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Q. Nitrogen and oxygen exist as diatomic but their cogeners are $P _{4}$ and $S _{8}$ respectively. This is due to

AIIMSAIIMS 2000The p-Block Elements - Part2

Solution:

As nitrogen and oxygen atoms are small and highly electronegative with no vacant d-orbitals available for bonding multiple bonds are formed between oxygen-oxygen and nitrogen-nitrogen atoms.
N ≡ N O $=$ O
As the size of P and S atoms is large so multiple bonds are not strong enough, also catenation is possible due to vacant d-orbitals.