Energy quantization and electron configurationEdit
The electrons which inhabit the space surrounding the nucleus are not able to have arbitrary energies. In fact they are restricted to a discrete set of energies while they are trapped in an atom. This discretization of energy values is known as "quantization", meaning that the allowed energies are separated by discrete energy differences, known as "quanta".
This startling behavior arises from the wavelike nature of electrons and the Schröedinger equation which governs them, both topics which should be addressed in a quantum physics course. Suffice it to say that when particles are in free space (meaning there are no potentials present), the allowed energy values are continuous. However, when they are within a potential, for instance in the potential generated by protons in the nucleus of an atom, their energy values become quantized.
The effects of this quantization are profound. Essentially all of the other natural sciences - chemistry, biology, and other derived sciences rely primarily on the atomic behavior resulting from this quantization.
These energy levels are associated with distances from the nucleus (quantum physics introduces a caveat here). That is, the higher the energy of an electron, the further it is from the nucleus. For some time between Rutherford's discovery of the nucleus-electron system within the atom and the development of quantum physics, electrons were pictured around the nucleus as planets in a solar system. In fact, an impressive body of correct predictions can be made using this classical orbit model, but eventually quantum mechanics must take over to provide the "complete" picture. It turns out that electrons exist as "wavefunctions". They can only be described by a field of probabilities for finding them at some location. These 3-D probability functions can be for visual purposes encapsulated by surfaces:
<<A nifty picture of 3-D electron orbitals would be great...anyone? anyone?>>
When researchers were first beginning to understand the electrical structure of the atom, the primary tool was the spectrometer.