Modern Physics
Modern Physics tests relativity, quantum ideas, atomic structure, the photoelectric effect, wave–particle duality, and nuclear physics. Expect photon-energy calculations, decay reasoning, and mass–energy relations.
Core rules
A photon has energy E = hf = hc/λ. In the photoelectric effect, Kmax = hf − φ, where φ is the work function; increasing intensity increases the number of photons, not the maximum kinetic energy of each electron. The threshold frequency satisfies hf0 = φ. Bohr energy levels produce line spectra: photon energy equals the energy-level difference. Mass–energy equivalence is E = mc². Radioactive decay is random but characterized by half-life; after n half-lives, the remaining fraction is (1/2)^n. Relativistic effects grow as speed approaches c, and no massive object reaches c.
Worked example
Light of wavelength 400 nm strikes a metal with work function 2.0 eV. Use hc = 1240 eV·nm, so E = 1240/400 = 3.10 eV. Then Kmax = 3.10 − 2.0 = 1.1 eV. The photon energy depends on wavelength, not intensity. If the wavelength were longer than the threshold wavelength, no electrons would be emitted regardless of intensity.
Traps
Do not increase Kmax by increasing intensity at fixed frequency. Do not confuse photon energy with wave amplitude. Use electronvolts and nanometers consistently, or convert to joules. Half-life is not a linear decay rate. In relativity, use the relativistic energy relation rather than classical ½mv² at speeds near c.