How do you calculate the Ionization energy of Hydrogen?

You are able to calculate the ionization energy of hydrogen because of a formula developed by Neils Bohr in his early quantum atom.

Besides his one postulate that limited a characteristic of the electron known as angular momentum, he used mostly classical mechanics to obtain a formula for the allowed energies of the hydrogen atom as

#E_n = -(1311 (kJ)/"mol")/n^2#

where #n# was the number of the orbit (n=1 being the orbit closest to the nucleus). n could take on only integer values. The numerator
was obtained by inserting a number of physical constants that included the mass and charge of the electron.

So, with the electron in the ground state (lowest energy), the value of #n# is 1, and the value of the energy of the atom was #-1311 (kJ)/"mol"#.

If the electron were to be removed from the atom, this corresponded to raising it past all possible values of #n#, (or to #nrarroo#). At this point, the energy of the system is zero.

To determine the ionization energy, one had only to determine the difference between these two states:

#DeltaE = 0 - (-1311) = +1311 (kJ)/"mol"#