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A direct measurement of the transition dipole moment, $\mu 3$, of the $\nu 3$ asymmetric C-H stretching vibration of the methyl radical has been made in a transverse-flow reactor using laser-photolysis transient infrared absorption spectroscopy. Cyano (CN) radicals (and Cl atoms) were produced by excimer laser photolysis of ClCN at 193 nm and reacted with methane to give both $CH3$ and HCN (and HCl). The intensities of 18 rotational lines of the $\nu 3$ fundamental band were measured relative to the R(8) line of the $\nu 3$ C-H stretching vibration of HCN. The transition dipole moment of the methyl radical was determined to be $\mu 3=0.0327\pm 0.0027$ D using the known absolute absorption cross section of the $\nu 3$ vibration of HCN.