Question

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

• A. $\left[\mathrm{Xe}\right]5{\mathrm{f}}^7\mathrm{and}7.9$
• B. $\left[\mathrm{Xe}\right]4{\mathrm{f}}^7\mathrm{and}7.9$
• C. $\left[\mathrm{Xe}\right]5{\mathrm{f}}^7\mathrm{and}8.9$
• D. $\left[\mathrm{Xe}\right]4{\mathrm{f}}^7\mathrm{and}8.9$

Answer 1

The correct option is B

$\left[\mathrm{Xe}\right]4{\mathrm{f}}^7\mathrm{and}7.9$

The correct option is (B):

Explanation for the correct answer:

Electronic configuration:-

1. It is basically the systematic arrangement of the electrons into the orbitals according to the energy levels.
2. Lanthanide series basically consist of Gadolinium and the general electronic configuration here for the lanthanides would be $\left[\mathrm{Xe}\right]4{\mathrm{f}}^{1-14}5{\mathrm{d}}^{0-1}6{\mathrm{s}}^2$ with the minor exceptions in it.
3. Lanthanides basically follow the Aufbau principle that means a maximum of two electrons can be put into the orbitals of the increasing orbital energy.
4. Actually the portion of the electronic configuration that must be equivalent to the noble gas of the preceding period must be depicted by that noble gas symbol (As such fully filled $5{\mathrm{p}}^6$ electronic configuration can be depicted as the$\left[\mathrm{Xe}\right]$ having the atomic number as 54).
5. So the 7th lanthanide element is actually Gadolinium ($\mathrm{Gd}$) having the atomic number as 64 and 7 $4\mathrm{f}$ electrons, so therefore the electronic configuration would be .$\left[\mathrm{Xe}\right]4{\mathrm{f}}^{7}5{\mathrm{d}}^{1}6{\mathrm{s}}^2$

Spin-only magnetic moment:-

1. So basically when an electron moves freely it will generate a magnetic field and this magnetic field is generated by the motion of the electrons and further which is known as magnetic moment.
2. So when the electron will rotate on its own axis by generating a magnetic field it would be known as spin-only magnetic moment.
3. Spin-only magnetic moment : $\mathrm{\mu }=$$\sqrt{\mathrm{n}(\mathrm{n}+2)}w$ where (n= number of unpaired electrons).
4. Hence, as the number of unpaired electrons are 7 so, $\sqrt{7(7+2)}=\sqrt{63}$ $=7.9\mathrm{BM}$.

Therefore, the correct answer is (B):-