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(D) $(I)$ Incorrect: $Li^+$ has the smallest size among alkali metals,so it gets most extensively hydrated. The hydrated radius is $Li^+ > Na^+ > K^+

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$(II)$ and $(III)$

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(D) $(I)$ Incorrect: $Li^+$ has the smallest size among alkali metals,so it gets most extensively hydrated. The hydrated radius is $Li^+ > Na^+ > K^+ > Rb^+ > Cs^+$. Larger hydrated ions have lower ionic mobility. Thus,the ionic mobility of hydrated $Li^+$ is less than that of hydrated $Na^+$.$(II)$ Correct: $P$ $(3s^2 3p^3)$ has a stable half-filled $p$-orbital,making its $IE_1$ higher than $S$ $(3s^2 3p^4)$. For $IE_2$,$P^+$ $(3s^2 3p^2)$ and $S^+$ $(3s^2 3p^3)$. $S^+$ has a half-filled $p$-orbital,making its $IE_2$ higher than $P^+$.$(III)$ Correct: Lithium has the highest negative standard electrode potential $(E^\circ = -3.04 \ V)$ due to its very high hydration energy,making it the strongest reducing agent in aqueous solution.

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