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A carbon nucleus has 6 protons. Therefore it can attract 6 electrons.

The first 2 electrons fill the first shell. The next 4 electrons go into the second shell. This shell can hold a maximum of 8 electrons. So it is 4 electrons short of a full shell.

Carbon can therefore share 4 electrons with other atoms, so it can form 4 covalent bonds.

In this diagram we see a carbon atom sharing electrons with 4 hydrogen atoms to form a methane molecule.

 

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