I assume we examine the processes....
F(g) + Delta_1rarrF^(+)(g) + e^- ;Delta_1=1681*kJ*mol^-1
F^+(g) + Delta_2rarrF^(2+)(g) + e^- ;Delta_2=3374.0*kJ*mol^-1
O(g) + Delta_1rarrO^(+)(g) + e^- ;Delta_1=1313.9*kJ*mol^-1
O^+(g) + Delta_2rarrO^(2+)(g) + e^- ;Delta_2=3388.3*kJ*mol^-1
We use the data from this [site.](https://en.wikipedia.org/wiki/Ionization_energies_of_the_elements_%28data_page%29)
Delta_1 is entirely straightforward. Ionization energies should INCREASE across the Period, from left to right as we face the Table, and they does. However Delta_2(O) is marginally greater than Delta_2(F). What's going on?
For fluorine's 2nd ionization we go from 1s^(2)2s^(2)2p^(4) to 1s^(2)2s^(2)2p^(3); for oxygen we go from 1s^(2)2s^(2)2p^(3) to 1s^(2)2s^(2)2p^(2). It is likely, therefore, that O^+ gains some stability from Hund's rule of maximum multiplicity (as does nitrogen in its first ionization energy); this would tend to DECREASE Delta_2. On the other hand, F^(2+) is somewhat stabilized by the "nitrogen atom-like" electronic configuration, and this stability decreases the magnitude of Delta_2.
I would be interested in the rationalization your prof provides. Would you relate it here?
