Question:
why does not carbon form only C2 bond ,such as the valency is completed by itself only
Answer:
Carbon has electronic configuration as 1S2, 2S2, 2P2. As you can see that the last shell of carbon has 4 electrons. This means that to complete the stable octet configuration, it needs 4 more electrons. Thus, carbon shares four more electrons with other elements to complete its octet.
Carbon is a stable element as existes in nature as monoatomic element itself.
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