The correct order of the number of unpaired electrons in the given complexes is
(A) $$[Fe(CN)_6]^{3-}$$
(B) $$FeF_6^{3-}$$
(C) $$CoF_6^{3-}$$
(D) $$[Cr(oxalate)_3]^{3-}$$
(E) $$Ni(CO)_4$$
Choose the correct answer from the options given below:

We need to determine the number of unpaired electrons in each complex and arrange them in increasing order.

The number of unpaired electrons depends on the metal's oxidation state, its d-electron count, and whether the ligand creates a strong field (low spin) or weak field (high spin) splitting.

(A) $$[Fe(CN)_6]^{3-}$$:

Iron is in the +3 oxidation state: $$Fe^{3+}$$ has the configuration $$[Ar] 3d^5$$.

$$CN^{-}$$ is a strong field ligand, so we get a low spin octahedral complex.

Low spin $$d^5$$: $$t_{2g}^5 \, e_g^0$$ → 1 unpaired electron.

(B) $$[FeF_6]^{3-}$$:

Iron is in the +3 oxidation state: $$Fe^{3+}$$ has the configuration $$[Ar] 3d^5$$.

$$F^{-}$$ is a weak field ligand, so we get a high spin octahedral complex.

High spin $$d^5$$: $$t_{2g}^3 \, e_g^2$$ → 5 unpaired electrons.

(C) $$[CoF_6]^{3-}$$:

Cobalt is in the +3 oxidation state: $$Co^{3+}$$ has the configuration $$[Ar] 3d^6$$.

$$F^{-}$$ is a weak field ligand, so we get a high spin octahedral complex.

High spin $$d^6$$: $$t_{2g}^4 \, e_g^2$$ → 4 unpaired electrons.

(D) $$[Cr(C_2O_4)_3]^{3-}$$:

Chromium is in the +3 oxidation state: $$Cr^{3+}$$ has the configuration $$[Ar] 3d^3$$.

For $$d^3$$ in an octahedral field, the configuration is always $$t_{2g}^3 \, e_g^0$$ (same for both strong and weak field).

$$d^3$$: $$t_{2g}^3 \, e_g^0$$ → 3 unpaired electrons.

(E) $$[Ni(CO)_4]$$:

Nickel is in the 0 oxidation state: $$Ni^{0}$$ has the configuration $$[Ar] 3d^{8} 4s^2$$.

$$CO$$ is a very strong field ligand. In the tetrahedral $$[Ni(CO)_4]$$ complex, the strong field of $$CO$$ causes all 10 electrons ($$3d^{10}$$) to pair up completely.

$$d^{10}$$ → 0 unpaired electrons.

• E: $$[Ni(CO)_4]$$ → 0 unpaired electrons
• A: $$[Fe(CN)_6]^{3-}$$ → 1 unpaired electron
• D: $$[Cr(C_2O_4)_3]^{3-}$$ → 3 unpaired electrons
• C: $$[CoF_6]^{3-}$$ → 4 unpaired electrons
• B: $$[FeF_6]^{3-}$$ → 5 unpaired electrons

$$ E(0) < A(1) < D(3) < C(4) < B(5) $$

The correct answer is Option A: $$E < A < D < C < B$$.