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Quantum Mechanics

Atomic Structure and Spectra

Atomic line spectra reveal sharply selected transition frequencies. Scattering reveals the concentration of charge inside an atom, while inelastic collisions reveal excitation energies. Together these observations motivated increasingly successful atomic models, each with limitations of its own.

Reading sequence

Section titled “Reading sequence”
  • Line Spectra introduces discrete emission and absorption lines as empirical facts that demanded atomic energy structure.
  • Balmer Formula explains the empirical integer pattern in visible hydrogen lines before a quantum atom theory existed.
  • Rydberg Formula generalizes hydrogen spectral series through inverse-wavelength differences and the Rydberg constant.
  • Thomson Model explains the diffuse positive-charge atom and why scattering made it untenable.
  • Rutherford Scattering explains the large-angle alpha-scattering evidence for the compact nuclear atom.
  • Nuclear Atom explains the compact nucleus as a conceptual shift that sharpened the stability problem.
  • Bohr Model presents Bohr’s hydrogen model as old quantum theory: historically crucial, mathematically useful, and incomplete.
  • Franck–Hertz Experiment explains how electron collisions with mercury vapor revealed discrete atomic excitation energies.
  • Sommerfeld Model explains elliptical orbits, action quantization, fine-structure successes, and why old quantum theory remained provisional.
  • Limits of Old Quantum Theory summarizes why the Bohr–Sommerfeld program had to be replaced by the modern state-observable-probability framework.

Put the ideas to work

Section titled “Put the ideas to work”

Follow line spectra → Balmer and Rydberg formulas → Bohr’s model for the spectroscopy route. Follow Thomson → Rutherford → nuclear atom for the structure route. Then compare the two with the modern hydrogen atom: agreement of leading spectral frequencies does not make a Bohr orbit a modern orbital.

References

Section titled “References”
  • Nobel Prize Outreach, Niels Bohr Facts.
  • N. Bohr, “On the Constitution of Atoms and Molecules,” Philosophical Magazine 26, 1-25 (1913), DOI: 10.1080/14786441308634955.
  • E. Rutherford, “The Scattering of α and β Particles by Matter and the Structure of the Atom,” Philosophical Magazine 21, 669-688 (1911), DOI: 10.1080/14786440508637080.
  • A. Sommerfeld, “Zur Quantentheorie der Spektrallinien,” Annalen der Physik 51, 1-94 and 125-167, 1916.