To identify the strong reducing agent, we examine the definition of reducing agents. A reducing agent donates electrons to another substance, undergoing oxidation itself. Its effectiveness correlates with its electron-donating propensity.
Analysis of each ion:
\(\text{Lu}^{3+}\): Lutetium commonly exists as the +3 ion. It does not readily lose electrons to reach a lower oxidation state, thus it is not a strong reducing agent.
\(\text{Gd}^{3+}\): Gadolinium also exhibits stability in the +3 oxidation state. Similar to Lutetium, it is disinclined to be reduced to a lower oxidation state, meaning it is not a strong reducing agent.
\(\text{Eu}^{2+}\): The +2 oxidation state of Europium is less stable than its +3 state. This makes \(\text{Eu}^{2+}\) more likely to donate electrons to achieve the stable +3 state, qualifying it as a strong reducing agent.
\(\text{Ce}^{4+}\): Cerium in the +4 oxidation state functions as a strong oxidizing agent because it readily accepts electrons to return to its more stable +3 state. Consequently, it acts as an oxidizing agent, not a reducing agent.
Based on this analysis, \(\text{Eu}^{2+}\) is identified as the strong reducing agent due to its inclination to donate an electron and attain the stable +3 oxidation state.
Therefore, the correct answer is \(\text{Eu}^{2+}\).
