Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level 𝑛=3 to the level 𝑛=1.

Answer 1

The difference in energy between hydrogen levels 3 and 1 is -1.51 -(-13.61) = 12.10 ev * (1.602 x 10^-19 J / 1 ev) = 1.938 x 10^-18 J. With photon energy E = hF = hc/λ, wavelength λ = hc/E = (6.626 x 10^-34 Js)*(2.998 x 10⁸ m/s) / (1.938 x 10^-18 J) = 1.025 x 10^-7 m = 102.5 nm.