Modern Physics and Quantum Concepts
Core concepts
Know the photoelectric effect (E = hf, work function, threshold frequency), the photon model of light, wave–particle duality, atomic energy levels and line spectra, and the basics of nuclear physics: isotopes, alpha/beta/gamma decay, half-life, and mass–energy equivalence E = mc². Understand that quantisation explains discrete spectra and that the photoelectric effect requires photon energy above the work function.
Common traps
- Intensity vs frequency: brighter light below threshold produces no emission; higher frequency increases electron kinetic energy.
- Half-life is the time for half the nuclei to decay - not for all to disappear; after n half-lives, fraction remaining is (1/2)ⁿ.
- Alpha, beta, gamma differ in charge, mass and penetrating power; balance mass and atomic numbers in decay equations.
- Confusing excitation (electron moves up a level) with ionisation (electron removed entirely).
- Forgetting that E = mc² uses SI units or appropriate conversion factors.
Worked example
A photon of frequency 6 × 10¹⁴ Hz strikes a metal with work function 2.0 eV. Photon energy = hf = 6.63 × 10⁻³⁴ × 6 × 10¹⁴ ≈ 3.98 × 10⁻¹⁹ J ≈ 2.49 eV. Maximum kinetic energy = 2.49 − 2.0 = 0.49 eV. Since this is positive, emission occurs.
Rule of thumb
Convert electron-volts and joules carefully (1 eV ≈ 1.6 × 10⁻¹⁹ J) and always check whether photon energy exceeds the work function.