Learning Objectives
- Understand the photoelectric effect and its experimental observations
- Learn Einstein's photoelectric equation
- Understand wave-particle duality and de Broglie hypothesis
- Study the Davisson-Germer experiment
- Apply concepts to JEE/NEET problems
Key Concepts
Photoelectric Effect
Emission of electrons from a metal surface when light of sufficient frequency falls on it.
Experimental observations:
- Below threshold frequency (ν₀), no emission regardless of intensity.
- Above ν₀, number of photoelectrons ∝ intensity of light.
- Maximum KE of photoelectrons depends on frequency, not intensity.
- Emission is instantaneous (no time lag).
These observations cannot be explained by wave theory but are explained by quantum theory.
Einstein's Photoelectric Equation
KE_max = hν - φ = hν - hν₀
or ½mv²_max = hν - φ
where h = 6.63 × 10⁻³⁴ J·s (Planck's constant), ν = frequency, φ = work function = hν₀.
Stopping potential: eV₀ = hν - φ → V₀ = (h/e)ν - φ/e
Graph of V₀ vs ν: straight line with slope h/e, x-intercept = ν₀, y-intercept = -φ/e.
Photon Properties
Energy: E = hν = hc/λ
Momentum: p = h/λ = hν/c = E/c
Rest mass: zero (photons always travel at speed c).
1 eV = 1.6 × 10⁻¹⁹ J. For λ in nm: E (eV) = 1240/λ(nm).
de Broglie Hypothesis (Wave-Particle Duality)
Every moving particle has an associated wavelength:
λ = h/p = h/(mv)
For an electron accelerated through potential V:
KE = eV = ½mv² → v = √(2eV/m)
λ = h/√(2meV) = 1.226/√V nm (for electron, V in volts).
For a particle with kinetic energy K: λ = h/√(2mK)
For a gas molecule at temperature T: λ = h/√(3mkT)
Davisson-Germer Experiment
Experimentally confirmed de Broglie's hypothesis by showing electron diffraction from a nickel crystal.
Electrons showed diffraction patterns consistent with their de Broglie wavelength, confirming wave nature of matter.
Summary
The photoelectric effect demonstrates the particle nature of light (photons). Einstein's equation KE_max = hν - φ explains all observations. Every moving particle has a de Broglie wavelength λ = h/mv, demonstrating wave-particle duality. The Davisson-Germer experiment confirmed electron diffraction. These concepts bridge classical and quantum physics.
Important Terms
- Photoelectric Effect: Emission of electrons by light above threshold frequency
- Work Function (φ): Minimum energy needed to eject an electron from metal surface
- Threshold Frequency (ν₀): Minimum frequency for photoelectric emission
- Stopping Potential (V₀): Potential needed to stop the fastest photoelectron
- de Broglie Wavelength: λ = h/mv, wave nature of matter
- Photon: Quantum of electromagnetic radiation
Quick Revision
- KE_max = hν - φ; eV₀ = hν - φ
- E = hν = hc/λ; p = h/λ; E(eV) = 1240/λ(nm)
- de Broglie: λ = h/mv = h/√(2mK)
- Electron: λ = 1.226/√V nm (V in volts)
- Photoelectric: depends on frequency (not intensity) for KE
- Davisson-Germer: confirmed electron wave nature