JEE Main · 2025 · 23 Jan 2025 · Shift 1 · d and f Block Elements

The spin-only magnetic moment is $\mu =\sqrt{n(n+2)}$ BM, where $n$ is the number of unpaired electrons.

For $\mu =3.95\mathrm{BM}$, testing $n=3$ gives $\sqrt{3\times 5}=\sqrt{15}=3.87\mathrm{BM}$, the closest match, so there are 3 unpaired electrons.

$\mathrm{C}{\mathrm{o}}^{2+}$ has the configuration $[\mathrm{Ar}]3d^7$. In a weak-field, high-spin octahedral environment the seven d-electrons fill $t_{2g}$ before any pairing forces electrons into $e_g$: the arrangement $t_{2g}^5{e}_g^2$ places one paired and three unpaired electrons in $t_{2g}$ and two unpaired electrons in $e_g$, a total of 3 unpaired electrons — consistent with the observed magnetic moment.

The configuration is $t_{2g}^5{e}_g^2$.