1. Identify the metal $M$

In the first transition series ($3d$-series), the metal with the highest enthalpy of atomisation is chromium.

This is because chromium has strong metallic bonding due to the presence of many unpaired electrons.

So, $M = \mathrm{Cr}$

2. Identify the green aquated ion

Chromium forms several ions, and one common green aquated ion is: $[\mathrm{Cr(H_2O)_6}]^{2+}$ which corresponds to $\mathrm{Cr}^{2+}$

Thus, in the statement, the relevant ion is $\mathrm{M}^{n+} = \mathrm{Cr}^{2+}$

3. Determine the oxide formed by this ion

The oxide of $\mathrm{Cr}^{2+}$ is: $\mathrm{CrO}$

Here chromium is in the +2 oxidation state.

4. Nature of $\mathrm{CrO}$

For transition metals, lower oxidation state oxides are basic, intermediate ones are amphoteric, and higher oxidation state oxides are acidic.

Since $\mathrm{CrO}$ is chromium in the low oxidation state $+2$, it is a basic oxide.

5. Check options

• A: basic $\rightarrow$ Correct
• B: neutral $\rightarrow$ Incorrect
• C: amphoteric $\rightarrow$ Incorrect
• D: acidic $\rightarrow$ Incorrect

Therefore, the correct answer is: $\boxed{\text{A: basic}}$