From left to right, identify the hybridization on the carbons in ch3cn.

           From left to right C-1 is sp³ hybridized and C-2 is sp hybridized.

Explanation:

Electronic Configuration of C in ground state is...

                                               1s², 2s², 2p²

Electronic Configuration of C in excited state is...

                                       1s², 2s¹, 2px¹, 2py¹, 2pz¹

Hybridization of C in H₃C- ;
                                          In this carbon the four orbitals 2s, 2px, 2py and 2pz with different energies mix together to four equivalent sp³ hybrid orbitals of same energy. Hence this carbon forms four sigma bonds.

Hybridization of C in -CN ;
                                          In this carbon two orbitals 2s and 2p with different energies mix together to form two equivalent sp hybrid orbital of same energy. Hence, this carbon forms two sigma bonds. And the remaining two orbitals form two pi bonds with Nitrogen atom.

C, small, hard spheres with insignificant volumes