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Why is the Neon molecule $ Ne_2 $ not possible?

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Hint :Neon belongs to the group of noble gases (group 18) in the periodic table. These noble gases have properties that are unique and no other group has the same. While forming a molecule, there are different bonds that are formed – most involving the outermost valence shell electrons.

Complete Step By Step Answer:
Noble gases make up a group of chemicals that have the same properties and are classified under Group $ 18 $ on the periodic table.
Under standard environmental conditions, they are colourless, odourless and monoatomic with very low chemical activity.
They are monatomic as they have a complete valence shell. Which implies that they have a complete set of $ 2 $ electrons (in Helium) and 8 electrons (Neon, Argon, Krypton, Xenon and Radon) in their outermost shells.
Due to the complete valence shell, they have the highest atomic stability, which prevents the donation and receiving of electrons from other atoms. Hence, their chemical reactivity is very low.
This is the most stable arrangement of electrons and thus, noble gases rarely react with other elements and form compounds.
Moreover, with all these factors, noble gases have essentially zero electron affinity.
As Neon is a part of this group, it also has a complete electronic configuration, which is:
 $ [Ne]=[He]2s^2 2p^6 $
With this additional stability, it does not combine with any other molecule.
Therefore, the Neon molecule - $ Ne_2 $ is not possible.

Note :
Understand the periodic trends and the general properties of all the groups in the periodic table. This will help you answer such questions. Also, know what the property of the valence shell is, how its filling makes a difference on the properties of elements. Knowing how to write the electronic configuration is an added bonus to answering questions like these.