Meaning of strongest oxidizing agent

An oxidizing agent is a species which gets reduced easily.

So among the given ions, the strongest oxidizing agent will be the one which has the greatest tendency to gain electron and convert to a more stable lower oxidation state.

Check each ion in terms of likely reduction

We examine the possible reduction of each ion:

• $\mathrm{Lu}^{3+} + e^- \to \mathrm{Lu}^{2+}$
• $\mathrm{Eu}^{2+} + 2e^- \to \mathrm{Eu}$ or $\mathrm{Eu}^{2+} + e^- \to \mathrm{Eu}^+$ (not favorable in lanthanides)
• $\mathrm{Tb}^{4+} + e^- \to \mathrm{Tb}^{3+}$
• $\mathrm{Ce}^{3+} + e^- \to \mathrm{Ce}^{2+}$

Use stability of lanthanide oxidation states

Important stable configurations in lanthanides are associated with:

• empty $f$ shell
• half-filled $f^7$
• filled $f^{14}$

Now consider the ions:

(A) $\mathrm{Lu}^{3+}$

Lutetium: $[Xe]4f^{14}5d^16s^2$

$\mathrm{Lu}^{3+} = [Xe]4f^{14}$, which is very stable due to completely filled $4f$ shell.

Hence $\mathrm{Lu}^{3+}$ does not tend to get reduced further easily. So it is not a strong oxidizing agent.

(B) $\mathrm{Eu}^{2+}$

Europium: $[Xe]4f^76s^2$

$\mathrm{Eu}^{2+} = [Xe]4f^7$, which is very stable due to half-filled $4f$ shell.

Therefore $\mathrm{Eu}^{2+}$ resists reduction and is not a strong oxidizing agent.

(C) $\mathrm{Tb}^{4+}$

Terbium: in lanthanides, $\mathrm{Tb}^{3+}$ is much more common and stable than $\mathrm{Tb}^{4+}$.

Reduction: $\mathrm{Tb}^{4+} + e^- \to \mathrm{Tb}^{3+}$

This reduction is favorable because $\mathrm{Tb}^{4+}$ is a relatively less stable higher oxidation state, while $\mathrm{Tb}^{3+}$ is the common stable lanthanide state.

Therefore $\mathrm{Tb}^{4+}$ has a strong tendency to accept an electron, so it acts as a strong oxidizing agent.

(D) $\mathrm{Ce}^{3+}$

Cerium commonly shows both $+3$ and $+4$ oxidation states, but $\mathrm{Ce}^{3+}$ getting reduced to $\mathrm{Ce}^{2+}$ is not favorable. The $+2$ state is not common for Ce.

Hence $\mathrm{Ce}^{3+}$ is not a strong oxidizing agent.

Conclusion

Among the given ions, $\mathrm{Tb}^{4+}$ most readily gets reduced to the stable $\mathrm{Tb}^{3+}$ state, so it is the strongest oxidizing agent.

Answer

$\boxed{\mathrm{Tb}^{4+}}$

So the correct option is C.