The simplest polyatomic molecular ion is  which can be thought of as molecular hydrogen with an additional proton. Infrared spectroscopic studies of interstellar space have identified this species in the atmosphere of Jupiter and other interstellar bodies. The rotational-vibrational spectrum of the  and band of  was first measured in the laboratory by T. Oka in 1980 [Phys. Rev. Lett. 45 (1980): 531]. The spectrum consists of a series of transitions extending from 2450 to 2950 cm^-1. Employing an average value of 2700. cm^-1. for the energy of the first excited rotational-vibrational state of this molecule relative to the ground state, what temperature is required for 10% of the molecules to populate this excited state?