Dual Nature of Radiation and Matter
Dual Nature tests the photoelectric effect and Einstein's equation, photon energy and momentum, and the de Broglie wavelength with the Davisson-Germer confirmation. Numericals on stopping potential and threshold frequency are standard.
Core rules
- Photon energy E = hν = hc/λ; in convenient units E(eV) = 1240/λ(nm). Momentum p = h/λ.
- Photoelectric equation: hν = φ + K(max), with φ the work function and K(max) = eV₀, V₀ the stopping potential.
- Threshold frequency ν₀ = φ/h; below it no emission occurs regardless of intensity.
- Intensity controls the number of photoelectrons (saturation current); frequency controls their maximum kinetic energy. Emission is instantaneous, contradicting classical wave theory.
- de Broglie: λ = h/p = h/√(2mK) = h/√(2mqV) for an accelerated charge. For electrons, λ ≈ 12.27/√V Å with V in volts.
- Davisson-Germer electron diffraction confirmed the wave nature of matter.
Worked example
Light of 400 nm falls on a metal of work function 2.1 eV. Photon energy = 1240/400 = 3.1 eV, so K(max) = 3.1 − 2.1 = 1.0 eV and the stopping potential is 1.0 V. An electron accelerated through 100 V has λ = 12.27/√100 = 1.23 Å.
Traps
- Thinking brighter light increases stopping potential; only frequency does.
- Mixing joules and electron-volts inside one equation.
- Using the photon wavelength where the de Broglie wavelength of the electron is wanted.