Question
Why are $\mathrm{Mn}^{2+}$ compounds more stable than $\mathrm{Fe}^{2+}$ towards oxidation to their $+3$ state?

Answer

Electronic configuration of $\mathrm{Mn}^{2+}$ is $[\mathrm{Ar}]^{18} 3 \mathrm{d}^5$
Electronic configuration of $\mathrm{Fe}^{2+}$ is $[\mathrm{Ar}]^{18} 3 \mathrm{d}^6$
It is known that half-filled and fully-filled orbitals are more stable. Therefore, Mn in $(+2)$ state has a stable $\mathrm{d}^5$ configuration. This is the reason $\mathrm{Mn}^{2+}$ shows resistance to oxidation to $\mathrm{Mn}^{3+}$ Also, $\mathrm{Fe}^{2+}$ has $3 \mathrm{d}^6$ configuration and by losing one electron, its configuration changes to a more stable $3 \mathrm{~d}^5$ configuration. Therefore, $\mathrm{Fe}^{2+}$ easily gets oxidized to $\mathrm{Fe}^{+3}$ oxidation state.

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