My question isn't how they receive the energy to jump, but why. When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals (else we would see a continuous spectrum). Electrons can be released in the form of beta decay, thus proving that they are capable of traveling outside of orbitals contrary to the statement my teacher said that they stay within orbitals. Then, to add to the confusion, the older model of rings floating around a nucleus has, from what I can tell, been outdated, which would support this model. My teacher's explanation was that the electrons made a quantum jump of some kind. How do electrons move between orbitals or do we know how they jump, excluding the reason that energy causes them to jump, and why are positrons formed sometimes instead of electrons in Beta decay? When I'm asking "how do electrons jump" I would like to know how an electron can jump between each orbital such as how it moves and how it knows where to jump since it appears to be a jump where the electron doesn't slow into a orbital position. Specifically how they jump what is this Atomic electron transition, I understand that they jump and that they do this through absorbing and releasing energy but what is this Atomic electron transition other than what is already on the wikipedia article http://en.wikipedia.org/wiki/Atomic_electron_transition.
Answer
Imagine an electron a great distance from an atom, with nothing else around. The electron doesn't "know" about the atom. We declare it to have zero energy. Nothing interesting is going on. This is our reference point.
If the electron is moving, but still far from the atom, it has kinetic energy. This is always positive. The electron, still not interacting with the atom, may move as it pleases. It has positive energy, and in any amount possible. Its wave function is a simple running plane wave, or some linear combination of them to make, for example, a spherical wave. Its wavelength, relating to the kinetic energy, may be any value.
When the electron is close to the atom, opposite charges attract, and the electron is said to be stuck in a potential well. It is moving, so has positive (always) kinetic energy, but the Coulomb potential energy is negative and in a greater amount. The electron must slow down if it moves away from the atom, to maintain a constant total energy for the system. It reaches zero velocity (zero kinetic energy) at some finite distance away, although quantum mechanics allows a bit of cheating with an exponentially decreasing wavefunction beyond that distance.
The electron is confined to a small space, a spherical region around the nucleus. That being so, the wavelength of its wavefunction must in a sense "fit" into that space - exactly one, or two, or three, or n, nodes must fit radially and circumferentially. We use the familiar quantum number n,l,m. There are discrete energy levels and distinct wavefunctions for each quantum state.
Note that the free positive-energy electron has all of space to roam about in, and therefore does not need to fit any particular number of wavelengths into anything, so has a continuous spectrum of energy levels and three real numbers (the wavevector) to describe its state.
When the atom absorbs a photon, the electron jumps from let's say for example from the 2s to a 3p orbital, the electron is not in any orbital during that time. Its wave function can be written as a time-varying mix of the normal orbitals. A long time before the absorption, which for an atom is a few femtoseconds or so, this mix is 100% of the 2s state, and a few femtoseconds or so after the absorption, it's 100% the 3p state. Between, during the absorption process, it's a mix of many orbitals with wildly changing coefficients. There was a paper in Physical Review A back around 1980 or 1981, iirc, that shows some plots and pictures and went into this in some detail. Maybe it was Reviews of Modern Physics. Anyway, keep in mind that this mixture is just a mathematical description. What we really have is a wavefunction changing from a steady 2s, to a wildly boinging-about wobblemess, settling to a steady 3p.
A more energetic photon can kick the electron out of the atom, from one of its discrete-state negative energy orbital states, to a free-running positive state - generally an expanding spherical wave - it's the same as before, but instead of settling to a steady 3p, the electron wavefunction ends as a spherical expanding shell.
I wish I could show some pictures, but that would take time to find or make...
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