Dual Nature of Matter and Radiation
Dual Nature of Matter and Radiation tests the photoelectric effect, Einstein's photoelectric equation, de Broglie waves and evidence for wave-particle duality. Numerical questions usually involve energy, frequency, wavelength or stopping potential.
Core rules
- Photon energy E = hν = hc/λ. h = 6.63×10⁻³⁴ J s; 1 eV = 1.6×10⁻¹⁹ J.
- Einstein's equation: hν = φ₀ + K_max, where φ₀ is the work function. Stopping potential eV₀ = K_max.
- Below threshold frequency ν₀ = φ₀/h, no emission occurs regardless of intensity. Above threshold, intensity controls the number of photoelectrons, not their maximum kinetic energy.
- de Broglie wavelength λ = h/p = h/(mv). For an electron accelerated through V volts, λ ≈ 1.227/√V nm.
- Davisson–Germer electron diffraction and the photoelectric effect together support wave-particle duality.
Worked example
A metal has work function 2.0 eV and is illuminated by light of photon energy 5.0 eV. Maximum kinetic energy = 5.0 - 2.0 = 3.0 eV. The stopping potential is therefore 3.0 V: a retarding potential of 3 V just stops the fastest photoelectrons. The threshold wavelength corresponds to 2.0 eV, not 5.0 eV.
Traps
Using incident intensity to predict K_max; forgetting to convert eV to joules when using SI formulae; and using the photon energy instead of the work function to find threshold frequency.