Absolute populations of the A¹II_u, and d³II_g, excited electronic states of the C₂ molecule that is formed in plasmochemical reactions are measured in a discharge in He-CO mixtures. From these data, the concentrations of C₂ in the ground X¹Σ_g⁺ and low-lying a³II_u states are obtained. The decay of these concentrations in a discharge at the afterglow stage is studied. The experimental data are used to obtain information about the mechanisms of formation and destruction of molecular carbon in plasma. The rate constants for intersystem crossing of C₂ in collisions with CO molecules and He atoms, which were previously unknown, are found.