Short History of the Quantum Theory of the Atom

The Development of the Quantum Theory of the Atom

The early beginnings of the quantum theory of the atom start with Niels Bohr, a German physicist. Many problems existed with the theories of the atom at his time, but many resources also existed for deriving more improved models. History previous to this needs to be covered in order to show how the Bohr model began and led to better models

J.J. Thomson proposed that an atom consist of protons and electrons in a sort of "pudding." However, Ernest Rutherford showed that a beam of positively charged alpha-radiation could be scattered by thin gold foil which showed that an atom is mostly empty space with a small positively charged nucleus to deflect alpha-particles. Thus Rutherford proposed that the electrons orbited the nucleus (but did not fall into it) like planets.1a

The line emission (and absorption) spectra of gases were also another important area of research that would prove useful to explaining the nature of the atom. Johannes Rydberg had found an equation to explain the line spectra of Hydrogen by developing the Rydberg Equation. Though this model had no theoretical basis it would still prove useful.1b

One last piece of information was necessary. The idea of the quantization of energy was proposed by Max Planck to explain black body radiation. However, this idea could be extended to explain the photoelectric effect and the particle nature of light, so it was only a matter of time before it was used in the model of the atom.1c

Bohr's model of the hydrogen atom utilized all three of these observations. Bohr proposed that electrons attain stationary states where they orbit the nucleus in a circular fashion, with constant energy. Even better, Bohr showed that the energy of these orbits was quantized (E= -13.6eV/n2), with each orbit's energy existing from n=1 (ground state) to infinity (removed from the atom).

Now to further show the validity of Bohr's idea, it must be tested against known experiments and ideas presented before. By solving for the difference in energy between two energy levels and dividing by Planck's constant, the frequency of radiation emitted from hydrogen can be found.

f = (13.6eV/h)x( 1/nf - 1/ni)

This is consistent with the line spectra of hydrogen and the Rydberg equation if the above equation is divided by the speed of light. Niels Bohr won the Nobel Prize in 1922.

Though Bohr's model was consistent with the physical nature of the atom (electrons outside the nucleus), explained the line spectra of hydrogen (Rydberg equation) and utilized the quantization of energy proposed before (Planck's constant, h), it had a major drawback, it could not explain the properties of atoms beyond single electron atoms. Bohr had left out one important idea still developing at the time, that matter had both particle and wave properties.

This idea had been postulated by Louis de Broglie in 1923, where he related the momentum of a particle to its wavelength. This idea was confirmed by the Davisson-Germer experiment where a diffraction pattern was observed for electron passing through nickel. De Broglie won the Nobel Prize in 1929 for his idea.1d

An important question arises, if electrons exist as waves then how can they exist as particles with definite position? They don't. Werner Heisenberg developed the Heisenberg uncertainty principle which explained that both a particle's position and momentum cannot be known simultaneously. The more information we gain about one quantity the more information we lose about the other. If we are to measure the momentum of a particle we must also know about its wave nature, which exists over space not at a certain point in space in accordance with the de Broglie wavelength. However, if we know its position accurately, we cannot know about its wave nature, therefore we cannot know about its momentum. Heisenberg won the Nobel Prize in 1932 for this extraordinary idea.1e

A model of the atom had to be developed to take into account both the wave nature and the probabilistic nature of electrons. Erwin Schrodinger formulated the wave equation (ш) which would help create a more complete model. A wave equation for an electron can be visualized as a string connected to itself around the nucleus. When the string vibrates its wave function must be continuous such as