Reading the Spectrum

An Introduction to Atoms, Molecules and Light in 7 chapters — from “Lines, series and the term diagram: what a spectrometer measures” to “Two nuclei on one curve: rotation, vibration and the spectrum of a diatomic molecule”.

Chapters

  1. Lines, series and the term diagram: what a spectrometer measures
    • Line spectra and the wavenumber
    • The grating spectrometer and its resolution
    • The spectral series of hydrogen
    • The Rydberg formula
    • The Ritz combination principle and term diagram
    • What the spectrum does not say
    • Problems
  2. The nuclear atom and the Bohr-Sommerfeld model
    • The nuclear atom and classical collapse
    • The Bohr postulates and standing waves
    • Bohr radii and energies
    • The Rydberg constant, reduced mass and hydrogenic ions
    • The Sommerfeld model
    • Four model failures
    • Problems
  3. The Coulomb spectrum from wave mechanics: quantum numbers and degeneracy
    • The time-independent Schrodinger equation
    • Orbital angular momentum and the effective potential
    • Quantisation by boundary condition
    • The Coulomb spectrum and three quantum numbers
    • Degeneracy in hydrogen and sodium
    • What n, l and ml​ leave undetermined
    • Problems
  4. Radial functions, orbital size and Rydberg states
    • The radial probability density
    • Radial nodes and the mean radius
    • Parity and the dipole selection rules
    • Rydberg scaling laws
    • The quantum defect of sodium
    • What n and l still do not determine
    • Problems
  5. Atoms in a magnetic field: moments, the Zeeman effect and the Paschen-Back limit
    • The orbital magnetic moment
    • Level-shift rule and energy in a field
    • The normal Zeeman triplet
    • The anomalous Zeeman pattern and spin one-half
    • The Lande g-factor and the sodium D pattern
    • The Paschen-Back limit
    • Magnetic splitting as a measuring tool
    • Problems
  6. Atoms in an electric field: the Stark effect and polarizability
    • Why an atom has no permanent dipole
    • Induced dipole and the quadratic Stark shift
    • A polarizability estimate
    • The linear Stark effect in hydrogen
    • Field ionisation at the saddle point
    • Comparing the two fields
    • Problems
  7. Two nuclei on one curve: rotation, vibration and the spectrum of a diatomic molecule
    • Two nuclei, one potential curve
    • Oscillator and rotor levels
    • Bond lengths from the rigid rotor
    • Vibration from curvature
    • Anharmonicity and dissociation
    • The rovibrational band
    • Boltzmann factor and intensity envelope
    • Isotope effect and the silent gases
    • What the molecule leaves unexplained
    • Problems