Modern Physics
What the exam tests
This domain covers the photoelectric effect, wave-particle duality, atomic energy levels and nuclear physics. Questions test photon calculations, stopping potential, de Broglie wavelength, spectral transitions, radioactive decay and nuclear equations.
Core rules
- Photon energy E = hf = hc/λ. Using eV, hc ≈ 1240 eV nm.
- Photoelectric equation: hf = Φ + Kmax, where Φ is the work function. Stopping potential Vs satisfies eVs = Kmax.
- No emission occurs below the threshold frequency, regardless of intensity. Intensity affects the number of photoelectrons, not their maximum kinetic energy.
- de Broglie wavelength λ = h/p.
- Atomic energy levels: photon energy = difference between levels, hf = E₂ − E₁.
- Radioactive decay is exponential; after n half-lives the remaining fraction is (1/2)ⁿ. Nuclear equations conserve nucleon number and charge.
Worked example
Light of wavelength 400 nm falls on a metal with work function 2.0 eV. Find the maximum kinetic energy of the emitted electrons and the stopping potential. Photon energy = 1240/400 = 3.1 eV. Kmax = 3.1 − 2.0 = 1.1 eV. Stopping potential Vs = Kmax/e = 1.1 V. The 400 nm photon energy exceeds the work function, so emission occurs. If the wavelength were longer than about 620 nm, the photon energy would fall below 2.0 eV and no electrons would be emitted.
Traps
Mixing electronvolts and joules; using intensity to predict maximum kinetic energy; forgetting the work function when finding stopping potential; treating half-life as a linear decay; failing to balance nucleon numbers and proton numbers in nuclear equations.