Editing Atom (section)

=== Energy levels ===
[[File:Atomic orbital energy levels.svg|thumb|right|These electron's energy levels (not to scale) are sufficient for ground states of atoms up to [[cadmium]] (5s<sup>2</sup> 4d<sup>10</sup>) inclusively. The top of the diagram is lower than an unbound electron state.]]
The [[potential energy]] of an electron in an atom is [[negative number|negative]] relative to when the [[distance]] from the nucleus [[limit at infinity|goes to infinity]]; its dependence on the electron's [[position (vector)|position]] reaches the [[minimum]] inside the nucleus, roughly in [[inverse proportion]] to the distance. In the quantum-mechanical model, a bound electron can occupy only a set of [[quantum state|states]] centered on the nucleus, and each state corresponds to a specific [[energy level]]; see [[time-independent Schrödinger equation]] for a theoretical explanation. An energy level can be measured by the [[ionization potential|amount of energy needed to unbind]] the electron from the atom, and is usually given in units of [[electronvolt]]s (eV). The lowest energy state of a bound electron is called the ground state, i.e., [[stationary state]], while an electron transition to a higher level results in an excited state.<ref name=zeghbroeck1998 /> The electron's energy increases along with [[principal quantum number|''n'']] because the (average) distance to the nucleus increases. Dependence of the energy on [[azimuthal quantum number|{{ell}}]] is caused not by the [[electrostatic potential]] of the nucleus, but by interaction between electrons.

For an electron to [[atomic electron transition|transition between two different states]], e.g. [[ground state]] to first [[excited state]], it must absorb or emit a [[photon]] at an energy matching the difference in the potential energy of those levels, according to the [[Niels Bohr]] model, what can be precisely calculated by the [[Schrödinger equation]]. Electrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see [[Atomic orbital|Electron properties]].

The energy of an emitted photon is proportional to its [[frequency]], so these specific energy levels appear as distinct bands in the [[electromagnetic spectrum]].<ref>{{cite book
|last=Fowles|first=Grant R.|year=1989
|title=Introduction to Modern Optics
|url=https://archive.org/details/introductiontomo00fowl_441|url-access=limited|publisher=Courier Dover Publications
|isbn=978-0-486-65957-2
|oclc=18834711|pages=[https://archive.org/details/introductiontomo00fowl_441/page/n233 227]–233}}</ref> Each element has a characteristic spectrum that can depend on the nuclear charge, subshells filled by electrons, the electromagnetic interactions between the electrons and other factors.<ref name=martin2007 />

[[File:Fraunhofer lines.svg|right|thumb|upright=1.5|An example of absorption lines in a spectrum]]

When a continuous [[electromagnetic spectrum|spectrum of energy]] is passed through a gas or plasma, some of the photons are absorbed by atoms, causing electrons to change their energy level. Those excited electrons that remain bound to their atom spontaneously emit this energy as a photon, traveling in a random direction, and so drop back to lower energy levels. Thus the atoms behave like a filter that forms a series of dark [[absorption band]]s in the energy output. (An observer viewing the atoms from a view that does not include the continuous spectrum in the background, instead sees a series of [[emission line]]s from the photons emitted by the atoms.) [[Spectroscopy|Spectroscopic]] measurements of the strength and width of [[atomic spectral line]]s allow the composition and physical properties of a substance to be determined.<ref name=avogadro />

Close examination of the spectral lines reveals that some display a [[fine structure]] splitting. This occurs because of [[spin–orbit interaction|spin–orbit coupling]], which is an interaction between the spin and motion of the outermost electron.<ref name=fitzpatrick20070216 /> When an atom is in an external magnetic field, spectral lines become split into three or more components; a phenomenon called the [[Zeeman effect]]. This is caused by the interaction of the magnetic field with the magnetic moment of the atom and its electrons. Some atoms can have multiple [[electron configuration]]s with the same energy level, which thus appear as a single spectral line. The interaction of the magnetic field with the atom shifts these electron configurations to slightly different energy levels, resulting in multiple spectral lines.<ref name=weiss2001 /> The presence of an external [[electric field]] can cause a comparable splitting and shifting of spectral lines by modifying the electron energy levels, a phenomenon called the [[Stark effect]].<ref>{{cite book
|last1=Beyer|first1=H.F.
|last2=Shevelko|first2=V.P.
|year=2003
|title=Introduction to the Physics of Highly Charged Ions
|publisher=CRC Press|isbn=978-0-7503-0481-8
|oclc=47150433|pages=232–236}}</ref>

If a bound electron is in an excited state, an interacting photon with the proper energy can cause [[stimulated emission]] of a photon with a matching energy level. For this to occur, the electron must drop to a lower energy state that has an energy difference matching the energy of the interacting photon. The emitted photon and the interacting photon then move off in parallel and with matching phases. That is, the wave patterns of the two photons are synchronized. This physical property is used to make [[laser]]s, which can emit a coherent beam of light energy in a narrow frequency band.<ref name=watkins_sjsu />