Dual Nature of Radiation and Matter
This domain covers the photoelectric effect, photons and matter waves. The exam tests whether you can separate intensity effects from frequency effects and use energy conservation in electron volts.
Core rules and concepts
- Photon energy E = hν = hc/λ; momentum p = h/λ. Useful shortcut: hc ≈ 1240 eV nm.
- Photoelectric equation: hν = φ + K_max, where φ is the work function. Threshold frequency ν0 = φ/h; stopping potential V0 satisfies eV0 = K_max.
- Photoelectric current depends on intensity (number of photons), but maximum kinetic energy depends on frequency and work function.
- de Broglie wavelength λ = h/p. For an electron accelerated through V volts, λ ≈ 12.27/√V Å.
- Davisson–Germer experiment confirmed electron diffraction and matter waves.
Worked example
Light of wavelength 400 nm falls on a metal of work function 2.0 eV. Find maximum kinetic energy and stopping potential. Photon energy = 1240/400 = 3.1 eV. K_max = 3.1 − 2.0 = 1.1 eV. Therefore stopping potential = 1.1 V.
Traps
- Increasing intensity increases photocurrent, not K_max; increasing frequency increases K_max.
- No electrons are emitted below threshold frequency, however intense the light.
- Convert wavelength to metres or use the 1240 eV nm shortcut consistently.
- Stopping potential is a magnitude; the applied retarding potential is negative.
- de Broglie wavelength is significant only for microscopic particles at ordinary speeds.