Step 1: Understanding the Question:
We are given four transition elements from the 3d series and need to identify which one shows the maximum variation in oxidation states, specifically spanning continuously from $+2$ to $+7$.
Step 2: Key Formula or Approach:
The number of oxidation states exhibited by a transition element depends on the availability of electrons in both the outermost $\mathrm{4s}$ subshell and the unpaired electrons in the inner $\mathrm{3d}$ subshell. The maximum oxidation state shown by a $3\text{d}$ element is generally given by:
$$\text{Maximum Oxidation State} = (\text{Number of electrons in }\mathrm{4s}) + (\text{Number of unpaired electrons in }\mathrm{3d})$$
Step 3: Detailed Explanation:
Let's analyze the valence electronic configuration of Manganese ($\mathrm{Mn}$, $Z = 25$):
$$\mathrm{Mn} = [\mathrm{Ar}]\, \mathrm{3d^5\, 4s^2}$$
Manganese has $2$ electrons in its $\mathrm{4s}$ orbital and $5$ unpaired electrons in its half-filled $\mathrm{3d}$ orbital. Because all $7$ valence electrons can actively participate in bonding, manganese can exhibit the highest number of oxidation states among the first transition series:
$+2$: e.g., $\mathrm{Mn^{2+}}$ in $\mathrm{MnSO_4}$
$+3$: e.g., $\mathrm{Mn_2O_3}$
$+4$: e.g., $\mathrm{MnO_2}$
$+6$: e.g., $\mathrm{MnO_4^{2-}}$ (Manganate ion)
$+7$: e.g., $\mathrm{MnO_4^-}$ (Permanganate ion)
Other options like $\mathrm{Cr}$ typically top out at $+6$, $\mathrm{V}$ at $+5$, and $\mathrm{Ni}$ at $+4$.
Step 4: Final Answer:
The element exhibiting oxidation states from $+2$ to $+7$ is Manganese ($\mathrm{Mn}$), corresponding to option (A).