The pair of lanthanoid ions which are diamagnetic is

Solution & Explanation

\textbf{Answer:} (d) $\mathrm{Ce}{}^{4+}$ and $\mathrm{Yb}{}^{2+}$ \textbf{Solution:} A species is diamagnetic only when it has zero unpaired electrons. $\mathrm{Ce}{}^{4+}$ has the configuration $[\mathrm{Xe}]4\mathrm{f}{}^0$ (empty 4f), and $\mathrm{Yb}{}^{2+}$ has $[\mathrm{Xe}]4\mathrm{f}{}^{14}$ (completely filled 4f). Both have all electrons paired, so the pair is diamagnetic. The other ions ($\mathrm{Ce}{}^{3+}$ 4f^1, $\mathrm{Eu}{}^{2+}$/$\mathrm{Gd}{}^{3+}$ 4f^7, $\mathrm{Eu}{}^{3+}$ 4f^6, $\mathrm{Pm}{}^{3+}$ 4f^4, $\mathrm{Sm}{}^{3+}$ 4f^5) all contain unpaired f-electrons and are paramagnetic.