A specific aqueous Lanthanide ion () situated deep within the block possesses an exactly half-filled — d and f Block Elements Chemistry Question
Question
A specific aqueous Lanthanide ion ($Ln^{3+}$) situated deep within the $4f$ block possesses an exactly half-filled, spherically symmetrical $f$ -subshell ($4f^7$), granting it massive thermodynamic stability and a maximum possible spin-only magnetic moment. What is the exact total number of unpaired electrons residing within the valence shell of this specific $Ln^{3+}$ ion?
💡 Solution & Explanation
The $f$ -subshell contains exactly $7$ degenerate orbitals. To achieve an exactly half-filled configuration (the $4f^7$ state), Hund's Rule of Maximum Multiplicity dictates that every single one of the $7$ orbitals must be singly occupied with electrons of parallel spin before any pairing can structurally occur. Thus, the $4f^7$ configuration intrinsically possesses exactly $7$ unpaired electrons (This corresponds specifically to the Gadolinium ion, $Gd^{3+}$).