how many valence electrons does a carbon radical possess?

It depends upon the charge of the carbon radical. For C neutral it is

1s2 2s2 2p2 so for C^+ it will be
1s2 2s2 2p so there are 3 electrons in the outer shell.

To determine the number of valence electrons a carbon radical possesses, we need to first understand what a radical is.

A radical is an atom or a group of atoms that has an unpaired electron. In the case of a carbon radical, it means that the carbon atom has an unpaired electron, making it highly reactive.

Carbon is located in Group 14 of the periodic table, meaning it has four valence electrons. Valence electrons are the electrons found in the outermost shell of an atom and determine the atom's chemical properties.

When a carbon atom becomes a radical, it loses or gains an electron, resulting in an unpaired electron. Since carbon typically forms four covalent bonds to complete its valence shell, losing or gaining one electron means it still has three remaining electrons to form those bonds.

Therefore, a carbon radical will have three valence electrons.