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The main difference is that one hydrogen does bond to another to form H2 but carbon doesn't form C2. Both bond covalently by sharing pairs of electrons, but carbon has four outer shell electrons and so must form four bonds. So it makes compounds such as methane CH4, or can link into long chains to form petrol C8H18, or link with lots of other carbons to form giant molecules diamond, graphite and fullerenes. You will easily find pictures illustrating bonding of these.

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Q: What is the main difference in the bonding of two hydrogen atoms H-H and two carbon atoms C-C?
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Carbon bonding is almost entirely hydrogen?

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