Ionization energy and wavelengths?

Question

Ionization energy is defined as the minimum energy required to remove an electron from the ground state (n0) to infinity (n∞). Determine the wavelength of radiation required to ionize the hydrogen electron from the n = 2 energy level. Calculate the energy (Joules) associated with this photon. (1 cm-1 = 1.986 x 10-23 J)

Answer 1

Without considering the fine structure, the electron energy level of the hydrogen atom can be written as:
En = -2.179×10^-18 J/ n^2
Take n = 2, we have E2 = -5.448×10^-19 J
Wavelength and this energy is related by Plank Constant h:
E = hc/L
Hence L = hc/E = (6.626x10^-34 Js)*(2.998x10^17nm/s) /(5.448×10^-19 J) = 365nm