Atomic Physics
Atomic Physics is about 10% of the GRE Physics Subject Test. It covers the Bohr model and its limits, hydrogenic energy levels and spectra, photons and the photoelectric effect, quantum numbers and selection rules, fine and hyperfine structure, the Zeeman effect, multi-electron atoms, and X-ray spectra.
Core rules
- Photon energy E = hf = hc/λ, and hc = 1240 eV·nm is the fastest route from energy to wavelength.
- Bohr model: E_n = −13.6 eV Z²/n², Bohr radius a₀ = 0.053 nm, and the Rydberg formula reproduces the series limits.
- Photoelectric effect: K_max = hf − φ, and the stopping potential satisfies eV_s = K_max. The threshold frequency is f₀ = φ/h.
- Quantum numbers: n, then l = 0…n−1, m_l = −l…l, and m_s = ±½. Electric-dipole selection rules are Δl = ±1 and Δm = 0, ±1.
- Spin-orbit coupling splits a level into j = l ± ½; because energy depends on j, fine structure lifts the degeneracy.
- Multi-electron atoms obey the Pauli principle. Screening makes orbital energy depend on both n and l, which is why 4s fills before 3d.
- X-rays follow Moseley's law: the Kα line comes from 2p→1s and scales roughly as (Z − 1)².
- Normal Zeeman splitting: ΔE = μ_B B, with μ_B = 5.79×10⁻⁵ eV/T.
Worked example
A hydrogen atom drops from n = 3 to n = 1. The energies are E₃ = −13.6/9 = −1.51 eV and E₁ = −13.6 eV, so ΔE = 12.09 eV. Then λ = 1240/12.09 ≈ 103 nm, an ultraviolet line in the Lyman series.
Traps
Forgetting that bound-state energies are negative while binding energies are positive; allowing Δl = 0 in an electric-dipole transition; confusing the Balmer series (visible, ending at n = 2) with the Lyman series (ultraviolet, ending at n = 1); applying the Bohr formula to multi-electron atoms; ignoring the Z² scaling of hydrogenic levels; missing the reduced-mass correction, which is occasionally the point of a question.