1) [Fe(CN)$$_6]^{4-}$$
Here, Fe is present as Fe$$^{2+}$$
Electronic configuration of Fe$$^{2+}$$ is [Ar]3d$$^6 4s^0$$
Since CN$$^-$$ is a strong field ligand so when it approaches Fe$$^{2+}$$ it pair up the e$$^-$$ s and result in the formation of low spin complex.
No. of unpaired e$$^-$$ s =0
So, magnetic moment for n unpaired e$$^-$$s
= $$\sqrt{n(n+2)} BM$$
=0
2) [Fe(CN)$$_6]^{3-}$$
Here, Fe is present as Fe$$^{3+}$$
Electronic configuration of Fe$$^{3+}$$ is [Ar]3d$$^5 4s^0$$
Since , CN$$^-$$ is a strong field ligand so when it approaches Fe$$^{2+}$$ it pair up the e$$^-$$s so,
No. of unpaired e$$^-$$ s =1
So, magnetic moment for n unpaired e$$^-$$s
= $$\sqrt{1\times (1+2)} $$
=$$\sqrt{3} $$ BM.
3) [Cr(NH$$_3)_6]^{3+}$$
Electronic configuration of Cr$$^{3+}$$ is [Ar]3d$$^3 4s^0$$
Since , NH$$_3$$ is a strong field ligand so it pairs up the electrons when it approaches when it approaches Cr$$^{3+}$$
No. of unpaired e$$^-$$ s =3
So, magnetic moment = $$\sqrt{3(3+2)} $$
=$$\sqrt{1\times 5} $$
=$$\sqrt{15}$$ BM
4)[Ni(H$$_2O)_4]^{2+}$$
Electronic configuration of Ni$$^{2+}$$ is [Ar]3d$$^8 4s^0$$
Since , H$$_2$$O is a weak field ligand. it does not pair up the e$$^-$$s and forms outer orbital complex.
No. of unpaired e$$^-$$ s =2
So, magnetic moment =$$\sqrt{2(2+2)} $$
=$$\sqrt{8}$$ BM
But because of orbital effect it will be little lesser. So, correct order is iii)>iv)> ii)> i)