Modern Physics
Modern Physics
This domain covers special relativity, quantum phenomena, atomic energy levels and spectra, and nuclear decay. Questions often test photon energy, the photoelectric effect, half-life, and the meaning of relativistic quantities.
Core rules
- Relativity: γ = 1/√(1 − v²/c²); moving clocks run slow (Δt = γΔτ), moving lengths contract (L = L₀/γ), and rest energy is E₀ = mc².
- Photon energy E = hf = hc/λ. A useful shortcut is E(eV) ≈ 1240/λ(nm). Intensity affects the number of photons, not each photon's energy.
- Photoelectric effect: K_max = hf − φ, where φ is the work function. No emission occurs below the threshold frequency, regardless of intensity.
- de Broglie wavelength λ = h/p. Bohr energy levels for hydrogen: E_n = −13.6 eV/n²; an emitted photon's energy equals the level difference.
- Nuclear decay: alpha emission reduces A by 4 and Z by 2; beta-minus increases Z by 1; gamma changes neither. After n half-lives, remaining amount = N₀(1/2)ⁿ.
Worked example
Light of wavelength 400 nm strikes a metal with work function 2.0 eV. Photon energy is E = 1240/400 = 3.1 eV. The maximum kinetic energy of emitted electrons is K_max = 3.1 − 2.0 = 1.1 eV. In joules, 1.1 eV × 1.60 × 10⁻¹⁹ J/eV ≈ 1.8 × 10⁻¹⁹ J. Doubling the light intensity doubles the number of electrons but does not increase K_max.
Traps
- Using wavelength in meters in the 1240 eV·nm shortcut without converting.
- Claiming brighter light gives faster photoelectrons; only higher frequency does.
- Treating half-life as a linear decrease.
- Forgetting that gamma rays are photons and do not change A or Z.