And we consider the ELEMENT not the molecule, inasmuch as this is how ionization enthalpies are defined......
"Atom(g)"+Deltararr"Atom(g)"^+ + e^(-)
For Be we gots Z=4, 1s^(2)2s^(2)
For B we gots Z=5, 1s^(2)2s^(2)2p^1
The ionization of boron involves removal of a "p-electron", which has NO electron density at the nuclear core, and thus should be easier to remove than a s electron, which can lie closer to the nuclear core.
For N we gots Z=7, 1s^(2)2s^(2)2p^3
For O we gots Z=8, 1s^(2)2s^(2)2p^4
For nitrogen, we have a half-filled "p-shell" which is energetically stabilized with respect to "Hund's rule" of maximum multiplicity. For the oxygen atom, even tho it has Z=8, the electronic configuration of the cation is SLIGHTLY stabilized by Hund's rule. None of this treatment is any substitute for reading the relevant section of your text.
