Quantum phenomena

What quantum phenomena covers

The observations classical wave theory could not account for, and the photon model that replaced it. Four lessons only, but examined heavily, because the arguments carry as many marks as the arithmetic. Everything here reappears in particles, in nuclear physics and in the turning points option.

The main ideas

• The photoelectric observations a wave model cannot explain, particularly the threshold frequency and the instant emission above it.
• Work function, threshold frequency and stopping potential, with the photoelectric equation applied as an energy budget for one electron.
• The graph of maximum kinetic energy against frequency, whose gradient is the Planck constant and whose intercepts give the work function and threshold.
• Excitation against ionisation in electron-atom collisions, and how a fluorescent tube uses both.
• Line spectra as evidence for discrete energy levels, and the transition equation for an emitted photon.
• Wave-particle duality: electron diffraction as evidence for matter waves, and the de Broglie wavelength.

The equations it turns on

E = hf = hcλ$E = hf = \frac{hc}{\lambda}$E = hf = hc/λ

the energy of a photon

hf = work function + E_k(max)$hf = \text{work function} + E_{k}(max)$hf = work function + E_k(max)

the photoelectric equation

hf = E₁ - E₂$hf = E_{1} - E_{2}$hf = E_1 - E_2

the photon emitted as an electron drops between levels

λ = hmv$\lambda = \frac{h}{mv}$λ = h/mv

the de Broglie wavelength of a particle

1 eV = 1.60 × 10^-19 J$1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$1 eV = 1.60 × 10^(-19) J

the conversion nearly every question here needs

Where it usually goes wrong

• Brighter light delivers more photons, not more energetic ones. Below the threshold frequency no intensity produces emission, and the unit is built to test that point.
• Energy levels are negative, with zero at ionisation, so a transition energy is a subtraction of two negatives and the signs have to be written out.
• The de Broglie wavelength needs a momentum, so a question giving an accelerating pd expects the speed from eV = half m v^2 first.
• Work functions come in electronvolts and photon energies in joules, and mixing the two is the commonest error in this unit.

Where to start

The photoelectric effect first, since it introduces the photon and holds most of the marks. Collisions of electrons with atoms and energy levels then work as one idea seen twice. Wave-particle duality last, because it sets that evidence against electron diffraction.