Which of the following presents the correct order of second ionization enthalpies of C, N, O and F?

The second ionization enthalpy (abbreviated $$IE_2$$) is the energy required for the process
$$M^{+}(g)\;\rightarrow\;M^{2+}(g)\;+\;e^{-}$$

For elements of the second period we must look at the electronic configuration of the monovalent cation $$M^{+}$$, because the stability of that ion controls how hard it is to remove the second electron.

Electron configurations

• Carbon, $$C\;(Z=6):$$ neutral $$1s^2\,2s^2\,2p^2$$
$$\Rightarrow$$ $$C^{+}: 1s^2\,2s^2\,2p^1$$ (one unpaired $$2p$$ electron)

• Nitrogen, $$N\;(Z=7):$$ neutral $$1s^2\,2s^2\,2p^3$$ (half-filled $$2p$$ subshell is extra stable)
$$\Rightarrow$$ $$N^{+}: 1s^2\,2s^2\,2p^2$$

• Oxygen, $$O\;(Z=8):$$ neutral $$1s^2\,2s^2\,2p^4$$
$$\Rightarrow$$ $$O^{+}: 1s^2\,2s^2\,2p^3$$ (again a half-filled $$2p$$ subshell, therefore very stable)

• Fluorine, $$F\;(Z=9):$$ neutral $$1s^2\,2s^2\,2p^5$$
$$\Rightarrow$$ $$F^{+}: 1s^2\,2s^2\,2p^4$$

Stability considerations for $$IE_2$$

1. Removing the second electron from $$O^{+}$$ destroys a half-filled $$2p$$ subshell ($$2p^3 \rightarrow 2p^2$$). Because half-filled configurations are especially stable, a very large amount of energy is required. Hence $$O$$ has the highest $$IE_2$$ of the four.

2. For $$F^{+}$$ the second removal changes $$2p^4 \rightarrow 2p^3$$, actually creating a half-filled subshell in $$F^{2+}$$. This is still energy-demanding but distinctly easier than for oxygen, so $$IE_2(F)$$ is lower than $$IE_2(O)$$ yet still sizeable.

3. From $$N^{+}$$ the second electron is taken from $$2p^2 \rightarrow 2p^1$$. No special stability is lost or gained, so the energy required is lower than for fluorine.

4. For $$C^{+}$$ we remove the single $$2p$$ electron ($$2p^1 \rightarrow 2p^0$$). The resulting $$C^{2+}$$ has a completely empty $$2p$$ subshell, making this removal the easiest of the set; hence $$IE_2(C)$$ is the smallest.

Order obtained

$$IE_2(O) \;>\; IE_2(F) \;>\; IE_2(N) \;>\; IE_2(C)$$

Therefore the correct option is:
Option D which is: $$O \;>\; F \;>\; N \;>\; C$$