PhysicsLAB: Famous Discoveries: Bohr Model

After Rutherford's discovery of the nucleus, he assigned to Neils Bohr, a graduate assistant, the task of aligning the empirical spectra behavior being studied by others with his nuclear model. Bohr centered his derivation around the concept of energy. He combined Einstein’s photons that were used to explain the photoelectric effect (1905) and Balmer’s empirical formula (1885) which successfully calculated hydrogen’s visible spectral lines to produce a revolutionary quantum theory.

Bohr (1913) began with two assumptions:

There existed steady orbitals for electrons. That is, when electrons orbited a nucleus at any of these special radii, they did not radiate energy. Electrons would not "spiral into the nucleus" because they had quantized angular momentum.
Electrons would however gain and lose energy as they moved from one permitted radius, energy level, to another. Electrons would accept energy during excitation and they would release radiant energy during de-excitation. This energy was quantized according to Planck's relationship E = hf = c/λ.

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This released energy was evidenced as the atom's spectral signature - that is, the discreet, unique, spectral lines that were being studied by Kirchoff, Rydberg, Balmer, and others.

The energy levels (in electron volts, eV) were calculated with the formula:

En = -13.6 Z²/n²

where Z is the atomic number and n is the energy level. The ground state presents n = 1, first excited state is n = 2, third excited state is n = 3, etc. 1 eV equals 1.6 x 10^-19 Joules

The wavelength of light emitted when an electron moved from a higher energy level to a lower energy level was calculated with the formula

λ = hc / ΔE
where ΔE represents the difference in the two energy level transitions.

See the following lessons to learn more details about atomic spectra and Bohr's derivation. In 1922, Bohr was awarded the Nobel Prize for his "services in the investigation of the structure of atoms and of the radiation emanating from them."