Determining Gd³⁺ Electronic Configuration and Magnetic Moment

Electronic Configuration of Gadolinium (Gd)

Gadolinium (Gd) has atomic number 64. Its ground state electronic configuration is typically written based on the filling order, preceded by the noble gas Xenon (Xe, Z=54). The configuration is: $ Gd: [Xe] 4f^7 5d^1 6s^2 $ Note: Due to the stability of the half-filled $4f$ subshell, this configuration is commonly cited, although variations exist due to close energy levels.

Electronic Configuration of Gd³⁺ Ion

To find the configuration of the $Gd^{3+}$ ion, we remove three electrons from the neutral Gadolinium atom, starting with the outermost shells (highest principal quantum number 'n', then highest angular momentum 'l').

• Electrons are removed from the $6s$ orbital first (2 electrons).
• Then, one electron is removed from the $5d$ orbital.

Therefore, the electronic configuration of $Gd^{3+}$ is: $ Gd^{3+}: [Xe] 4f^7 $ This configuration features a half-filled $4f$ subshell ($4f^7$), which is particularly stable.

Spin-Only Magnetic Moment Calculation

The spin-only magnetic moment ($\mu_s$) is calculated using the number of unpaired electrons ($n$).

• In the $4f^7$ configuration, all 7 electrons are unpaired according to Hund's rule, occupying separate $f$ orbitals with parallel spins.
• Number of unpaired electrons, $n = 7$.

The formula for the spin-only magnetic moment is: $ \mu_s = \sqrt{n(n+2)} \text{ BM} $ Substituting $n=7$: $ \mu_s = \sqrt{7(7+2)} = \sqrt{7 \times 9} = \sqrt{63} $ $ \mu_s \approx 7.94 \text{ BM} $ This value is approximately 7.9 BM.

Conclusion

The correct electronic configuration for $Gd^{3+}$ is $[Xe]4f^7$, and its spin-only magnetic moment is approximately 7.9 BM. This matches Option 1.