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'Triplet oxygen' is the ground state of the oxygen molecule. The electron configuration of the molecule has two unpaired electrons occupying two degenerate molecular orbitals. These orbitals are classified as antibonding, so the O-O bond is weaker than the N-N bond in molecular nitrogen, where all bonding molecular orbitals are filled.
Unpaired electrons in degenerate orbitals can have the same spin, so the total spin S of the molecule is 1. This is known as a triplet configuration because the spin has three possible alignments in an external magnetic field.
Because the molecule has a non-zero spin magnetic moment, liquid oxygen is paramagnetic i.e. it can be attracted to the poles of a magnet. The Lewis structure O=O does not accurately represent the diradical nature of molecular oxygen; molecular orbital theory must be used to adequately account for the unpaired electrons.
The unusual electron configuration prevents molecular oxygen from reacting directly with many other molecules, which are often in the singlet state. Triplet oxygen will, however, readily react with molecules in a doublet state, such as radicals, to form a new radical. Conservation of spin quantum number would require a triplet transition state in a reaction of triplet oxygen with a closed shell (i.e. a molecule in a singlet state.) The extra energy required is sufficient to prevent direct reaction at ambient temperatures with all but the most reactive substrates e.g. white phosphorus. At higher temperatures or in the presence of suitable catalysts the reaction proceeds more readily. For instance, most flammable substances are characterised by an autoignition temperature at which they will undergo combustion in air without an external flame or spark.
Singlet oxygen, where the electron spins are opposed in a higher energy state, is many times more reactive than triplet oxygen, and extremely hazardous to organic matter. It is used for the extermination of heavy infestations of persistent pests in houses and buildings.

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References

References

★ http://www.missouri.edu/~chemrg/wade4e/chapter15/dioxygen_t.html

★ http://www.meta-synthesis.com/webbook/16_diradical/diradical.html