Calculate the exact theoretical spin-only magnetic moment squared () in standard units of for an iso — d and f Block Elements Chemistry Question
Question
Calculate the exact theoretical spin-only magnetic moment squared ($\mu^2$) in standard units of $B.M.^2$ for an isolated Europium trivalent cation ($Eu^{3+}$) strictly based on its ground state electronic configuration. (Given Atomic Number of $Eu = 63$).
💡 Solution & Explanation
The neutral Europium atom ($Eu$, $Z=63$) possesses the electronic configuration $[Xe] 4f^7 6s^2$. When ionized to $Eu^{3+}$, it loses both $6s$ electrons and exactly one $4f$ electron, resulting in a $[Xe] 4f^6$ core. According to Hund's rule, these $6$ electrons occupy six separate $f$ -orbitals, yielding exactly $n=6$ unpaired electrons. The formula for spin-only magnetic moment is $\mu = \sqrt{n(n+2)}$. Substituting $n=6$ yields $\mu = \sqrt{6(6+2)} = \sqrt{48}$. Thus, $\mu^2 = 48$.