Unit 4: How Can Two Contradictory Models Both Explain Light?
Core concepts
Unit 4 explores the wave–particle duality of light and the quantum and nuclear models. You must understand the photoelectric effect and explain why it supports photons: light arrives in quanta of energy E = hf, and emission depends on frequency, not intensity. Know the work function, threshold frequency, and Einstein's equation hf = W + Kmax. Understand the Compton effect and the de Broglie wavelength λ = h/p as evidence for particle behaviour.
For atomic and nuclear physics, describe quantised energy levels and emission and absorption spectra, and use E = hf to relate photon energy to transitions. Understand nuclear stability, radioactive decay types (alpha, beta, gamma), half-life, and mass–energy equivalence E = mc². Apply conservation of mass number and charge in decay equations.
Traps examiners set
- Believing brighter light of low frequency will eventually cause emission - it will not; frequency is the gatekeeper.
- Confusing intensity (photons per second) with photon energy.
- Forgetting Kmax is the maximum kinetic energy; emitted electrons have a range of energies.
- Mixing up alpha and beta decay: alpha reduces mass number by 4 and charge by 2.
- Misapplying half-life: after n half-lives, the fraction remaining is (1/2)ⁿ, not a linear decrease.
Worked example
Light of frequency 8.0 × 10¹⁴ Hz strikes a metal with work function 2.0 eV. Find the maximum kinetic energy of emitted electrons.
Photon energy E = hf = 6.63 × 10⁻³⁴ × 8.0 × 10¹⁴ ≈ 5.30 × 10⁻¹⁹ J. Converting the work function: 2.0 × 1.6 × 10⁻¹⁹ = 3.2 × 10⁻¹⁹ J. Then Kmax = 5.30 × 10⁻¹⁹ − 3.2 × 10⁻¹⁹ = 2.1 × 10⁻¹⁹ J, about 1.3 eV.
Rule of thumb
Convert all energies to the same unit (joules or electronvolts) before subtracting, and check whether the question asks for a photon's energy or an electron's kinetic energy.