Concept: The number of electrons involved in a redox process corresponds to the change in the oxidation state of the atom being reduced.
• Initial State: In Permanganate ($MnO_4^-$), the oxidation state of Mn is +7.
• Reduction: $e^- \text{ involved} = (\text{Initial Oxidation State}) - (\text{Final Oxidation State})$.
Step 1: Calculate the change for each Manganese species.
1. To Manganese(II) salt ($Mn^{2+}$):
Change = $(+7) - (+2) = 5$ electrons. (Occurs in acidic medium).
2. To Manganate ($MnO_4^{2-}$):
Change = $(+7) - (+6) = 1$ electron. (Occurs in strongly alkaline medium).
3. To Manganese dioxide ($MnO_2$):
Change = $(+7) - (+4) = 3$ electrons. (Occurs in neutral or faintly alkaline medium).
Step 2: Identify the sequence.
The calculated electron counts are 5, 1, and 3 respectively. This matches the sequence in Option (A).