Pair of lanthanide ions which show significant deviation between the experimental and calculated magnetic moments, considering contribution from the ground state only
(a)Gd and Lu
(b)Sm and Th
(c)Eu and Tb
(d)Sm and Eu
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
The configurations and magnetic moments are:
$M^{3+}$
$f^{n}$
$\mu_{\text{observed}}$
$\mu_{\text{calculated}}$
$\mathrm{Gd^{3+}}$
$4f^{7}$
7.97
7.94
$\mathrm{Lu^{3+}}$
$4f^{14}$
0
0
$\mathrm{Tb^{3+}}$
$4f^{8}$
9.8
9.7
$\mathrm{Sm^{3+}}$
$4f^{5}$
1.64
0.85
$\mathrm{Eu^{3+}}$
$4f^{6}$
3.36
0
$\mathrm{Gd^{3+}}$ ($f^7$) and $\mathrm{Lu^{3+}}$ ($f^{14}$) follow the spin-only formula $\mu = \sqrt{n(n+2)}$. While for the remaining, $\mu_{\text{eff}} = g\sqrt{J(J+1)}$ is valid.