Modern Physics: Relativity, Quantum, Atomic, Nuclear
Core concepts
Special relativity: Lorentz factor γ = 1/√(1 − v²/c²), time dilation, length contraction, relativistic momentum and energy (E² = (pc)² + (mc²)²). Photoelectric effect: E = hf, work function, threshold frequency. de Broglie wavelength λ = h/p. Bohr model: energy levels, photon emission/absorption. Nuclear physics: binding energy, mass defect, radioactive decay (half-life, exponential law), conservation of charge and nucleon number in reactions.
Traps
- Applying classical kinetic energy at relativistic speeds.
- Forgetting that photons have momentum but no rest mass.
- Confusing half-life with mean lifetime.
- Ignoring conservation laws in nuclear equations.
- Using the wrong frame for time dilation (proper time is in the rest frame).
Worked example
A muon at rest lives 2.2 μs. If it travels at 0.99c, γ ≈ 7.1, so lab-frame lifetime ≈ 15.6 μs, giving a distance ~4.6 km. Rule of thumb: proper time is always measured in the frame where the two events happen at the same place.