The transition elements exhibit variable oxidation states because (n −1)d electrons can also participate in bonding as the energy difference between (n −1)d and ns orbitals is very small. The oxidation states of transition elements change in units of one whereas in p-block elements oxidation states normally differ by two units. The minimum oxidation state exhibited by a transition element is equal to the number of electrons in the ns orbital. The maximum oxidation state that can be exhibited by a transition element is equal to the total number of electrons present in both ns and (n −1)d orbitals. The elements in the middle exhibit more oxidation states, e.g., manganese exhibits from +2 to +7. The elements at the extreme ends exhibit a lesser number of oxidation states. This is because of the availability of lesser electrons to lose or to share in the earlier elements or too many d electrons due to which lesser number of unpaired electrons to share at the end. Due to anomalous electronic configuration, chromium and copper can exhibit a minimum oxidation state of +1. In the first series, the maximum oxidation state increases up to Mn and then decreases from Fe onwards. In the first series, Mn exhibits the maximum oxidation state +7. In the second series, a stable maximum oxidation state is exhibited by technetium, and an unstable maximum oxidation state +8 is exhibited by ruthenium. In the third series, stable maximum oxidation +8 is exhibited by osmium. The transition metal ions having completely filled and exactly half-filled d-sub level and those having octet in their outermost shell are stable. The stabilities of Cr³⁺ and Mn⁴⁺ ions is due to high lattice energy in solid state and high hydration energy in their aqueous solutions. Fe³⁺ ion is more stable than Fe²⁺ ion because of the stable half-filled 3d⁵ electronic configuration in Fe³⁺. In the last five elements of the 3d series, the 3d electrons are stabilized and require more energy for their removal because the 3d orbital contracts more and come nearer to the nucleus with an increase in nuclear charge. Thus in the last five elements, the +2 oxidation state becomes more stable (except Fe³⁺ ).

The stability of ferric ions is due to

half-filled d-orbitals

The correct answer is option 2. half-filled d-orbitals.

The stability of the ferric ion (\(\text{Fe}^{3+}\)) is attributed to its electron configuration, specifically the half-filled d-orbitals. Here is a detailed explanation:

1. Electron Configuration of Iron:

The atomic number of iron (Fe) is 26, so its ground-state electron configuration is \([ \text{Ar} ] 3d^6 4s^2\).

2. Formation of \(\text{Fe}^{3+}\) Ion:

When iron loses three electrons to form the \(\text{Fe}^{3+}\) ion, the electrons are removed first from the 4s orbital and then from the 3d orbitals.  The electron configuration of \(\text{Fe}^{3+}\) becomes \([ \text{Ar} ] 3d^5\).

3. Half-Filled d-Orbitals:

The \(\text{Fe}^{3+}\) ion has five electrons in its 3d orbitals (3d^5 configuration). A half-filled d^5 configuration is particularly stable due to several factors:

Symmetrical Distribution: The d orbitals are symmetrically filled with one electron in each of the five d orbitals, reducing electron-electron repulsion.

Exchange Energy: This configuration maximizes the number of parallel spins, which increases the exchange energy and thus stabilizes the atom or ion.

Subshell Stability: A half-filled subshell (such as \(3d^5\)) is more stable than other configurations due to the overall balance and minimal repulsion among electrons.

These factors collectively contribute to the enhanced stability of the ferric ion.

Therefore, the stability of ferric ions (\(\text{Fe}^{3+}\)) is due to: half-filled d-orbitals.