If the electron is a wave, it cannot occupy “just any” orbit around the nucleus: it can only stay where its wave “finds itself again”, that is, where it does not interfere destructively with itself. From this idea the quantisation of the atom’s physical quantities — radii, energies, angular momentum — arises naturally, no longer varying continuously but only in discrete “steps”.
This section reconstructs Bohr’s model of the hydrogen atom: from the problem of classical instability, to de Broglie’s wave-based justification, to the four equations that give radii and energies, up to the direct experimental proofs (Franck-Hertz, photoelectric effect) and the consequences for electronic structure and spectra.
- Il modello dell’atomo di idrogeno
- L’elettrone come onda stazionaria
- Le quattro equazioni del modello di Bohr
- Livelli energetici dell’atomo di idrogeno
- L’esperimento di Franck-Hertz
- Lo spin elettronico e il principio di Pauli
- Spettri di assorbimento
- L’esperimento storico dell’effetto fotoelettrico
- Effetto fotoelettrico e bande di energia
Try it — quantum simulator
In a potential well the energy is not continuous: only certain stationary wavefunctions are allowed, and their energies form discrete levels.