Information about Diatomic

Diatomic molecules are molecules made only of two atoms, of either the same or different chemical elements. The prefix di- means two in Greek.

Description and occurrence in nature

Huber and Herzberg's book, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules^[1], lists hundreds of diatomic molecules, some which have been detected spectroscopically in interstellar space. However, few diatomics are found to occur naturally on Earth outside of laboratories. About 99% of the Earth's atmosphere is composed of diatomic molecules, specifically oxygen O₂ (21%) and nitrogen N₂ (78%), with the remaining 1% being mostly argon (0.9340%). The natural abundance of hydrogen (H₂) in the Earth's atmosphere is only on the order of parts per million, but H₂ is, in fact, the most abundant molecule seen in nature, dominating the composition of stars.

Elements that consist of diatomic molecules, under typical laboratory conditions of 1 bar and 25 ^oC, include hydrogen (H₂), nitrogen (N₂), oxygen (O₂), and the halogens: fluorine (F₂), chlorine (Cl₂), bromine (Br₂), iodine (I₂), and, perhaps, astatine (At₂).^[2] Again note that many other diatomics are possible, such as metals heated to their gaseous states. Also, many diatomic molecules are unstable and highly reactive, such as diphosphorus. A few compounds are made of diatomic molecules, including CO and HBr.

If a diatomic molecule consists of two atoms of the same element, such as H₂ and O₂, then it is said to be homonuclear, but otherwise it is said to heteronuclear, such as with CO or NO. The bond in a homonuclear diatomic molecule is non-polar and fully covalent.

Historical significance

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 8 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.

As early as 1805, Gay-Lussac and 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.

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.^[3]

Energy levels

It is convenient, and common, to represent a diatomic molecule as two point masses (the two atoms) 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 energies
• The rotational energies
• The vibrational energies

Translational energies

The translational energy of the molecule is simply given by the kinetic energy expression:

where m is the mass of the molecule and v is its velocity.

Rotational energies

Classically, the kinetic energy of rotation is

:

where

: is the angular momentum

: is the moment of inertia of the molecule

For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by

:

where l is a positive integer and is Planck's reduced constant.

Also, for a diatomic molecule the moment of inertia is

:

where

: is the reduced mass of the molecule and

: is the average distance between the two atoms in the molecule.

So, substituting the angular momentum and moment of inertia into E_rot, the rotational energy levels of a diatomic molecule are given by:

:

Vibrational energies

Another way a diatomic molecule can move is to have each atom oscillate - or vibrate - along a line (the bond) connecting the two atoms. The vibrational energy is approximately that of a quantum harmonic oscillator:

:

where

:n is an integer

:h is Planck's constant and

:f is the frequency of the vibration.

Comparison between rotational and vibrational energy spacings

The lowest rotational energy level of a diatomic molecule occurs for and gives E_rot = 0. For O₂, the next highest quantum level () has an energy of roughly:

:

This spacing between the lowest two rotational energy levels of O₂ is comparable to that of a photon in the microwave region of the electromagnetic spectrum.

The lowest vibrational energy level occurs for , and a typical vibration frequency is 5 x 10¹³ Hz. Doing a calculation similar to that above gives:

:.

So 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.

See also

•  • [ e] Diatomic Elements
Hydrogen H2	|		Nitrogen N2	|		Oxygen O2	|		Fluorine F2
Chlorine Cl2	|		Bromine Br2	|		Iodine I2	|		Astatine At2

Further reading

• Huber, K. P. and Herzberg, G. (1979). Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules. New York: Van Nostrand: Reinhold. 
• Tipler, Paul (1998). Physics For Scientists and Engineers : Vol. 1 (4th ed.). W. H. Freeman. ISBN 1-57259-491-8. 

Notes and references

1. ^ Huber, K. P. and Herzberg, G. (1979). Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules. New York: Van Nostrand: Reinhold. 
2. ^ Astatine is so rare in nature, with its most stable isotope having a half-life of only 8.3 hours, that it is usually not considered in discussions of this subject. For details on astatine, see Emsley, J. (1989). The Elements. Oxford: Clarendon Press, 22-23. 
3. ^ Ihde, Aaron J. (1961). "The Karlsruhe Congress: A centennial retrospective.". Journal of Chemical Education 38: 83-86. Retrieved on 2007-08-24. 

External links

• Hyperphysics - Rotational Spectra of Rigid Rotor Molecules
• Hyperphysics - Quantum Harmonic Oscillator

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chemical element, or element, is a type of atom that is defined by its atomic number; that is, by the number of protons in its nucleus. The term is also used to refer to a pure chemical substance composed of atoms with the same number of protons.
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Earth's atmosphere is a layer of gases surrounding the planet Earth and retained by the Earth's gravity. It contains roughly (by molar content/volume) 78% nitrogen, 20.95% oxygen, 0.93% argon, 0.
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2, −1
(neutral oxide)
Electronegativity 3.44 (Pauling scale)
Ionization energies
(more) 1st: 1313.9 kJmol⁻¹
2nd: 3388.3 kJmol⁻¹
3rd: 5300.5 kJmol⁻¹

Atomic radius 60 pm
Atomic radius (calc.
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3, 5, 4, 2
(strongly acidic oxide)
Electronegativity 3.04 (Pauling scale)
Ionization energies
(more) 1st: 1402.3 kJmol⁻¹
2nd: 2856 kJmol⁻¹
3rd: 4578.1 kJmol⁻¹

Atomic radius 65 pm
Atomic radius (calc.
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Argon (IPA:/ˈɑːgɒn/) is a chemical element designated by the symbol Ar. Argon has atomic number 18 and is the third element in group 18 of the periodic table (noble gases).
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1, −1
(amphoteric oxide)
Electronegativity 2.20 (Pauling scale) More

Atomic radius 25 pm
Atomic radius (calc.) 53 pm
Covalent radius 37 pm
Van der Waals radius 120 pm
Miscellaneous

Thermal conductivity (300 K) 180.
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3, 5, 4, 2
(strongly acidic oxide)
Electronegativity 3.04 (Pauling scale)
Ionization energies
(more) 1st: 1402.3 kJmol⁻¹
2nd: 2856 kJmol⁻¹
3rd: 4578.1 kJmol⁻¹

Atomic radius 65 pm
Atomic radius (calc.
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2, −1
(neutral oxide)
Electronegativity 3.44 (Pauling scale)
Ionization energies
(more) 1st: 1313.9 kJmol⁻¹
2nd: 3388.3 kJmol⁻¹
3rd: 5300.5 kJmol⁻¹

Atomic radius 60 pm
Atomic radius (calc.
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halogens or halogen elements are a series of nonmetal elements from Group 17 (old-style: VII or VIIA; Group 7 IUPAC Style) of the periodic table, comprising fluorine, F; chlorine, Cl; bromine, Br; iodine, I; and astatine, At.
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100% F is stable with 10 neutrons
References

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1, 3, 5, 7
(strongly acidic oxide)
Electronegativity 3.16 (Pauling scale)
Ionization energies
(more) 1st: 1251.2 kJmol⁻¹
2nd: 2298 kJmol⁻¹
3rd: 3822 kJmol⁻¹

Atomic radius 100 pm
Atomic radius (calc.
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Astatine (IPA: /ˈastətiːn/) is a chemical element in the periodic table that has the symbol At and atomic number 85.
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Covalent bonding is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms, or between atoms and other covalent bonds.
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John Dalton (September 6, 1766 – July 27, 1844) was an English chemist, meteorologist and physicist, born at Eaglesfield, near Cockermouth in Cumbria. He is best known for his pioneering work in the development of modern atomic theory, and his research into colour blindness
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von Humboldt may refer to:

• Wilhelm von Humboldt - a Prussian minister, linguist and philosopher
• Alexander von Humboldt - a Prussian naturalist and explorer

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Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto (August 9, 1776–July 9, 1856) was an Italian savant. He is most noted for his contributions to the theory of molarity and molecular weight.
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Avogadro's law (Avogadro's Hypothesis, or Avogadro's Principle) is a gas law named after Amedeo Avogadro, who in 1811 hypothesized that:

Equal volumes of gases, at the same temperature and pressure, contain the same number of particles, or molecules.

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