam trap is covered.