Chapter 11 — Dual Nature of Radiation and Matter

Chapter 11 of Class 12 Physics Part II covers the dual nature of radiation and matter, explaining the photoelectric effect, Einstein's photon theory, and de Broglie's hypothesis that moving particles exhibit wave-like properties described by the relation λ = h/p.

This chapter establishes that light and matter both exhibit dual wave-particle nature. It covers electron emission mechanisms (thermionic, field, and photoelectric), the experimental observations of the photoelectric effect by Hertz, Hallwachs, and Lenard, and the failure of classical wave theory to explain those observations. Einstein resolved the contradictions in 1905 by proposing that radiation energy is quantised into photons, each carrying energy hν. His photoelectric equation Kmax = hν − φ₀ explains threshold frequency, instantaneous emission, and intensity dependence. De Broglie extended this duality to matter, proposing that any moving particle of momentum p has an associated wavelength λ = h/p.

1. 01The work function (φ₀) is the minimum energy an electron needs to escape a metal surface; it varies by metal and is measured in electron volts (1 eV = 1.602 × 10⁻¹⁹ J).
2. 02Photoelectric current is directly proportional to the intensity of incident light, but the maximum kinetic energy of emitted photoelectrons depends only on the frequency of light, not its intensity.
3. 03Below the threshold frequency ν₀ = φ₀/h, no photoelectric emission occurs regardless of how intense the incident radiation is; emission is instantaneous (within ~10⁻⁹ s) above the threshold.
4. 04Einstein's photoelectric equation Kmax = hν − φ₀ (equivalently eV₀ = hν − φ₀) accounts for all observed features of the photoelectric effect and was experimentally confirmed by Millikan.
5. 05Each photon carries energy E = hν and momentum p = hν/c; photons are electrically neutral and travel at the speed of light.
6. 06De Broglie proposed that matter particles have an associated wavelength λ = h/p = h/(mv); this wave character is measurable for sub-atomic particles but negligibly small for macroscopic objects.