Editing Diatomic molecule (section)

== Excited electronic states ==
Diatomic molecules are normally in their lowest or ground state, which conventionally is also known as the <math>X</math> state. When a gas of diatomic molecules is bombarded by energetic electrons, some of the molecules may be excited to higher electronic states, as occurs, for example, in the natural aurora; high-altitude nuclear explosions; and rocket-borne electron gun experiments.<ref name=gilmore1992/> Such excitation can also occur when the gas absorbs light or other electromagnetic radiation. The excited states are unstable and naturally relax back to the ground state. Over various short time scales after the excitation (typically a fraction of a second, or sometimes longer than a second if the excited state is [[metastability|metastable]]), transitions occur from higher to lower electronic states and ultimately to the ground state, and in each transition results a [[photon]] is emitted. This emission is known as [[fluorescence]]. Successively higher electronic states are conventionally named <math>A</math>, <math>B</math>, <math>C</math>, etc. (but this convention is not always followed, and sometimes lower case letters and alphabetically out-of-sequence letters are used, as in the example given below). The excitation energy must be greater than or equal to the energy of the electronic state in order for the excitation to occur.

In quantum theory, an electronic state of a diatomic molecule is represented by the [[molecular term symbol]]
<math display="block">^{2S+1} \Lambda (v)^{+/-}_{(g/u)}</math>
where <math>S</math> is the total electronic spin quantum number, <math>\Lambda</math> is the total electronic angular momentum quantum number along the internuclear axis, and <math>v</math> is the vibrational quantum number. <math>\Lambda</math> takes on values 0, 1, 2, ..., which are represented by the electronic state symbols <math>\Sigma</math>, <math>\Pi</math>, <math>\Delta</math>, ...
For example, the following table lists the common electronic states (without vibrational quantum numbers) along with the energy of the lowest vibrational level (<math>v=0</math>) of diatomic nitrogen (N<sub>2</sub>), the most abundant gas in the Earth's atmosphere.<ref name=laher1991/> 

The subscripts and superscripts after <math>\Lambda</math> give additional quantum mechanical details about the electronic state. The superscript <math>+</math> or <math>-</math> determines whether reflection in a plane containing the internuclear axis introduces a sign change in the wavefunction. The sub-script <math>g</math> or <math>u</math> applies to molecules of identical atoms, and when reflecting the state along a plane perpendicular to the molecular axis, states that does not change are labelled <math>g</math> (gerade), and states that change sign are labelled <math>u</math> (ungerade).

{| class="wikitable" style="margin-left:1em;"
|-
! State !! Energy{{efn|The "energy" units here are actually the reciprocal of the wavelength of a photon emitted in a transition to the lowest energy state. The actual energy can be found by multiplying the given statistic by the product of ''c'' (the speed of light) and ''h'' (the Planck constant); i.e., about 1.99 × 10<sup>−25</sup> joule-metres, and then multiplying by a further factor of 100 to convert from cm<sup>−1</sup> to m<sup>−1</sup>.}} (<math>T_0</math>, cm<sup>−1</sup>)
|-
| <math>X ^1\Sigma_g^+</math> || 0.0
|-
| <math>A ^3\Sigma_u^+</math> || 49754.8
|-
| <math>B ^3\Pi_g</math> || 59306.8
|-
| <math>W ^3\Delta_u</math> || 59380.2
|-
| <math>B' ^3\Sigma_u^-</math> || 65851.3
|-
| <math>a' ^1\Sigma_u^-</math> || 67739.3
|-
| <math>a ^1\Pi_g</math> || 68951.2
|-
| <math>w ^1\Delta_u</math> || 71698.4
|}
{{noteslist}}

The aforementioned [[fluorescence]] occurs in distinct regions of the [[electromagnetic spectrum]], called "[[emission spectrum|emission bands]]": each band corresponds to a particular transition from a higher electronic state and vibrational level to a lower electronic state and vibrational level (typically, many vibrational levels are involved in an excited gas of diatomic molecules). For example, N<sub>2</sub> <math>A</math>-<math>X</math> emission bands (a.k.a. Vegard-Kaplan bands) are present in the spectral range from 0.14 to 1.45 μm (micrometres).<ref name=gilmore1992/> A given band can be spread out over several nanometers in electromagnetic wavelength space, owing to the various transitions that occur in the molecule's rotational quantum number, <math>J</math>. These are classified into distinct sub-band branches, depending on the change in <math>J</math>.<ref name=levine1975/> The <math>R</math> branch corresponds to <math>\Delta J = +1</math>, the <math>P</math> branch to <math>\Delta J = -1</math>, and the <math>Q</math> branch to <math>\Delta J = 0</math>. Bands are spread out even further by the limited [[spectral resolution]] of the [[spectrometer]] that is used to measure the [[spectrum]]. The spectral resolution depends on the instrument's [[point spread function]].