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What is the relationship between diatomic molecules and diatomic elements?
Diatomic are a subgroup of diatomic molecules.
Every molecule that consists of two atoms is diatomic. Only if the two atoms are the same there is a diatomic element.
So ##O_2## is a diatomic element (and thus a diatomic molecule) ##HCl## is a diatomic molecule, but not a diatomic element.