The imprisonment of the 2537-A resonance radiation from mercury in the mercury-argon discharge of fluorescent lamps is treated by a Monte Carlo method. The effects of emission and absorption linewidths, hyperfine splitting, isotopic composition, collisional transfers of excitation, and quenching are explicitly incorporated in the calculations. The calculated spectra of emitted radiation are in good agreement with measured spectra for several combinations of lamp temperature and mercury composition. Also in agreement with experiments, the addition of '80Hg to natural mercury is found to increase lamp efficiency. The method is useful for a number of problems in radiation transfer.