In the molecule CH3^+, carbon is bonded to three hydrogen atoms and carries a positive charge. To determine the number of valence electrons in carbon, we look at its electron configuration and take into account the charge.
Carbon has an atomic number of 6, which means it has 6 electrons. The electron configuration of carbon is 1s² 2s² 2p². In its neutral state, carbon has 4 valence electrons, occupying the 2s and 2p orbitals.
In CH3^+, carbon carries a positive charge (+1). This means it has lost one electron and now has only 3 valence electrons. The loss of an electron results in the formation of a cation, giving carbon a positive charge.
Therefore, in CH3^+, carbon has 3 valence electrons.