SUMMARY

This unit developed the dual (particle-and-wave) nature of both radiation and matter across four connected stages. Electron emission is the liberation of electrons from a metal's surface, requiring a minimum energy called the work function ($\phi_0$, in eV, where $1\ \text{eV}=1.602\times10^{-19}$ J), and comes in four flavours -- thermionic (heat), field (a strong external electric field), photoelectric (light or other radiation) and secondary (impact of fast electrons) emission. The photoelectric effect, first hinted at by Hertz and confirmed by Hallwachs and Lenard, showed that photocurrent is directly proportional to light intensity, while the stopping potential -- and hence the maximum kinetic energy of the photoelectrons, $K_{max}=eV_0$ -- is independent of intensity but grows linearly with frequency above a metal-specific threshold frequency. Classical wave theory could explain none of this; Planck's proposal that oscillator energy is quantized ($E=nh\nu$) and Einstein's 1905 extension of this to light itself -- treating light as a stream of photons, each carrying energy $h\nu$ -- gave Einstein's photoelectric equation $K_{max}=h\nu-\phi_0$, which explains every observed law at once and establishes that light behaves as a wave while propagating and as a particle while interacting with matter. A photo cell exploits this effect to convert light energy directly into electrical energy. Turning the duality around, de Broglie's 1924 hypothesis proposed that every moving matter particle -- electrons, protons, neutrons -- has an associated de Broglie (matter) wave of wavelength $\lambda=h/p=h/mv$, confirmed experimentally by Davisson and Germer in 1927 through electron diffraction off a nickel crystal, and exploited practically in the electron microscope, whose far shorter illuminating wavelength gives it much higher resolving power than any optical microscope. Finally, X-rays -- highly penetrating electromagnetic radiation produced when fast electrons are suddenly decelerated at a target - …