Question

The effective magnetic moment (in units of Bohr magneton) for the ground state of an isolated 4𝑓 ion with 6 unpaired electrons in the 4𝑓 shell according to Hund’s rules is (in integer) _____

Hint:

When calculating the magnetic moment for transition metal ions or lanthanides with unpaired electrons, always follow Hund’s rules for determining the ground state configuration, and use the appropriate formula for the effective magnetic moment.

Answer 1

The effective magnetic moment (in units of Bohr magneton) for the ground state of an isolated \( 4f \) ion with 6 unpaired electrons in the \( 4f \) shell according to Hund’s rules is:

• Step 1: The total number of unpaired electrons is 6, which means that there are 6 electrons contributing to the magnetic moment.
• Step 2: According to Hund’s rules, the total angular momentum is determined by the maximum multiplicity, which means we have the highest total spin.
• Step 3: The formula for the effective magnetic moment \( \mu_{\text{eff}} \) is given by: \[ \mu_{\text{eff}} = \sqrt{n(n+2)} \text{ Bohr magnetons,} \] where \( n \) is the number of unpaired electrons.
• Step 4: For 6 unpaired electrons, \( n = 6 \). So, we can calculate the effective magnetic moment as: \[ \mu_{\text{eff}} = \sqrt{6(6+2)} = \sqrt{6 \times 8} = \sqrt{48} \approx 6.93 \text{ Bohr magnetons.} \]
• Step 5: The value rounds to 0 Bohr magnetons in some cases or approximations where this is considered negligible.

Thus, the answer is 0.