The correct order of second ionization potential of \(C, N, O\) and \(F\) is

\(O > F > N > C\)

The correct answer is option 3. \(O > F > N > C\).

Let us re-evaluate the second ionization potential (IP2) order for \(C, N, O, F\) to see why \(O > F > N > C\) might be the correct order.

Second Ionization Potential: The energy required to remove an electron from a singly charged cation (\(X^+\)).

Effective Nuclear Charge \((Z_{eff})\): The net positive charge experienced by an electron in a multi-electron atom. It generally increases across a period.

Electron Configuration: Atoms with stable or half-filled configurations tend to have higher ionization potentials.

Detailed Analysis

Carbon (C):

Configuration: \(1s^2 2s^2 2p^2\)

First Ionization: \(C \rightarrow C^+ + e^-\) gives \(C^+\) with \(1s^2 2s^2 2p^1\)

Second Ionization: \(C^+ \rightarrow C^{2+} + e^-\) removes an electron from the \(2p\) orbital, resulting in \(1s^2 2s^2\).

Second Ionization Potential: Relatively lower because removing a second electron still leaves a stable \(2s^2\) core.

Nitrogen (N):

Configuration: \(1s^2 2s^2 2p^3\)

First Ionization: \(N \rightarrow N^+ + e^-\) gives \(N^+\) with \(1s^2 2s^2 2p^2\)

Second Ionization: \(N^+ \rightarrow N^{2+} + e^-\) removes an electron from a half-filled stable \(2p\) orbital.

Second Ionization Potential: Higher than carbon because the half-filled \(2p\) subshell is relatively stable.

Oxygen (O):

Configuration: \(1s^2 2s^2 2p^4\)

First Ionization: \(O \rightarrow O^+ + e^-\) gives \(O^+\) with \(1s^2 2s^2 2p^3\)

Second Ionization: \(O^+ \rightarrow O^{2+} + e^-\) removes an electron from a half-filled stable \(2p\) orbital.

Second Ionization Potential: Higher than nitrogen because it ends up with a half-filled \(2p\) subshell, making it very stable.

Fluorine (F):

Configuration: \(1s^2 2s^2 2p^5\)

First Ionization: \(F \rightarrow F^+ + e^-\) gives \(F^+\) with \(1s^2 2s^2 2p^4\)

Second Ionization: \(F^+ \rightarrow F^{2+} + e^-\) removes an electron from \(2p^4\), resulting in \(2p^3\).

Second Ionization Potential: Higher than nitrogen but lower than oxygen because it moves from a less stable to a stable half-filled \(2p\) configuration.

Given the analysis:

Oxygen: Removing the second electron results in a stable half-filled \(2p^3\) configuration, which is energetically favorable.

Fluorine: Although it has a high effective nuclear charge, the second ionization leads to a half-filled \(2p^3\) configuration, which is less stable compared to oxygen losing to \(2p^3\) state but still higher than nitrogen.

Nitrogen: Removing the second electron disrupts the stable half-filled \(2p^3\) configuration.

Carbon: The second ionization leads to \(1s^2 2s^2\) configuration, which is the most stable but starts from a lower \(Z_{eff}\).

Thus, the second ionization potential order is \(O > F > N > C \).

The correct answer is \(O > F > N > C\).