Modern Physics and Atomic/Nuclear Physics
This domain covers quantisation of energy and its consequences: the photoelectric effect, photon energy, de Broglie wavelength, line spectra and energy levels, then nuclear structure, radioactive decay, half-life, mass defect and binding energy. Items are usually short calculations with one decisive formula plus conceptual checks.
Core rules
- A photon carries E = hf = hc/λ. A convenient working value is hc ≈ 1240 eV·nm, so E(eV) ≈ 1240/λ(nm).
- Photoelectric effect: emission is instantaneous above a threshold frequency f₀; the work function W = hf₀; KEmax = hf − W. Increasing intensity raises the number of photoelectrons (saturation current), not their maximum kinetic energy.
- de Broglie relation λ = h/p, so electrons diffracted by a crystal give evidence of wave behaviour.
- Atoms emit line spectra because energy levels are quantised; a transition gives ΔE = hf.
- Nuclear notation ᴬ_Z X: A is the nucleon (mass) number, Z the proton number; isotopes share Z but differ in A.
- Alpha emission reduces A by 4 and Z by 2; beta-minus emission leaves A unchanged and raises Z by 1 with an antineutrino emitted; gamma emission changes neither A nor Z.
- Decay equations must conserve both A and Z.
- Half-life: N = N₀(½)^(t/T), and activity is measured in becquerels (decays per second). Radioactive decay is random and spontaneous.
- Mass defect Δm gives binding energy Δmc²; 1 u corresponds to 931.5 MeV.
Worked example
Light of wavelength 500 nm falls on a metal of work function 2.00 eV. Find the maximum kinetic energy of the emitted electrons and the threshold wavelength. Photon energy = 1240/500 = 2.48 eV. KEmax = 2.48 − 2.00 = 0.48 eV. Threshold wavelength λ₀ = hc/W = 1240/2.00 = 620 nm, so any wavelength longer than 620 nm produces no emission at all.
Traps that cost marks
- Explaining KEmax in terms of intensity rather than frequency.
- Using wavelength where frequency belongs, or forgetting to convert nm to m.
- Mixing up A and Z when completing a decay equation, or omitting the antineutrino in beta decay.
- Treating half-life as though the activity falls by a fixed amount each half-life rather than halving.
- Forgetting that gamma emission alters neither mass number nor proton number.
- Giving binding energy in joules when the question specifies MeV, or using the wrong conversion for atomic mass units.