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Why nitrogen exists as diatomic molecule and Phosphorus as ?

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Nitrogen exists as diatomic molecule (N)  with triple bond between two N atoms and phosphorus as P. Nitrogen can form multiple bonds. Phosphorous cannot form such bonds due to repulsion between non bonded electrons of inner core. In case of nitrogen, there is no such repulsion as it has only 1s electrons in inner shell so that the overlap of p orbitals to form pi bonds is easy.

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