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Allotropes are two or more forms of the same element in the same physical state (solid, liquid, or gas) that differ from each other in their physical, and sometimes chemical, properties. The most notable examples of allotropes are found in groups 14, 15, and 16 of the periodic table. Gaseous oxygen, for example, exists in three allotropic forms: monatomic oxygen (O), a diatomic molecule (O2), and in a triatomic molecule known as ozone (O3).

A striking example of differing physical properties among allotropes is the case of carbon. Solid carbon exists in two allotropic forms: diamond and graphite. Diamond is the hardest naturally occurring substance and has the highest melting point (more than 6,335°F [3,502°C]) of any element. In contrast, graphite is a very soft material, the substance from which the "lead" in lead pencils is made.

The allotropes of phosphorus illustrate the variations in chemical properties that may occur among such forms. White phosphorus, for example, is a waxy white solid that bursts into flame spontaneously when exposed to air. It is also highly toxic. On the other hand, a second allotrope of phosphorus known as red phosphorus is far more stable, does not react with air, and is essentially nontoxic.

Allotropes differ from each other structurally depending on the number of atoms in a molecule of the element. There are allotropes of sulfur, for example, that contain 2, 6, 7, 8, 10, 12, 18, and 20 atoms per molecule (formulas S2 to S20). Several of these, however, are not very stable.

The term allotrope was first suggested by Swedish chemist J. J. Berzelius (1779-1848). He took the name from the Greek term allotropos, meaning other way. Berzelius was unable to explain the structure of allotropes, however. The first step in that direction was accomplished by British father and son crystallographers W. H. and L.W. Bragg in 1914. The Braggs used x-ray diffraction to show that diamond and graphite differ from each other in their atomic structure.

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