Read the passage given and answer the question.

The transition elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example, exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at extreme ends stems from either too few electrons to lose or share (Sc, Ti) on too many d-electrons (hence fewer orbitals available in which to share electrons with others) for higher valence (Cu, Zn). Thus early in the early series scandium (II) is virtually unknown and titanium (IV) is more stable than Ti(III) or Ti(II). At the other end, the only oxidation state of zinc is +2 (no d electrons are involved). The maximum oxidation states of reasonable stability correspond in value to the sum as s- and d-electrons upto  manganese \((Ti^{IV}O_2, V^VO_2^+, Cr^{VI}O_4^{2}, Mn^{VII}O_4 )\) followed by a rather abrupt decrease in stability of higher oxidation states, so that the typical species to follow are \(Fe^{II, III}\), \(Co^{II, III}\), \(Cu^{I, II}\), \(Zn^{II}\).

The variability of oxidation states, a characteristic of transition elements, arises out of incomplete filling of d-orbitals in such a way that their oxidation states differ from each other by unity, e.g., \(V^{II}\), \(V^{III}\), \(V^{IV}\), \(V^V\). This is in contrast with the variability of oxidation states of non transition elements where oxidation states normally differ by a unit or two.

An interesting feature in the variability of oxidation states of the d-block elements is noticedamong the groups (groups 4 through 10). Although in the p-block, the lower oxidation states are favoured by the heavier members (due to inert pair effect), the opposite is true in the groups of d-block. For example, in group 6, \(Mo^{(VI)}\) and \(W^{(VI)}\) are found to be more stable than \(Cr^{(VI)}\). The \(Cr^{(VI)}\) in the form of dichromate in acidic medium is a strong agent, whereas \(MoO_3\) and \(WO_3\) are not.

Low oxidation states are found when a complex compound has ligands capable of \(\pi \)-acceptor character in addition to the \(\sigma \)-bonding. For example, in \(Ni(CO)_4\) and \(Fe(CO)_5\), the oxidation state of nickel and iron is zero.

Identify the stable pair of ions:

\(Mn^{2+},\, \ Fe^{3+}\)

The correct answer is option 2. \(Mn^{2+},\, \ Fe^{3+}\).

Transition metals can exhibit various oxidation states. The stability of these oxidation states often depends on the electronic configuration of the ion and the inherent stability of the resulting electronic configuration.

Pair 1: \(Mn^{3+}\) and \(Fe^{3+}\)

\(Mn^{3+}\)

Electronic Configuration: Manganese (Mn) has the configuration \([Ar] 3d^5 4s^2\).

For \(Mn^{3+}\): Loses three electrons (two from \(4s\) and one from \(3d\)). The resulting configuration is \([Ar] 3d^4\).

Stability: The \(3d^4\) configuration is less stable because it is not a particularly stable electron arrangement compared to half-filled or fully-filled orbitals. \(Mn^{3+}\) is relatively unstable compared to \(Mn^{2+}\) or \(Mn^{4+}\).

\(Fe^{3+}\)

Electronic Configuration: Iron (Fe) has the configuration \([Ar] 3d^6 4s^2\).

For \(Fe^{3+}\): Loses three electrons (two from \(4s\) and one from \(3d\)). The resulting configuration is \([Ar] 3d^5\).

Stability: The \(3d^5\) configuration is a half-filled \(3d\) orbital, which is relatively stable. \(Fe^{3+}\) is a common and stable oxidation state due to this configuration.

Conclusion: \(Fe^{3+}\) is stable, but \(Mn^{3+}\) is less stable compared to its other oxidation states.

Pair 2: \(Mn^{2+}\) and \(Fe^{3+}\)

\(Mn^{2+}\)

Electronic Configuration: The configuration for Mn is \([Ar] 3d^5 4s^2\).

For \(Mn^{2+}\): Loses two electrons (from \(4s\)). The resulting configuration is \([Ar] 3d^5\).

Stability: The \(3d^5\) configuration is half-filled and relatively stable. \(Mn^{2+}\) is a common and stable oxidation state.

\(Fe^{3+}\)

Electronic Configuration: The configuration for Fe is \([Ar] 3d^6 4s^2\).

For \(Fe^{3+}\): Loses three electrons (two from \(4s\) and one from \(3d\)). The resulting configuration is \([Ar] 3d^5\).

Stability: As noted, \(Fe^{3+}\) with a half-filled \(3d\) configuration is relatively stable.

Conclusion: Both \(Mn^{2+}\) and \(Fe^{3+}\) are relatively stable ions. \(Mn^{2+}\) has a stable half-filled \(3d\) configuration, and \(Fe^{3+}\) is also stable due to its half-filled \(3d\) configuration.

Pair 3: \(Ti^{3+}\) and \(Sc^{3+}\)

\(Ti^{3+}\)

Electronic Configuration: Titanium (Ti) has \([Ar] 3d^2 4s^2\).

For \(Ti^{3+}\): Loses three electrons (two from \(4s\) and one from \(3d\)). The resulting configuration is \([Ar] 3d^1\).

Stability: The \(3d^1\) configuration is less stable compared to half-filled or fully-filled \(3d\) orbitals. \(Ti^{3+}\) is less stable compared to \(Ti^{2+}\) or \(Ti^{4+}\).

\(Sc^{3+}\)

Electronic Configuration: Scandium (Sc) has \([Ar] 3d^1 4s^2\).

For \(Sc^{3+}\): Loses three electrons (two from \(4s\) and one from \(3d\)). The resulting configuration is \([Ar]\).

Stability: \(Sc^{3+}\) is relatively stable with a noble gas configuration, but \(Ti^{3+}\) is less stable.

Conclusion: While \(Sc^{3+}\) is relatively stable, \(Ti^{3+}\) is less stable compared to other states.

Pair 4: \(Ti^{4+}\) and \(Sc^{2+}\)

\(Ti^{4+}\)

Electronic Configuration: Titanium (Ti) has \([Ar] 3d^2 4s^2\).

For \(Ti^{4+}\): Loses four electrons (two from \(4s\) and two from \(3d\)). The resulting configuration is \([Ar]\).

Stability: The \(Ti^{4+}\) ion is stable with a noble gas configuration, but it is highly oxidizing and less common in comparison to lower oxidation states.

\(Sc^{2+}\)

Electronic Configuration: Scandium (Sc) has \([Ar] 3d^1 4s^2\).

For \(Sc^{2+}\): Loses two electrons (from \(4s\)). The resulting configuration is \([Ar] 3d^1\).

Stability: \(Sc^{2+}\) is not common and generally less stable compared to \(Sc^{3+}\).

Conclusion: \(Ti^{4+}\) is relatively stable, but \(Sc^{2+}\) is not common and generally less stable.

Overall Conclusion

The pair of ions that are both relatively stable are \(Mn^{2+}\) and \(Fe^{3+}\). Both ions exhibit stability in their respective oxidation states and are commonly encountered.

The correct answer is option 2: \(Mn^{2+}\), \(Fe^{3+}\).