1. Find the electronic configuration of neutral Gd

Gadolinium has atomic number $Z=64$.

Its ground-state electronic configuration is:

$[Xe]4f^7 5d^1 6s^2$

2. Form $Gd^{3+}$

To form $Gd^{3+}$, remove three electrons from the outermost orbitals first:

• first from $6s^2$
• then from $5d^1$

So,

$Gd^{3+} = [Xe]4f^7$

Thus, the correct configuration is $[Xe]4f^7$.

3. Calculate the spin-only magnetic moment

For $4f^7$, there are $7$ unpaired electrons.

Spin-only magnetic moment is given by:

$\mu = \sqrt{n(n+2)}\ \text{BM}$

where $n$ is the number of unpaired electrons.

Here, $n=7$:

$\mu = \sqrt{7(7+2)} = \sqrt{63}$

$\mu \approx 7.94\ \text{BM}$

So the magnetic moment is approximately:

$7.9\ \text{BM}$

4. Check options

• A: $[Xe]5f_7$ and $8.9$ ❌
• B: $[Xe]4f_7$ and $7.9$ ✅
• C: $[Xe]5f_7$ and $7.9$ ❌
• D: $[Xe]4f_7$ and $8.9$ ❌

Hence, the correct option is B.