Step 1 : Understanding the Question:
This question covers periodic properties, specifically focusing on the energetics of electron gain processes. We need to identify which of the given processes corresponds to a positive electron affinity, which represents an endothermic process where energy is absorbed.
Step 2 : Key Formulas and Approach:
The first electron affinity is the energy change when an electron is added to a neutral gaseous atom. This process is generally exothermic (negative change in enthalpy):
\[ \text{X}(g) + e^- \rightarrow \text{X}^-(g) \quad (\Delta H<0) \]
When an additional electron is added to a negatively charged ion, strong electrostatic repulsion occurs between the incoming electron and the negatively charged ion. Work must be done to overcome this repulsion, making the process endothermic:
\[ \text{X}^-(g) + e^- \rightarrow \text{X}^{2-}(g) \quad (\Delta H>0) \]
Step 3 : Detailed Explanation:
Let us analyze the formation of oxide ions. Adding the first electron to a neutral oxygen atom releases energy because the attractive nuclear force dominates:
\[ \text{O}(g) + e^- \rightarrow \text{O}^-(g) \quad (\Delta H<0) \]
To form the divalent oxide ion (\( \text{O}^{2-} \)), a second electron must be added to the monovalent oxygen anion (\( \text{O}^- \)):
\[ \text{O}^-(g) + e^- \rightarrow \text{O}^{2-}(g) \]
The incoming electron experiences significant electrostatic repulsion from the existing electron cloud of the \( \text{O}^- \) anion.
External energy must be supplied to force the electron into the anion against this repulsive force, making the process endothermic. Therefore, the electron affinity is positive.
The other processes listed in options (C) and (D) describe the removal of electrons from oxygen, which represents ionization energy rather than electron affinity.
Step 4 : Final Answer:
The electron affinity is positive for the process \( \text{O}^- \rightarrow \text{O}^{2-} \), which corresponds to option (B).