= Solution
{c}
The <Curie constant> measures the squared <magnetic moment> averaged over all orientations of the $J$ multiplet, giving
$$
\boxed{m_{\rm eff}=|\widetilde g|\sqrt{J(J+1)},\qquad
\mu_{\rm eff}=|\widetilde g|\mu_B\sqrt{J(J+1)}.}
$$
For the usual positive <Landé g-factor> of the <ion> here, the absolute-value sign can be omitted. This <effective paramagnetic moment> differs from the maximum projected or <saturation magnetic moment>, $\mu_{\rm sat}=|\widetilde g|J\mu_B$.
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