Quantum and Atomic Physics
Core concepts
The photoelectric effect: light arrives in photons of energy E = hf. Emission occurs only above a threshold frequency f₀, with maximum kinetic energy K_max = hf − W, where W is the work function. Increasing intensity increases the number of photoelectrons, not their maximum kinetic energy. This supports the photon model and contradicts classical wave predictions.
Atomic structure: the Bohr model gives discrete energy levels E_n = −13.6 eV/n² for hydrogen. Photon absorption or emission corresponds to energy differences: hf = E_final − E_initial. The line spectrum of hydrogen is a direct consequence of quantized levels.
Nuclear physics: the nucleus contains protons and neutrons; mass number A = Z + N. Radioactive decay follows exponential law N = N₀e^(−λt), with half-life T₁/₂ = ln2/λ. Alpha decay reduces A by 4 and Z by 2; beta-minus increases Z by 1; gamma emission changes neither. Mass–energy equivalence E = mc² explains binding energy and mass defect.
Traps
- Confusing intensity with photon energy.
- Forgetting that K_max depends on frequency, not intensity.
- Sign errors in Bohr energy differences.
- Mixing up alpha and beta decay changes in Z and A.
- Using half-life as a decay constant.
Worked rule of thumb
For hydrogen transitions, photon energy in eV equals 13.6 × (1/n_low² − 1/n_high²).