How many unpaired electrons does carbon have in its ground state?

The ground state electron configuration of carbon is 1s² 2s² 2p². In this configuration, the 1s and 2s orbitals are fully filled with a total of four electrons (two in 1s and two in 2s). The 2p subshell, however, has only two electrons.

When examining the 2p subshell, we must consider how the electrons are distributed among the available orbitals. The p subshell consists of three orbitals, each capable of holding a maximum of two electrons. According to Hund's rule, electrons will fill degenerate (equal energy) orbitals singly before pairing up. Thus, for carbon, the two electrons in the 2p subshell will occupy two of the three available p orbitals singly.

This distribution results in two unpaired electrons because neither of the p electrons has a partner within its orbital. Therefore, carbon in its ground state has a total of two unpaired electrons.