Long before the advent of quantum mechanics, physicists had developed an empirical formula to predict the wavelengths of the emission lines of hydrogen. Specifically, for an electron transition from the mth energy level down to the nth level (m > n), the wavelength of the emitted photon is given by 1/λ (10,973,731.57)(1/n² = 1/m²) m^-1.

Use this equation to confirm that the first member of the Balmer series has a wavelength of 656.3 nm. What is the wavelength of a photon emitted by hydrogen during a transition from the ninth excited state (m = 10) to the second excited state (n = 3)? In what part of the EM spectrum does this spectral line reside? What wavelength photon would be required to ionize a hydrogen atom from the n = 8 level?