Dual Nature of Matter and Radiation
The Dual Nature of Matter and Radiation tests the photon picture, the photoelectric effect and matter waves, with numerical work on stopping potential, threshold frequency and de Broglie wavelength.
Core rules
- Photon energy E = hν = hc/λ; the handy value is hc = 1240 eV nm.
- Photoelectric equation: hν = φ₀ + K(max), with K(max) = eV₀ where V₀ is the stopping potential.
- Threshold frequency ν₀ = φ₀/h. Below ν₀ no emission occurs, however intense the light.
- Above ν₀ the saturation current grows with intensity, but K(max) depends only on frequency.
- Emission is essentially instantaneous, which classical wave theory cannot explain.
- de Broglie wavelength λ = h/p = h/mv; for an electron accelerated through V volts, λ ≈ 1.227/√V nm.
- Davisson–Germer electron diffraction confirmed the wave nature of matter.
Worked example
Light of 400 nm falls on a metal of work function 2.0 eV. Photon energy = 1240/400 = 3.10 eV. Hence K(max) = 3.10 − 2.00 = 1.10 eV, and the stopping potential is 1.10 V. An electron with this kinetic energy has λ ≈ 1.227/√1.10 ≈ 1.17 nm.
Traps
Using intensity to predict K(max); mixing electron-volts and joules; forgetting that the stopping potential opposes the fastest electrons; inserting photon momentum into λ = h/mv for a particle.