Modern Physics
What Modern Physics tests
This domain samples special relativity, photons and the photoelectric effect, de Broglie waves, atomic energy levels, and nuclear decay. The math is usually proportional and unit-sensitive rather than lengthy.
Core rules
- Photon energy E = hf = hc/λ. A useful shortcut is hc ≈ 1240 eV·nm.
- Photoelectric equation: Kmax = hf − φ = eVstop. Intensity changes current; frequency controls whether emission occurs.
- de Broglie wavelength λ = h/p. For a nonrelativistic particle, p = √(2mK).
- Bohr transitions: ΔE = hf. Emitted photon energy equals the energy-level difference.
- Mass-energy E = mc^2; nuclear decay follows N = N0(1/2)^(t/T1/2). Half-life is the time for half the nuclei to decay, not a linear rate.
Worked example
Light of wavelength 400 nm strikes a metal with work function 2.0 eV. Find the maximum kinetic energy of emitted electrons and the stopping potential.
E = hc/λ = 1240 eV·nm/400 nm = 3.10 eV. Kmax = E − φ = 3.10 − 2.0 = 1.10 eV. The stopping potential is Vstop = Kmax/e = 1.10 V. No electrons are emitted if the photon energy is below 2.0 eV, regardless of intensity.
Traps
Using wavelength in meters with the eV·nm shortcut without converting; thinking brighter light increases electron kinetic energy; confusing stopping potential with photon energy; applying a relativistic formula when v is much less than c; treating half-life as a constant number of decays per second.