What allows carbon to act as the "backbone" for biologically important macromolecules is that Carbon's valence electron shell has four open spots, allowing it to form covalent bonds with up to four other atoms at any time.
The valence electron shell is the outer electron layer of an atom. These valence electrons are responsible for bonding elements together to form complex molecules. They achieve this by sharing electrons in pairs. In the most common case, the carbon atom shares electrons with a hydrogen atom forming covalent bonds in pairs of electrons.
The reason Carbon is the backbone of all biological life and is essential in the formation of macromolecules is that the outer shell of a carbon atom has four valence electrons, allowing it to form covalent bonds with up to four different atoms at a time and achieve structurally stable shapes.
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