A space-filling model of the diatomic molecule dinitrogen, N₂. Space-filling models (also known as calotte models or CPK models by Corey, Pauling and Koltun like Ball-and-stick models belong

Diatomic molecules are molecules made only of two atoms, of either the same or different chemical elements. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny A chemical element is a type of Atom that is distinguished by its Atomic number; that is by the number of Protons in its nucleus. 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. Gerhard Herzberg, PC, CC, FRSC, FRS ( December 25, 1904 &ndash March 3, 1999) was a pioneering Molecular Spectra and Molecular Structure IV Constants of Diatomic Molecules ia a classic comprehensive multidisciplinary reference text contains a critical compilation of available Wikipedia_talkFeatured_lists#Proposed_change_to_all_featured_lists for an explanation of this and other inclusion tags below -->This is a list of Molecules 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. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 This article pertains to the chemical element For other uses see Argon (disambiguation. 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. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1

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). Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Abundance Owing to their high Reactivity, the halogens are found in the environment only in compounds or as Ions Halide ions and oxoanions Fluorine, fluorum meaning "to flow" is the Chemical element with the symbol F and Atomic number 9 Chlorine (ˈklɔriːn from the Greek word 'χλωρóς' ( khlôros, meaning 'pale green' is the Chemical element with Atomic number 17 and Iodine (ˈaɪədaɪn ˈaɪədɪn or /ˈaɪədiːn/ from ιώδης iodes "violet" is a Chemical element that has the symbol I and Atomic Astatine (ˈæstətiːn is a Radioactive Chemical element with the symbol At and Atomic number 85 ^[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. Diphosphorus, P2 is the Diatomic form of Phosphorus. Unlike its Nitrogen group neighbour Nitrogen which forms a stable N2 Many compounds are made of diatomic molecules, including CO and HBr. A chemical compound is a substance consisting of two or more different elements chemically bonded together in a fixed proportion by Mass.

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.

Molecular Geometry

The diatomic molecule molecular geometry is the simplest spatial arrangement of atoms. Molecular geometry or molecular structure is the three- Dimensional arrangement of the Atoms that constitute a Molecule. Stereochemistry, a subdiscipline of Chemistry, involves the study of the relative spatial arrangement of Atoms within Molecules An important branch ^[3]. This configuration is more commonly referred to in the VSEPR theory as the AX1E*. Valence shell electron pair repulsion (VSEPR theory (1957 is a model in Chemistry, which is used for predicting the shapes of individual Molecules based Unlike other systems in VSEPR, there is no central atom. ^[4][3]

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. John Dalton FRS (6 September 1766 &ndash 27 July 1844 was an English Chemist, Meteorologist and Physicist. 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. Joseph Louis Gay-Lussac (also Louis Joseph Gay-Lussac, December 6, 1778 – May 9, 1850) was a French chemist Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto, Count of Quaregna and Cerreto was an Italian Savant. Avogadro's law ( Avogadro's Hypothesis, or Avogadro's Principle) is a Gas law named after Amedeo Avogadro, who in 1811 hypothesized 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. In Chemical physics and Physical chemistry, chemical affinity can be defined as electronic properties by which dissimilar Chemical species are capable of

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. The Karlsruhe Congress was an international meeting of chemists held in Karlsruhe, Germany from September 3 1860 to September 5 1860 These weights were an important pre-requisite for the discovery of the periodic law by Dmitri Mendeleev and Lothar Meyer. The periodic table of the chemical elements is a tabular method of displaying the Chemical elements Although precursors to this table exist its invention is Dmitri Ivanovich Mendeleev (sometimes spelled Mendeleyev; Дми́трий Ива́нович Менделе́ев) ( &ndash) was a Russian chemist and Julius Lothar Meyer ( August 19, 1830 - April 11, 1895) was born in Varel, at that time belonging to the duchy of Oldenburg ^[5]

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. The kinetic energy of an object is the extra Energy which it possesses due to its motion

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. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position This article is about the moment of inertia of a rotating object. The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta.

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. Reduced mass is the "effective" Inertial mass appearing in the Two-body problem of Newtonian mechanics.

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. Vibration refers to mechanical Oscillations about an equilibrium point. 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. The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. Frequency is a measure of the number of occurrences of a repeating event per unit Time.

Comparison between rotational and vibrational energy spacings

The lowest rotational energy level of a diatomic molecule occurs for l = 0 and gives E_rot = 0. For O₂, the next highest quantum level (l = 1) 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. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0

The lowest vibrational energy level occurs for n = 0, 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. The rotational energy or angular kinetic energy is the Kinetic energy due to the rotation of an object and is part of its total kinetic energy.

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.  

See also

• AXE method
• Octatomic element

Notes and references

External links

• Hyperphysics - Rotational Spectra of Rigid Rotor Molecules
• Hyperphysics - Quantum Harmonic Oscillator
• 3D Chem - Chemistry, Structures, and 3D Molecules
• IUMSC - Indiana University Molecular Structure Center