ATM-00 · laboratory
Rydberg, Bohr, selection rules, fine structure, Zeeman and Stern–Gerlach.
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36 governing sheets
E_n = −13.6 Z² / n² eV. Bound hydrogenic levels.
Spectraa₀ = 4π ε₀ ħ² / (m e²) ≈ 0.529 Å, r_n = n² a₀ / Z.
Structureα = e² / (4π ε₀ ħ c) ≈ 1/137. The dimensionless electromagnetic coupling.
StructureΔE = μ_B B g m_J. Linear Zeeman energy of a magnetic sublevel.
SpectraF_z = μ_z dB/dz, μ_z = − g μ_B m_s. Beam split by a field gradient.
StructureAllowed electric-dipole: Δℓ = ±1, Δm = 0, ±1. This sheet flags |Δℓ| = 1.
Spectraω_L = e B / (2 m). Orbital precession of a magnetic moment in B.
StructureA term ²ˢ⁺¹L_J has multiplicity 2S+1 and (2J+1) magnetic sublevels.
Spectraμ = m M / (m+M), R_μ = R_∞ μ / m_e. Finite-mass shift of the spectrum.
StructureI = 13.6 Z² / n² eV. Energy to strip the last electron from level n.
SpectraE_{SO} = (A/2) [J(J+1) − L(L+1) − S(S+1)]. Landé interval rule.
StructureΔE ≈ 1057 (Z/1)⁴ (2/n)³ MHz for the 2S–2P hydrogenic sketch.
Structureν = 1420.4 MHz, λ = c/ν ≈ 21.1 cm. The I·J splitting of hydrogen 1s.
Spectraf = (8π² m ν / 3 h e²) |μ|² × (degeneracy sketch). Dimensionless line strength.
SpectraA_{21} = 1/τ. Spontaneous emission rate from a lifetime.
SpectraΔν_D = (ν₀ / c) √(2 k T / m). FWHM is 2√(ln 2) times this 1/e half-width.
SpectraΓ = ħ / τ, Δν = A / 2π. Lorentzian core of a line.
SpectraΣ f = Z. The remaining oscillator strength after two known lines.
SpectraS = n_unpaired / 2. First Hund rule: maximise spin in an open subshell.
StructureΔE = μ_B B (m_L + 2 m_S). Strong-field decoupling of L and S.
SpectraΔE = e E ⟨z⟩. First-order Stark shift of a permanent electric dipole.
Spectrag_J = 1 + [J(J+1)+S(S+1)−L(L+1)] / [2 J(J+1)]. Anomalous Zeeman g.
StructureΩ = μ E / ħ. Coherent driving rate of a two-level atom.
Structure1/λ = R (1/4 − 1/n²), n = 3,4,5,… Visible hydrogen from n=2.
SpectraHydrogen series lines.
AtomicHydrogen-like levels.
AtomicMost-probable hydrogen radius.
AtomicSeries limit. He⁺ is 54.4 eV.
AtomicSpontaneous emission.
AtomicElectric dipole rule.
AtomicRussell–Saunders term.
AtomicNucleus recoils.
AtomicThermal broadening.
AtomicLifetime broadening.
Atomic≫1 uncouples L and S.
AtomicStrong lines have f~1.
Atomic