Match the statement of set of orbitals given in List-I with orbitals…

The correct answer is Option (2) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

List-I Statements	List-II Orbitals and energy separation
(A) $t_{2g}$ set of orbitals in octahedral crystal field and energy separation from barycentre	(IV) $d_{xy},y_{xz}, d_{yz}$ and $2/5\,Δ_0$
(B) $e_g$ set of orbitals in octahedral crystal field and energy separation from barycentre	(III) ${d_x}^2-y^2, {d_z}^2$ and $3/5\,Δ_0$
(C) $t_2$ set of orbitals in tetrahedral crystal field and energy separation from barycentre	(II) $d_{xy},y_{xz}, d_{yz}$ and $2/5\,Δ_t$
(D) $e$ set of orbitals in tetrahedral crystal field and energy separation from barycentre	(I) ${d_x}^2-y^2, {d_z}^2$ and $3/5\,Δ_t$

(A) $t_{2g}$ set in octahedral crystal field

The $t_{2g}$ orbitals are:

• $d_{xy}, d_{yz}, d_{zx}$

In an octahedral field, these lie below the barycentre by $2/5 \Delta_o$.

So it matches with

(IV) $d_{xy}, d_{yz}, d_{zx}$ and $2/5 \Delta_o$

(B) $e_g$ set in octahedral crystal field

The $e_g$ orbitals are:

• $d_{x^2-y^2}, d_{z^2}$

These lie above the barycentre by $3/5 \Delta_o$.

So it matches with

(III) $d_{x^2-y^2}, d_{z^2}$ and $3/5 \Delta_o$

(C) $t_2$ set in tetrahedral crystal field

The $t_2$ orbitals are:

• $d_{xy}, d_{yz}, d_{zx}$

These lie above the barycentre by $2/5 \, \Delta_t$.

So it matches with

(II) $d_{xy}, d_{yz}, d_{zx}$ and $2/5 \, \Delta_t$

(D) $e$ set in tetrahedral crystal field

The $e$ orbitals are:

• $d_{x^2-y^2}, d_{z^2}$

These lie below the barycentre by $3/5 \, \Delta_t$.

So it matches with

(I) $d_{x^2-y^2}, d_{z^2}$ and $3/5 \, \Delta_t$