The hybridization of carbon atoms in C - C
single bond of is:
(A) sp3 - sp3

(B) sp2 - sp3

(C) sp - sp2

(D) sp3 - sp

To determine the hybridization of the carbon atoms in a carbon-carbon (C-C) single bond, we can follow these steps:

Identify the Type of Bond: A single bond between two carbon atoms consists of one sigma (σ) bond.

Count the Bonds and Lone Pairs: For each carbon atom in a C-C single bond:

Each carbon atom is typically bonded to other atoms, and in the case of the simplest alkanes, it can be bonded to hydrogen atoms.
Each carbon atom can have up to four bonds. In a single bond scenario, it could be bonding to one other carbon and up to three hydrogens.
Determine the Hybridization:

sp³ Hybridization: If a carbon atom has four bonds (single bonds), it undergoes sp³ hybridization. In sp³ hybridization, one s orbital and three p orbitals mix to form four equivalent sp³ hybrid orbitals, arranged in a tetrahedral geometry.
sp² Hybridization: If a carbon atom has one double bond and two single bonds, it undergoes sp² hybridization. This involves one s orbital and two p orbitals mixing, forming three sp² hybrid orbitals and one unhybridized p orbital.
sp Hybridization: If a carbon atom forms one triple bond (or two double bonds), it undergoes sp hybridization, involving one s orbital and one p orbital mixing, resulting in two sp hybrid orbitals.
Application to the Question: In a C-C single bond, both carbon atoms are bonded through one sigma bond, with their other valencies filled by hydrogen (in a simple alkane like ethane, for example). Thus, both carbon atoms are sp³ hybridized.

Conclusion
In the C-C single bond, the hybridization of both carbon atoms is sp³ - sp³.

So, the correct answer is: (A) sp³ - sp³.