Energy of an electron

This question takes me back to my chemistry days, yes I believe it is. I seem to remember also that with hydrogen oribitals it's fairly easy, however the more electrons you have the harder it is to work out an individual electrons energy and thus: the larger the electron number the harder it becomes to determine the exact energy of an electron. At a simple level though it should be possible to give values for all electrons in a certain arrangement, although of course at the quantum level the arrangements are hardly that clearly defined :/

You'll have to forgive me though it's been years since I had to work out energy levels and oribitals etc, I'm sure someone else has something more detailed; all I can vaguely remember really is that an electron needs a precise amount of energy or quanta to jump to a higher state or orbital, which is both where the term quantum mechanics comes from and quantum leap. IIRC

Here's a simple-more complicated overview, should explain it:-

http://en.wikipedia.org/wiki/Atomic_orbital

 

The energy of the electron in the ground state of hydrogen is -13.6eV. Here's a link discussing the other energy levels of the hydrogen atom: http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c2.

It get's a bit more complicated when we discuss elements other than hydrogen, so it's best to study hydrogen first.

 

It is the difference between the energy levels of the atom. For example, an electron in hydrogen in the ground state (n=1) has an binding energy of -13.6eV. The binding energy at n=2 is -3.4eV, hence for an electron transition from n=1 to n=2 the electron must 'absorb' a photon of energy E = |-13.6 + 3.4 | = 10.2eV. This energy corresponds to the wavelength of a photon in the UV range. Equally, when an electron becomes 'de-excited' i.e. transitions from n=2 to n=1 the electron will emit a photon of the same corresponding energy and hence wavelength. The process becomes a little more complicated if you start looking at the hyperfine structure of hydrogen or other elements in general (as cristo said).

 

The energy of an electron in any orbital of any element is the solution to its Schrodinger equation for that specific case. With more than one electron it's hard; with more than two no analytic solutions exist and these must be computed at great length. The difficulty arises because each electron in the system also has a potential that must be applied to the nuclear potential - each of which varies in an equally complex fashion as the wavefunction of the electron you're studying. Things are complicated further by relativistic corrections to the electron's kinetic energy which become more important the larger the atom and the higher the energy levels. The Schrodinger equation with the simplest set of relativistic corrections is known as the Dirac Equation.

 

Actually, Hydrogen does have spectral lines in the visible range, take a transition from n=3 to n=2 for example; this correspond to an energy of about 1.9eV which results in a wavelength of about 656nm which is in visible [red] light. There are more transitions which occur at the violet end of the spectrum. The energy of IR radiation also 'happens' to correspond to the energies separating the quantum states of molecular vibrations (which results in temperature), its not only atoms and electrons that have quantum states...