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| | Hey guys !! I am SUZANNE EMERSON. I live in Dallas. My age is 32. I want to study at The Revolutionary Institute which has a branch in Derby. I am self employed as a Economist. I like to do Bringing Food To The Disabled. My father name is John and he is a Designer. My mother is a Baker.<br><br>my web page :: [http://Www.kidsgametoys.com/ baby toys online shop] |
| [[Image:Nitrogen-3D-vdW.png|thumb|A [[space-filling model]] of the diatomic molecule dinitrogen, N<sub>2</sub>]]
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| '''Diatomic molecules''' are [[molecule]]s composed of only two [[atom]]s, of either the same or different [[chemical element]]s. The prefix di- is of Greek origin, meaning "two". If a diatomic molecule consists of two atoms of the same element, such as [[hydrogen]] (H<sub>2</sub>) or [[oxygen]] (O<sub>2</sub>), then it is said to be [[Homonuclear molecule|homonuclear]]. Otherwise, if a diatomic molecule consists of two different atoms, such as [[Carbon_monoxide|carbon monoxide]] (CO) or [[Boron_monoxide|boron monoxide]] (BO), the molecule is said to [[Heteronuclear molecule|heteronuclear]].
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| ==Homonuclear molecules==
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| [[File:Diatomic molecules periodic table.svg|thumb|300px|A [[periodic table]] showing the elements that exist as [[homonuclear molecule|homonuclear]] diatomic molecules under typical laboratory conditions.]]
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| The only [[chemical elements]] which are stable two atom [[homonuclear]] [[molecules]] at [[standard temperature and pressure]] (STP), are [[hydrogen]] (H<sub>2</sub>), [[nitrogen]] (N<sub>2</sub>) and [[oxygen]] (O<sub>2</sub>), plus the [[halogens]] [[fluorine]] (F<sub>2</sub>) and [[chlorine]] (Cl<sub>2</sub>). Those diatomic elements that are gaseous at STP, when grouped together with the [[monatomic]] [[noble gases]], such as [[argon]], are called "elemental gases" or "molecular gases" to distinguish them from molecules that are also [[chemical compounds]].
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| The [[noble gases]] do not form diatomic molecules: this can be explained using [[molecular orbital theory]].
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| The halogens [[bromine]] (Br<sub>2</sub>) and [[iodine]] (I<sub>2</sub>) can also form diatomic gas at slightly elevated temperatures.<ref name=Chemistry>{{cite book|title=Chemistry|authors=Whitten, Kenneth W.; Davis, Raymond E.; Peck, M. Larry; Stanley, George G.|year=2010|publisher=Brooks/Cole, Cengage Learning|pages=337–338|url=http://books.google.ca/books?id=6Zwu9-qT0qQC&pg=PA337#v=onepage&q&f=false|edition=9th}}</ref><!--Please do not add astatine; see [[Astatine#General characteristics]].--> <br />
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| Other elements that can form two atom molecules are [[diphosphorus|phosphorus]] (P<sub>2</sub>) and [[disulfur|sulfur]] (S<sub>2</sub>) although neither of these molecules are stable in atmospheric conditions.
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| ==Heteronuclear molecules==
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| All other diatomic molecules are [[chemical compounds]] of two different elements, for example, [[nitric oxide]] (NO). Many different elements combine to form heteronuclear diatomic molecules, and this phenomenon, in general, depends on temperature and pressure. Many [[chemical compound]]s form diatomic molecules when evaporated.
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| ==Occurrence==
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| Hundreds of diatomic molecules have been characterized<ref>{{Cite book| author = Huber, K. P. and Herzberg, G. | title = Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules | publisher = New York: Van Nostrand: Reinhold | year = 1979 | id= }}</ref> in the terrestrial environment, laboratory, and [[List of molecules in interstellar space|interstellar medium]]. About 99% of the [[Earth's atmosphere]] is composed of two diatomic molecules: oxygen (21%) and nitrogen (78%). The natural abundance of [[hydrogen|hydrogen (H<sub>2</sub>)]] in the Earth's atmosphere is only on the order of parts per million, but H<sub>2</sub> is, in fact, the most abundant diatomic molecule in nature. The interstellar medium is, indeed, dominated by hydrogen atoms.
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| The bond in a homonuclear diatomic molecule is non-polar. In most diatomic molecules, the elements are nonidentical. Prominent examples include [[carbon monoxide]], [[nitric oxide]], and [[hydrogen chloride]], but other important examples include gaseous MgO, SiO, and many other species not normally considered diatomic because they [[polymerize]] near room temperature. All halogens are diatomic, excepted [[astatine]].
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| Elements that consist of diatomic molecules, under typical laboratory conditions of 1 bar and 25 °C, include hydrogen (H<sub>2</sub>), nitrogen (N<sub>2</sub>), oxygen (O<sub>2</sub>), and the halogens (although it is not yet known whether [[astatine]] forms diatomic astatine molecules<ref>{{cite book|last=Hammond|first=C.R.|title=Handbook of Chemistry and Physics|year=2012|url=http://www.hbcpnetbase.com//articles/04_01_91.pdf|chapter=Section 4: Properties of the Elements and Inorganic Compounds}}</ref>).<ref>{{Cite book| author = Emsley, J. | title = The Elements | publisher = Oxford: Clarendon Press | year = 1989 | pages = 22–23| id= }}</ref> Other elements form homonuclear diatomics when evaporated, but these diatomic species repolymerize at lower temperatures. For example, heating ("cracking") elemental phosphorus gives [[diphosphorus]], P<sub>2</sub>.
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| ==Molecular geometry==
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| {{Main|Molecular geometry}}
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| Diatomic molecules cannot have any [[molecular geometry|geometry]] but linear, as any two points always lie in a line. This is the simplest [[stereochemistry|spatial arrangement of atoms]] after the sphericity of single atoms.<ref name = "qpxlgb">"VSEPR - A Summary". University of Berkeley College of Chemistry. 20 January 2008. http://mc2.cchem.berkeley.edu/VSEPR/</ref>
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| ==Historical significance==
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| Diatomic elements played an important role in the elucidation of the concepts of element, atom, and molecule in the 19th century, because some of the most common elements, such as hydrogen, oxygen, and nitrogen, occur as diatomic molecules. [[John Dalton]]'s original atomic hypothesis assumed that all elements were monatomic and that the atoms in compounds would normally have the simplest atomic ratios with respect to one another. For example, Dalton assumed that water's formula was HO, giving the atomic weight of oxygen as eight times that of hydrogen, instead of the modern value of about 16. As a consequence, confusion existed regarding atomic weights and molecular formulas for about half a century.
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| As early as 1805, [[Gay-Lussac]] and [[Alexander von Humboldt|von Humboldt]] showed that water is formed of two volumes of hydrogen and one volume of oxygen, and by 1811 [[Amedeo Avogadro]] had arrived at the correct interpretation of water's composition, based on what is now called [[Avogadro's law]] and the assumption of diatomic elemental molecules. However, these results were mostly ignored until 1860. Part of this rejection was due to the belief that atoms of one element would have no [[chemical affinity]] towards atoms of the same element, and part was due to apparent exceptions to Avogadro's law that were not explained until later in terms of dissociating molecules.
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| At the 1860 [[Karlsruhe Congress]] on atomic weights, [[Cannizzaro]] resurrected Avogadro's ideas and used them to produce a consistent table of atomic weights, which mostly agree with modern values. These weights were an important pre-requisite for the discovery of the [[periodic law]] by [[Dmitri Mendeleev]] and [[Lothar Meyer]].<ref>{{Cite journal| author = Ihde, Aaron J. | title = The Karlsruhe Congress: A centennial retrospective | journal = Journal of Chemical Education | year = 1961 | volume = 38 | pages = 83–86 | url = http://search.jce.divched.org:8081/JCEIndex/FMPro?-db=jceindex.fp5&-lay=wwwform&combo=karlsruhe&-find=&-format=detail.html&-skip=0&-max=1&-token.2=0&-token.3=10 | accessdate=2007-08-24 | doi = 10.1021/ed038p83| issue = 2 |bibcode = 1961JChEd..38...83I }}</ref>
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| ==Excited electronic states==
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| Diatomic molecules are normally in the lowest or ground state, which is also known as the <math>X</math> state. When a gas of diatomic molecules is bombarded by energetic electrons, the molecules are excited to higher electronic states, such as occurs, for example, in the natural aurora, high-altitude nuclear explosions, and rocket-born electron gun experiments.<ref name=gilmore1992/> The 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 the higher to lower electronic states and ultimately to the ground state, and each transition results in the emission of a photon. This emission is known as [[fluorescence]]. Successively higher electronic states are traditionally 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 can be seen 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.
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| In quantum theory, an electronic state of a diatomic molecule is represented by
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| :<math>^{2S+1} \Lambda (v)</math>
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| 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 traditionally are represented by the electronic state symbols <math>\Sigma</math>, <math>\Pi</math>, <math>\Delta</math>,….
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| 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 the the Earth's atmosphere.<ref name=laher1991/> In the table, the subscripts and superscripts after <math>\Lambda</math> give additional quantum mechanical details about the electronic state.
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| {| class="wikitable"
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| |-
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| ! State !! Energy (<math>T_0</math>, cm<math>^{-1}</math>)
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| |-
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| | <math>X ^1\Sigma_g^+</math> || 0.0
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| |-
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| | <math>A ^3\Sigma_u^+</math> || 49754.8
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| |-
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| | <math>B ^3\Pi_g</math> || 59306.8
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| |-
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| | <math>W ^3\Delta_u</math> || 59380.2
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| |-
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| | <math>B' ^3\Sigma_u^-</math> || 65851.3
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| |-
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| | <math>a' ^1\Sigma_u^-</math> || 67739.3
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| |-
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| | <math>a ^1\Pi_g</math> || 68951.2
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| |-
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| | <math>w ^1\Delta_u</math> || 71698.4
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| |}
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| ==Energy levels==
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| The [[molecular term symbol]] is a shorthand expression of the angular momenta that characterize the electronic quantum state of a diatomic molecule, which is an eigenstate of the electronic molecular [[Hamiltonian (quantum mechanics)|Hamiltonian]]. It is also convenient, and common, to represent a diatomic molecule as two-point masses connected by a massless spring. The energies involved in the various motions of the molecule can then be broken down into three categories: the translational, rotational, and vibrational energies.
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| ===Translational energies===
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| The translational energy of the molecule is simply given by the [[kinetic energy]] expression:
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| :<math>E_{trans}=\frac{1}{2}mv^2</math>
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| where ''m'' is the mass of the molecule and ''v'' is its velocity.
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| ===Rotational energies===
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| Classically, the kinetic energy of rotation is
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| ::<math>E_{rot} = \frac{L^2}{2 I} \,</math>
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| :where
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| ::<math>L \,</math> is the [[angular momentum]]
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| ::<math>I \,</math> is the [[moment of inertia]] of the molecule
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| For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by
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| ::<math>L^2 = l(l+1) \hbar^2 \,</math>
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| :where ''l'' is a non-negative integer and <math>\hbar</math> is the [[reduced Planck constant]].
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| Also, for a diatomic molecule the moment of inertia is
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| ::<math>I = \mu r_{0}^2 \,</math>
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| :where
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| ::<math>\mu \,</math> is the [[reduced mass]] of the molecule and
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| ::<math>r_{0} \,</math> is the average distance between the centers of the two atoms in the molecule.
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| So, substituting the angular momentum and moment of inertia into E<sub>rot</sub>, the rotational energy levels of a diatomic molecule are given by:
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| ::<math style>E_{rot} = \frac{l(l+1) \hbar^2}{2 \mu r_{0}^2} \ \ \ \ \ l=0,1,2,... \,</math>
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| ===Vibrational energies===
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| Another way a diatomic molecule can move is to have each atom oscillate—or [[Vibration|vibrate]]—along a line (the bond) connecting the two atoms. The vibrational energy is approximately that of a [[quantum harmonic oscillator]]:
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| ::<math>E_{vib} = \left(n+\frac{1}{2} \right)\hbar \omega \ \ \ \ \ n=0,1,2,.... \,</math>
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| :where
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| ::''n'' is an integer
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| ::<math>\hbar</math> is the [[reduced Planck constant]] and
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| ::<math>\omega</math> is the [[angular frequency]] of the vibration.
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| ===Comparison between rotational and vibrational energy spacings===
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| The spacing, and the energy of a typical spectroscopic transition, between vibrational energy levels is about 100 times greater than that of a typical transition between [[rotational energy]] levels.
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| ==Hund's cases==
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| {{main|Hund's cases}}
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| The [[good quantum number]]s for a diatomic molecule, as well as good approximations of rotational energy levels, can be obtained by modeling the molecule using [[Hund's cases]].
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| ==Further reading==
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| * {{Cite book| author = Huber, K. P. and Herzberg, G. | title = Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules | publisher = New York: Van Nostrand: Reinhold | year = 1979 | id= }}
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| * {{Cite book| author=Tipler, Paul | title=Physics For Scientists and Engineers : Vol. 1 (4th ed.) | publisher=W. H. Freeman | year=1998 | isbn=1-57259-491-8}}
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| ==See also==
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| *[[AXE method]]
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| *[[Octatomic element]]
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| *[[Shared pair]]
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| *[[Industrial gas]]
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| ==Notes and references==
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| {{Reflist|2
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| <ref name=gilmore1992> | |
| {{cite journal
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| | last = Gilmore
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| | first = Forrest R.
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| | display-authors = 3
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| | last2 = Laher
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| | first2 = Russ R.
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| | last3 = Espy
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| | first3 = Patrick J.
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| | year = 1992
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| | title = Franck-Condon Factors, r-Centroids, Electronic Transition Moments, and Einstein Coefficients for Many Nitrogen and Oxygen Band Systems
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| | journal = [[Journal of Physical and Chemical Reference Data]]
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| | volume = 21
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| | issue = 5
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| | pages = 1005-1107
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| }}
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| </ref> | |
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| <ref name=laher1991>
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| {{cite journal
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| | last = Laher
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| | first = Russ R.
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| | display-authors = 2
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| | last2 = Gilmore
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| | first2 = Forrest R.
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| | year = 1991
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| | title = Improved Fits for the Vibrational and Rotational Constants of Many States of Nitrogen and Oxygen
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| | journal = [[Journal of Physical and Chemical Reference Data]]
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| | volume = 20
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| | issue = 4
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| | pages = 685-712
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| }}
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| </ref>
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| }}
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| ==External links==
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| * [http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/rotrig.html#c3 Hyperphysics] – Rotational Spectra of Rigid Rotor Molecules
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| * [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc.html Hyperphysics] – Quantum Harmonic Oscillator
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| * [http://www.3dchem.com/ 3D Chem] – Chemistry, Structures, and 3D Molecules
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| * [http://www.iumsc.indiana.edu/ IUMSC] – Indiana University Molecular Structure Center
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| {{MolecularGeometry}}
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| {{diatomicelements}}
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| {{DEFAULTSORT:Diatomic Molecule}}
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| [[Category:Molecules]]
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| [[Category:Stereochemistry]]
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| [[Category:Molecular geometry]]
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