Modern Physics
Domain 6: Modern Physics
Modern Physics covers quantization, the photoelectric effect, atomic spectra and the Bohr model, de Broglie waves, nuclear decay and binding energy, and special relativity. Items test both conceptual distinctions and short calculations.
Core rules
- Photon energy E = hf = hc/λ; useful value hc ≈ 1240 eV·nm. Photoelectric effect: Kmax = hf − φ; stopping potential Vstop = Kmax/e. Intensity changes current, not photon energy.
- Bohr model: En = −13.6 eV/n² for hydrogen; transitions give ΔE = hf. Spectral lines converge at the series limit.
- de Broglie: λ = h/p; uncertainty principle ΔxΔp ≥ ħ/2.
- Nuclear: A = Z + N; alpha decay reduces A by 4 and Z by 2; beta-minus raises Z by 1. Activity halves each half-life. Mass defect converts via E = Δmc²; binding energy per nucleon peaks near Fe-56.
- Relativity: γ = 1/√(1 − v²/c²); moving clocks run slow, moving lengths contract along the motion; rest mass is invariant.
Worked example
Light of 400 nm strikes a metal with work function 2.0 eV. Photon energy = 1240/400 = 3.1 eV. Kmax = 3.1 − 2.0 = 1.1 eV, so the stopping potential is 1.1 V. Doubling the intensity doubles the number of electrons but leaves Kmax at 1.1 eV; using 500 nm light (2.48 eV) still ejects electrons, while 700 nm (1.77 eV) does not.
Traps
- Thinking brighter light gives faster photoelectrons.
- Confusing half-life (statistical, never 'all atoms decay') with a fixed lifetime.
- Forgetting that gamma decay changes energy, not Z or A.
- Applying time dilation to a clock in the observer's own frame.
- Mixing up atomic number Z and mass number A in decay equations.