Summary

• Photoelectric effect: Einstein’s equation $K_{\text{max}} = h\nu - \phi_0$, where $\phi_0$ is the work function. Stopping potential $V_0$ satisfies $eV_0 = h\nu - \phi_0$. The effect proves light is quantised as photons of energy $h\nu$.

• Matter waves: de Broglie wavelength $\lambda = \frac{h}{p} = \frac{h}{mv}$ for a particle of momentum $p$. For an electron accelerated through $V$ volts, $\lambda = \frac{h}{\sqrt{2meV}} \approx \frac{1.227}{\sqrt{V}}$ nm.

• Davisson–Germer experiment: Verified de Broglie waves by observing diffraction of electrons from a nickel crystal. The intensity peak at $54^\circ$ for $54$ eV electrons matched $\lambda = 0.165$ nm.

• Wave–particle duality: Light and matter exhibit both wave and particle properties. Which aspect is observed depends on the experiment (e.g., interference vs. photoelectric effect).

• Photon properties: Energy $E = h\nu$, momentum $p = \frac{h}{\lambda}$, rest mass $= 0$, speed $c$ in vacuum. Intensity $I = n h\nu$ where $n$ is photon flux.

• Key experimental facts: Photoelectric emission is instantaneous ($< 10^{-9}$ s), depends on frequency (not intensity) for threshold, and $K_{\text{max}}$ varies linearly with $\nu$ (slope $h$, intercept $-\phi_0$).

• Dual nature of radiation: Electromagnetic radiation behaves as waves (interference, diffraction) and as particles (photoelectric effect, Compton effect).

Physical quantities, symbols, dimensions and units used in this chapter.