CBSE Class 12 Physics: Dual Nature of Radiation — Notes 2026

Wave-Particle Duality of Light

• Light exhibits both wave properties (interference, diffraction) and particle properties (photoelectric effect)
• Photon: quantum of electromagnetic energy; E = hf = hc/λ; momentum p = h/λ (de Broglie)
• Planck's constant h = 6.626 × 10⁻³⁴ J·s; fundamental constant of quantum physics

Photoelectric Effect

• When light hits metal surface, electrons emitted if frequency ≥ threshold frequency ν₀
• Einstein's equation: KE_max = hν − φ where φ = work function (hν₀)
• Key observations: 1) below ν₀, no effect regardless of intensity; 2) above ν₀, KE independent of intensity; 3) emission instantaneous

Work Function and Stopping Potential

• Work function φ: minimum energy needed to eject electron from metal surface; unit eV
• Stopping potential V₀: voltage to stop most energetic photoelectrons; eV₀ = hν − φ
• Graph of V₀ vs. ν: straight line; slope = h/e; x-intercept = ν₀; used to find h experimentally

de Broglie Hypothesis

• Matter also has wave nature; de Broglie wavelength λ = h/mv = h/p
• For electron accelerated through V volts: λ = 12.27/√V Å (Angstroms)
• Bohr's quantisation condition: derived from de Broglie — electrons in orbit = standing waves; 2πr = nλ

Davisson-Germer Experiment

• Proved wave nature of electrons; electron beam diffracted by nickel crystal (1927)
• Diffraction pattern showed wavelength matching de Broglie prediction for electrons at that energy
• Nobel Prize: Davisson (1937); confirmed wave-particle duality for matter

Applications

• Electron microscope: short wavelength electrons (λ ~ 0.01 nm) gives 100,000× magnification vs light microscope
• CRT (Cathode Ray Tube): TV screens, oscilloscopes — based on thermionic emission and electron deflection
• Photovoltaic cells: photoelectric effect → solar cells; photoelectric threshold material-specific

CBSE Board Focus

• Dual Nature: 5–6 marks; photoelectric effect (explain observations using Einstein's equation)
• Numerical: find stopping potential, KE, λ; de Broglie wavelength given velocity or accelerating voltage
• Plot V₀ vs ν: label slope h/e, x-intercept ν₀, y-intercept −φ/e