Match the electronic configurations in List-I with appropriate metal complex ions in List-II and choose the correct option.

List-I	List-II
(P) $t_{2g}^6{e}_g^0$	(1) ${\left[\mathrm{Fe}\right(H_{2}O\left)6\right]}^{\mathrm{2+}}$
(Q) $t_{2g}^3{e}_g^2$	(2) ${\left[\mathrm{Mn}\right(H_{2}O\left)6\right]}^{\mathrm{2+}}$
(R) $e_g^2{t}_{2g}^3$	(3) ${\left[\mathrm{Co}\right({\mathrm{NH}}_3\left)6\right]}^{\mathrm{3+}}$
(S) $t_{2g}^4{e}_g^2$	(4) ${\left[\mathrm{FeCl}4\right]}^{-}$
	(5) ${\left[\mathrm{CoCl}4\right]}^{\mathrm{2-}}$

The correct option is P → 3; Q → 2; R → 4; S → 1.

To match each electronic configuration with its corresponding metal complex ion, we determine the oxidation state, d-electron count, geometry, and crystal field splitting (high spin vs. low spin) for each complex in List-II.

1. Analysis of (3)

${\left[\mathrm{Co}\right({\mathrm{NH}}_3\left)6\right]}^{3+}$

• The oxidation state of cobalt is +3 (Co³⁺).
• The electronic configuration of Co³⁺ is 3d⁶.
• Ammonia (NH₃) acts as a strong field ligand for Co³⁺ in an octahedral geometry, causing strong pairing of electrons (low spin complex).
• Therefore, all 6 electrons pair up in the lower-energy t_2g orbitals.

The electronic configuration is:

$t_{2g}^6{e}_g^0$

Hence, P → 3.

2. Analysis of (2)

${\left[\mathrm{Mn}\right(H_{2}O\left)6\right]}^{2+}$

• The oxidation state of manganese is +2 (Mn²⁺).
• The electronic configuration of Mn²⁺ is 3d⁵.
• Water (H₂O) is a weak field ligand, forming an octahedral high-spin complex.
• The 5 electrons occupy the orbitals singly according to Hund's rule.

The electronic configuration is:

$t_{2g}^3{e}_g^2$

Hence, Q → 2.

3. Analysis of (4)

${\left[\mathrm{FeCl}4\right]}^{-}$

• The oxidation state of iron is +3 (Fe³⁺).
• The electronic configuration of Fe³⁺ is 3d⁵.
• This complex is tetrahedral. In tetrahedral field splitting, lower-energy orbitals are e_g (or e) and higher-energy orbitals are t_2g (or t₂).
• Tetrahedral complexes are high-spin due to small crystal field splitting energy (Δ_t).

The electronic configuration is:

$e_g^2{t}_{2g}^3$

Hence, R → 4.

4. Analysis of (1)

${\left[\mathrm{Fe}\right(H_{2}O\left)6\right]}^{2+}$

• The oxidation state of iron is +2 (Fe²⁺).
• The electronic configuration of Fe²⁺ is 3d⁶.
• Water (H₂O) is a weak field ligand, forming an octahedral high-spin complex.
• Five electrons fill all 5 d-orbitals singly, and the 6th electron pairs up in one of the t_2g orbitals.

The electronic configuration is:

$t_{2g}^4{e}_g^2$

Hence, S → 1.

Combining all matching pairs, we get:

P → 3; Q → 2; R → 4; S → 1