The first ionization enthalpies of $$Be$$, $$B$$, $$N$$ and $$O$$ follow the order

First Ionization Energy Values:

$$\mathrm{Be = 899\ kJ\ mol^{-1}}$$

$$\mathrm{B = 801\ kJ\ mol^{-1}}$$

$$\mathrm{N = 1402\ kJ\ mol^{-1}}$$

$$\mathrm{O = 1314\ kJ\ mol^{-1}}$$

Generally, ionization energy increases across a period due to increasing effective nuclear charge.

However, exceptions occur because completely filled and half-filled subshells possess extra stability.

1. Beryllium vs Boron

Electronic configurations:

$$\mathrm{Be : 1s^2\ 2s^2}$$

$$\mathrm{B : 1s^2\ 2s^2\ 2p^1}$$

Beryllium has a completely filled $$\mathrm{2s}$$ subshell, which is highly stable.

In boron, the outermost electron enters the higher-energy $$\mathrm{2p}$$ orbital.

It is easier to remove the single $$\mathrm{2p}$$ electron from boron than to disturb the stable filled $$\mathrm{2s}$$ subshell of beryllium.

Therefore:

$$\mathrm{IE(Be) > IE(B)}$$

2. Nitrogen vs Oxygen

Electronic configurations:

$$\mathrm{N : 1s^2\ 2s^2\ 2p^3}$$

$$\mathrm{O : 1s^2\ 2s^2\ 2p^4}$$

Nitrogen has an exactly half-filled $$\mathrm{2p}$$ subshell, giving extra stability due to symmetry and exchange energy.

In oxygen, one $$\mathrm{2p}$$ orbital contains paired electrons, producing inter-electronic repulsion.

Hence, it is easier to remove one electron from oxygen than to break the stable half-filled configuration of nitrogen.

Therefore:

$$\mathrm{IE(N) > IE(O)}$$