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Nonmetals gain electrons under certain conditions to attain a noble-gas electron configuration. how many electrons must be gained by the element c?

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System is said to have achieved noble-gas configuration, when it's valance shell is completely filled.

Atomic number of carbon is 6. Thus, it has 6 electrons.

The electronic configuration of carbon is 1s2 2s2 2p2

Now, the inert gas closest to C is Ne, whose atomic number is 10.

Thus, there are excess of 4 electrons in Ne as compared to C.

Hence, carbon must gain 4 electrons to achieve noble-gas configuration.

Alternatively,  C can also lose 4 electron to achieve noble gas configuration of He.

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