ATM-005 · Structure of the atom Sample material

Bohr's postulates and theory. The Franck–Hertz experiment

Bohr's postulates and their confirmation in the Franck–Hertz experiment, Bohr's theory of hydrogen-like atoms, quantum transitions (spontaneous and stimulated), the relativistic generalization, the isotope shift, the muonic atom and the shortcomings of the theory.

Estimated time: 3 h 5 activities

Learning objective

Know Bohr's postulates and their experimental basis.
Derive and calculate the orbit radius, speed and energy for hydrogen-like atoms.
Understand spontaneous and stimulated transitions, nuclear motion, the isotope shift and relativistic corrections.
Assess the achievements and limits of Bohr's theory.

Expected outcomes

Interprets the results of the Franck–Hertz experiment and finds the excitation energy of an atom.
Calculates $r_n$, $v_n$, $E_n$ and the transition wavelength for arbitrary $Z$ and $n$.
Uses the reduced mass to estimate the isotope shift and the parameters of a muonic atom.
Performs simple calculations with Einstein coefficients, level populations and the natural linewidth.

Interactive modelBohr model: quantum transitions in hydrogen
Interactive modelThe Franck–Hertz experiment

Activities

Lecture
Lecture · 1 h 20 min · required
Relativistic generalization of Bohr's atomic model. Main shortcomings of Bohr's theory. Quantum transitions. Spontaneous and stimulated transitions.
Practice · 1 h 20 min · required
Study of the Franck–Hertz experiment
Laboratory · 1 h 30 min · optional
Isotope shift of atomic levels. The muonic hydrogen atom
Self-study · 6 h 10 min · optional
Final test
Test · 20 min · required · pass ≥ 70%

Completion conditions

  • Lecture
  • Relativistic generalization of Bohr's atomic model. Main shortcomings of Bohr's theory. Quantum transitions. Spontaneous and stimulated transitions.
  • Final test — at least 70%