Chlorine is a halogen and all halogens and oxygen, nitrogen and hydrogen are diatomics
Neon is in group 8/0, which means that it has a full outer shell. Atoms react to get a full outer shell but as neon already has a full outer shell, it doesn't react and stays monatomic.
However, chlorine is in group 7, so it needs 1 more electron to complete its outer shell, two chlorine atom share one electron each with each other so they have full outer shells. This is why chlorine is diatomic. ;
Neon is monatomic because it has a full outer electron shell, making it chemically stable and independent. In contrast, chlorine is diatomic as it needs to share an electron with another chlorine atom to achieve a full outer shell. This difference in electron configuration is key to their differing forms.
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