Quantum Mechanics and Atomic Physics
Core concepts
Wave–particle duality, the de Broglie relation λ = h/p, and the photoelectric effect with E = hf and work function φ. The uncertainty principle ΔxΔp ≥ ℏ/2 limits simultaneous knowledge. Schrödinger's equation yields quantized bound states; know the particle-in-a-box energies E_n = n²h²/(8mL²), the hydrogen levels E_n = −13.6 eV/n², and the harmonic oscillator spacing. Quantum numbers n, ℓ, m_ℓ, m_s and the Pauli exclusion principle build the periodic table. Photon emission and absorption follow ΔE = hf, giving spectral lines (Lyman, Balmer series).
Traps
Students confuse the photoelectric threshold frequency with intensity effects-brighter light raises current, not electron energy. The uncertainty principle is not about instrument error. Remember ℓ ranges from 0 to n−1, and each subshell holds 2(2ℓ+1) electrons. In the Bohr model, angular momentum is quantized in units of ℏ, but the model fails for multi-electron atoms. Ionization energy from n = 1 is 13.6 eV; from n = 2 it is 3.4 eV.
Worked example
A photon of 400 nm has energy E = hc/λ ≈ 1240 eV·nm / 400 nm ≈ 3.1 eV. If the work function is 2.0 eV, the maximum photoelectron kinetic energy is 1.1 eV. Rule of thumb: hc ≈ 1240 eV·nm is a handy constant for quick spectral calculations.