Step 1: Write electronic configurations after first ionisation.
\[
O \rightarrow O^+ (2p^3)
\]
\[
N \rightarrow N^+ (2p^2)
\]
\[
C \rightarrow C^+ (2p^1)
\]
\[
F \rightarrow F^+ (2p^4)
\] Step 2: Analyze stability of configurations.
Half-filled $2p^3$ configuration is most stable.
Completely filled and half-filled orbitals show extra stability. Step 3: Compare second ionisation energies.
Removing an electron from stable $2p^3$ requires more energy than from $2p^4$.
Thus, IE increases from left to right but irregular due to electronic stability. Step 4: Final order.
\[
O<C<N<F
\]