energy difference?

Question

Calculate the energy difference (E) for the photon absorbed when a hydrogen atom undergoes a transition from n = 1 to n = 4 for 1 mol H atoms.

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
Thus for n = 4: E4 = -1.362x10^-19 J
For n = 1: E1 = -2.179×10^-18 J
Hence the energy of the photon absorbed is:
E4 - E1 = 2.043x10^-18 J
For 1 mole or 6.022e23 such photons, the total energy is:
2.043x10^-18 J x 6.022e23 = 1.23x10^3 kJ.