# Bohr's Model of Hydrogen

Neils Bohr studied with Rutherford shortly after Geiger and Marsden had completed their experiments. He became convinced of the general validity of Rutherford's nuclear model. Bohr expanded upon Rutherford's nuclear model. The Bohr model of the atom is not the full and final picture but it is perhaps the last time we have a model we can easily picture in our minds. The "real" structure of the atom is more mathematical. Even when we realize that Bohr's model is not complete and turn to more detailed mathematics for calculations and predictions, it will probably be Bohr's model that we picture in our minds. It is for this reason that it is worth looking at this model in some detail. Neils Bohr was a Danish Physicist whose group in Copenhagen did much in developing and advancing the early understanding of Quantum Mechanics in general.

Bohr proposed a model for the structure of hydrogen, the lightest and simplest atom. It can be extended to hydrogen-like ions which have a single electron. Bohr proposed that the electron does, indeed, orbit the positively-charged nucleus in circular orbits. He proposed that these orbits had only certain, particular, discrete radii and that these orbits were "stationary"--that the EM radiation and spiraling into the nucleus predicted by classical electromagnetic theory simply did not occur! But electrons could "jump" from one stationary orbit to another

When an electron makes such a transition between orbits, a photon of EM radiation would be emitted whose energy was equal to the energy lost by the atom due to the transition. The energy of the emitted photon is related to its frequency just as in the photoelectric effect by

E = h f

Therefore,

h f = E = Ei - Ef

where Ei is the energy of the atom in its initial state with the electron in its initial orbit and Ef is the energy of the atom in its final state with the electron in its final orbit (and Ei > Ef). It is the energy of the entire atom that we are concerned with--the energy of the system composed of the electron and the nucleus. However, for convenience in conversation, it is common to speak of "the energy of the electron" or say that the energy of the emitted photon is equal to the change in the electron's energy as it jumps from one stationary orbit to another.