For the second-period elements, the correct increasing order of first ionisation enthalpy is:

Generally, ionization enthalpy increases across a period from left to right due to increased nuclear charge and smaller atomic radius. However, there are two anomalies in the second period:

1. Boron (B) < Beryllium (Be): Beryllium has a stable full-filled electronic configuration ($1s^2 2s^2$), while Boron ($1s^2 2s^2 2p^1$) has a single electron in the 2p orbital. It is easier to remove the 2p electron from Boron because it is less penetrating towards the nucleus and more shielded by the inner core than the 2s electrons of Beryllium .
2. Oxygen (O) < Nitrogen (N): Nitrogen ($1s^2 2s^2 2p^3$) has a stable half-filled p-orbital configuration. In Oxygen ($1s^2 2s^2 2p^4$), two of the four 2p electrons occupy the same orbital, resulting in increased electron-electron repulsion. Consequently, it is easier to remove an electron from Oxygen than from the stable Nitrogen configuration .

Thus, the correct order is Li < B < Be < C < O < N < F < Ne.