Which of the following electronic configuration would be associated with the highest magnetic moment?

The magnetic moment is given by $$\mu = \sqrt{n(n+2)}$$ BM, where $$n$$ is the number of unpaired electrons. Higher $$n$$ gives higher magnetic moment.

Counting unpaired electrons for each configuration:

- $$[Ar] \; 3d^7$$: $$\uparrow\downarrow \; \uparrow\downarrow \; \uparrow \; \uparrow \; \uparrow$$ = 3 unpaired

- $$[Ar] \; 3d^8$$: $$\uparrow\downarrow \; \uparrow\downarrow \; \uparrow\downarrow \; \uparrow \; \uparrow$$ = 2 unpaired

- $$[Ar] \; 3d^3$$: $$\uparrow \; \uparrow \; \uparrow \; \_ \; \_$$ = 3 unpaired

- $$[Ar] \; 3d^6$$: $$\uparrow\downarrow \; \uparrow \; \uparrow \; \uparrow \; \uparrow$$ = 4 unpaired

$$[Ar] \; 3d^6$$ has the maximum number of unpaired electrons (4), giving the highest magnetic moment:

$$\mu = \sqrt{4(4+2)} = \sqrt{24} = 2\sqrt{6}$$ BM

The answer corresponds to Option (4).