The emission from C can be used for wavelength calibration of instruments in the ultraviolet. This is generally performed by electron-impact initiated decomposition of a precursor (for example, CF₄) resulting in the production of electronically excited C, which relaxes to the ground-electronic state by emitting a photon at 193.09 nm. Suppose one wanted to take another approach, where C is heated until 5% of the atoms occupy the electronically excited state. Considering only the lowest-energy ground state and the electronically excited state, what temperature is required to achieve this excited-state population?