1. Magnetic moment depends on the number of unpaired electrons

For transition metal ions/atoms (spin-only approximation), the magnetic moment is:

where $n$ is the number of unpaired electrons.

So, the configuration with the maximum number of unpaired electrons will have the highest magnetic moment.

2. Find the number of unpaired electrons in each configuration

We fill the five $d$ orbitals according to Hund's rule.

Option A: $[\mathrm{Ar}]3d^7$

For $d^7$:

• First 5 electrons occupy all 5 orbitals singly.
• Next 2 electrons pair up in two orbitals.

So unpaired electrons $= 3$.

Option B: $[\mathrm{Ar}]3d^8$

For $d^8$:

• First 5 electrons singly occupy 5 orbitals.
• Next 3 electrons pair up in three orbitals.

So unpaired electrons $= 2$.

Option C: $[\mathrm{Ar}]3d^3$

For $d^3$:

• Three electrons occupy three different $d$ orbitals singly.

So unpaired electrons $= 3$.

Option D: $[\mathrm{Ar}]3d^6$

For $d^6$:

• First 5 electrons singly occupy all 5 orbitals.
• The 6th electron pairs in one orbital.

So unpaired electrons $= 4$.

3. Compare magnetic moments

• $3d^7 \rightarrow n=3 \rightarrow \mu=\sqrt{15}$
• $3d^8 \rightarrow n=2 \rightarrow \mu=\sqrt{8}$
• $3d^3 \rightarrow n=3 \rightarrow \mu=\sqrt{15}$
• $3d^6 \rightarrow n=4 \rightarrow \mu=\sqrt{24}$

Since

the highest magnetic moment is for:

4. Final answer

The correct option is D.