Quantum and Photon Physics: Photoelectric Effect, Wave–Particle Duality and Energy Levels
Photons and the photoelectric effect
A photon has energy E = hf = hc/λ. The photoelectric equation is hf = φ + K_max, where φ is the work function. The threshold frequency satisfies hf0 = φ. Stopping potential V_s gives K_max = eV_s. Intensity changes the number of photons per second, not the maximum kinetic energy.
Wave–particle duality
De Broglie wavelength λ = h/p = h/(mv). Electrons show diffraction through graphite, confirming wave behaviour; photons show particle behaviour in the photoelectric effect and Compton scattering. Energy levels are discrete: a transition gives a photon of energy hf = E2 − E1. Ionisation removes an electron completely.
Worked example
Light of wavelength 250 nm falls on a metal of work function 2.30 eV. Using hc = 1240 eV nm, photon energy = 1240/250 = 4.96 eV. K_max = 4.96 − 2.30 = 2.66 eV. The stopping potential is 2.66 V. Increasing intensity increases the photocurrent but leaves 2.66 eV unchanged.
Traps
Mixing electronvolts and joules; using intensity to predict K_max; forgetting that λ must be in metres when using hc in J m; confusing threshold frequency with frequency; using the photon energy as kinetic energy without subtracting the work function.