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# Which one of the following ions has zero CFSE (crystal field stabilisation energy) in octahedral field ? Options 1. Fe3+ (low spin) 2. Fe3+ (high spin) 3. Co2+ (low spin) 4. Cr+3 (high spin)

##"Fe"^(3+) ->## high spin

Right from the start, you can eliminate options **(1)** and **(3)** because those ions form a **low spin complex**.

Now, I will not go into too much detail about crystal field theory in general because I assume you're familiar with it.

So, you know that transition metal ions placed in symmetric fields have **degenerate** d-orbitals that are higher in energy than they would have been in an isolated cation.

When you place such a cation in a field with **octahedral symmetry**, the five degenerate d-orbitals will **split** into two ##e_g## orbitals, which are **higher** in energy, and three ##t_(2g)## orbitals, which are **lower** in energy.

The **crystal field stabilization energy**, or **CFSE**, ##Delta##, is defined as the **stability** gained by the ion after placing it in a crystal field.

The idea here is that electrons placed in the ##t_(2g)## orbitals will **increase** the stability of the ion because these orbitals are lower in energy than the degenerate d-orbitals.

On the other hand, electrons placed in the ##e_g## orbitals will **reduce** the stability of the ion because the orbitals are higher in energy than the degenerate d-orbitals.

A **low field complex** is characterized by the fact that the electrons found in the d-orbitals are **all** placed in the lower energy ##t_(2g)## orbitals. This means that the CFSE for such an ion **cannot** be equal to zero, since the ion is gaining stability relative to the initial energy level of the d-orbitals.

However, a **high spin complex** has the potential of having a **zero** CFSE if the increase in stability resulting from the electrons being placed in the ##t_(2g)## orbitals is **cancelled out** by the **decrease** in stability resulting from electrons being placed in the ##e_g## orbitals.

So, your two candidates are ##"Fe"^(3+)## and ##"Cr"^(3+)##, which have the following electron configurations

##"Fe"^(3+): ["Ar"] 3d^5 " "## and ##" " "Cr"^(3+): ["Ar"] 3d^3##

As you can see, the chromium(III) cation only has **three electrons** in its d-orbitals, which means that it cannot form a high-spin complex. All three electrons will thus be placed in the lower energy ##t_(2g)## orbitals.

Let's do the calculations for the iron(III) cation to make sure that its CFSE will indeed be equal to **zero**.

So, the iron(III) cation will have **three electrons** in the lower energy ##t_(2g)## orbitals and **two electrons** in the higher energy ##e_(g)## orbitals.

In an **octahedral; field**, for every electron placed in a ##t_(2g)## orbital, you need to **add** ##2/5 * Delta_"oct"## to the total. At the same time, for every electron placed in the ##e_g## orbitals, you need to **subtract** ##3/5 * Delta_"oct"## from the total.

This means that you have

##Delta = overbrace( 3 xx 2/5 Delta_"oct")^(color(blue)("3 electrons in " t_(2g))) - overbrace(2 xx 3/5Delta_"oct")^(color(red)("2 electrons in " e_g)) = 0##

The answer will indeed be **(2)** ##"Fe"^(3+) ->## high spin