Relativity and modern physics (quantum and nuclear phenomena)
Modern physics in the PAU covers special relativity (time dilation, length contraction, mass–energy), the photoelectric effect and de Broglie waves, atomic energy levels and spectra, and nuclear decay, binding energy and reactions. Calculations are short; the marks come from correct units, correct conservation statements and correct interpretation of the results.
Core rules
- Postulates: the laws of physics are the same in all inertial frames, and c is invariant. γ = 1/√(1 − v²/c²); Δt = γΔτ (proper time is the shortest) and L = L₀/γ (proper length is the longest).
- Energy: E = γmc², rest energy E₀ = mc², kinetic energy (γ − 1)mc². Total energy and momentum are conserved in decays and collisions.
- Photoelectric effect: hf = W + E_c,max, threshold f₀ = W/h. Shortcut: E(eV) = 1240/λ(nm).
- de Broglie: λ = h/p. Bohr atom: Eₙ = −13.6/n² eV, transitions give hf = E_f − E_i.
- Radioactive decay: N = N₀e^(−λt), T½ = ln2/λ, activity A = λN.
- Nuclear reactions conserve Z, A, energy and momentum; the mass defect gives Q = Δm c², with 1 u = 931.5 MeV/c².
Worked example
Light of 300 nm strikes a metal of work function 2.0 eV. The photon energy is 1240/300 = 4.13 eV, so the fastest photoelectrons carry 2.13 eV ≈ 3.4×10⁻¹⁹ J. The threshold wavelength is 1240/2.0 = 620 nm, so red light of 650 nm would eject nothing whatever its intensity. Doubling the intensity doubles the number of emitted electrons but leaves their maximum kinetic energy unchanged, because that depends only on the photon frequency.
Marks lost here
Converting eV to joules carelessly (1 eV = 1.60×10⁻¹⁹ J). Confusing work function with binding energy per nucleon. Treating the half-life as a fixed lifetime for every nucleus instead of a statistical constant. Applying the time-dilation factor the wrong way round so that the proper time comes out longer. Balancing charge but not mass number in a nuclear equation.