Dual Nature of Radiation and Matter

• Introduction

  • Wave-particle duality concept
  • Radiation showing particle nature
  • Matter showing wave nature

• Electron Emission

  • Types of Emission
    • Thermionic emission (via heat)
    • Field emission (via strong electric field)
    • Photoelectric emission (via light)
  • Work Function ($\phi_0$): Minimum energy needed to eject an electron

• Photoelectric Effect

  • Experimental Setup
    • Evacuated glass tube with photosensitive plate and collector
  • Key Observations
    • Instantaneous emission
    • Threshold frequency ($\nu_0$): Minimum frequency for emission
    • Intensity affects current, not kinetic energy
    • Frequency affects stopping potential/kinetic energy
  • Failure of Wave Theory
    • Could not explain frequency dependence and instantaneous nature

• Einstein's Photoelectric Equation

  • Explanation using Planck's Quantum Theory
  • Photon: Energy packet ($E = h\nu$)
  • Equation: $K_{max} = h\nu - \phi_0$
  • Explanation of threshold frequency and stopping potential ($V_0$)

• Particle Nature of Light (The Photon)

  • Characteristics of Photons
    • Rest mass is zero
    • Energy: $E = h\nu = \frac{hc}{\lambda}$
    • Momentum: $p = \frac{h}{\lambda} = \frac{E}{c}$
    • Electrically neutral

• Wave Nature of Matter (De Broglie Waves)

  • De Broglie Hypothesis: Matter possesses wave-like properties
  • De Broglie Wavelength formula: $\lambda = \frac{h}{p} = \frac{h}{mv}$
  • De Broglie wavelength for an accelerated electron: $\lambda = \frac{1.227}{\sqrt{V}}$ nm

• Davisson and Germer Experiment

  • Objective: To verify the wave nature of electrons
  • Setup: Electron gun, nickel crystal, and detector
  • Observation: Diffraction peak observed at 54V and $50^\circ$ angle
  • Conclusion: Confirmed de Broglie's wave equation for matter waves