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Why are \[{\text{M}}{{\text{n}}^{{\text{ + 2}}}}\]compounds more stable than \[{\text{F}}{{\text{e}}^{{\text{ + 2}}}}\]towards oxidation to their +3 state?

Answer
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Hint: Oxidation state means a number which is assigned to an element to represent the number of electrons lost from that element or the number of electrons consumed by the element. Oxidation state can be both positive or negative. Transition elements show more than one oxidation state.

Complete step by step answer:
In case of transition elements due to presence of electrons at d orbitals , which is closer to the outermost shell of the metal. They show variable oxidation state. With increasing the number of electrons of the d orbitals (up to 5 electrons), the numbers of oxidation state increases.
The electronic configuration of \[{\text{M}}{{\text{n}}^{{\text{ + 2}}}}\] is \[\left[ {{\text{Ar}}} \right]{\text{3}}{{\text{d}}^{\text{5}}}{\text{4}}{{\text{s}}^{\text{0}}}\]
The electronic configuration of \[{\text{F}}{{\text{e}}^{{\text{ + 2}}}}\]is \[\left[ {{\text{Ar}}} \right]{\text{3}}{{\text{d}}^{\text{6}}}{\text{4}}{{\text{s}}^{\text{0}}}\]
In the case of \[{\text{M}}{{\text{n}}^{{\text{ + 2}}}}\] the number of d electrons is 5 which is a stable half-filled configuration of the ion. Due to this stable configuration , removal of one electron from the d orbital to get the +3 oxidation state is not possible. On the other hand, in case of \[{\text{F}}{{\text{e}}^{{\text{ + 2}}}}\] the number of d electrons is 6. Removal of one electron forms a stable half-filled configuration. That is why \[{\text{M}}{{\text{n}}^{{\text{ + 2}}}}\] compounds are more stable than \[{\text{F}}{{\text{e}}^{{\text{ + 2}}}}\] towards oxidation to their +3 state.

Note:
Actinides are F-block elements(atomic number 89 to103) with the general electronic configuration of outermost shell is \[\left[ {{\text{Rn}}} \right]{\text{5}}{{\text{f}}^{{\text{1 - 14}}}}{\text{6}}{{\text{d}}^{{\text{0 - 1}}}}{\text{7}}{{\text{s}}^{\text{2}}}\]. Where the last electron enters to the inner 5f-orbital of the actinides. Actinides are also known as rare earth metals.Now according to the Aufbau principle(L+S value) the energy order of the orbitals should be 5f<6d<7s. but due to the more diffuse orbitals their energy becomes more or less the same. As a result, electrons can be excited easily . Due to this reason actinides shows greater range of oxidation states. But if we consider lanthanides due to comparatively small size of 4f orbital they have limited number of oxidation states