What carbon doesn't make quadruple type(4-bond) bond??
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The reason a carbon atom cannot bond with four electrons with another carbon is due to the carbon electron orbitals. Since it has a s and 3 p orbitals, it must create one sigma and at most 2 pi bonds with another carbon. Hence, you'll have to bond them with another atom.
Carbon can and does routinely form triple bonds with itself (as in C2H2, acetylene), in cyano compounds (CN-) and in carbon monoxide (CO). Some students wonder why 2 carbon atoms do not form quadruple bonds with themselves to complete both atom’s orbitals. They are likely wondering about this given that carbon’s neighbor to the right, nitrogen, forms a triple with itself in the N2 molecule so each atom can have a complete electron count. If this was your train of thought, I commend you for it. This is using an underlying pattern to predict the behavior of other systems.
But there is more to bonding than just the tendency to achieve a noble gas configuration. The formation of some types of bonds may be less stable (or unstable) compared to others due to repulsive forces. A quadruple-bonded C2 molecule might exist at the low temperatures of space, but it is unlikely to be stable at ambient temperatures and pressures. Remember that carbon has a small atomic radius, and in the case of a C2 quadruple bond, that is 8 electrons packed into a very small region. The amount of repulsion would be immense.
The C2 molecule has been the subject of extensive research for many decades. Chemists continue to wonder carbon can form a quadruple bond with itself. If you are interested in the topic here are a handful of papers exploring the possibility of a quadruple bond in C2