The time dependent optical emission model developed by Liu and Pasko (2004) is applied to studies of far-UV emissions of sprite streamers due to N2 Lyman-Birge-Hopfield (LBH) band system. Modeling results indicate that the LBH emissions of sprite streamers at 70 km are generally stronger by up to a factor of 10 than those from the first negative band system of N2+, and experimental measurements of the ratio of these two emissions at sprite altitudes can be used to determine poorly known quenching altitude of the N2 (a1Πg) state.