# The correct electronic configuration and spin-only magnetic moment

Question:

The correct electronic configuration and spin-only magnetic moment $(\mathrm{BM})$ of $\mathrm{Gd}^{3+}(\mathrm{Z}=64)$, respectively, are:

1. $[\mathrm{Xe}] 4 f^{7}$ and $8.9$

2. $[\mathrm{Xe}] 4 f^{7}$ and $7.9$

3. $[\mathrm{Xe}] 5 f^{7}$ and $8.9$

4. $[\mathrm{Xe}] 5 f^{7}$ and $7.9$

Correct Option: , 2

Solution:

Electronic configuration of

${ }_{64} \mathrm{Gd}=[\mathrm{Xe}] 4 f^{7} 5 d^{1} 6 s^{2}$

${ }_{64} \mathrm{Gd}^{3+}=[\mathrm{Xe}] 4 f^{7}$

No. of unpaired electron $=7$

$\mu=\sqrt{n(n+2)} \mathrm{BM}=\sqrt{63}=7.93 \mathrm{BM}$