Analyze Statement I

• Sodium has metallic radius approximately $1.86\,\text{Å}$.
• When sodium forms $\mathrm{Na^+}$, it loses one electron: $\mathrm{Na} : 1s^2 2s^2 2p^6 3s^1$ $\mathrm{Na^+} : 1s^2 2s^2 2p^6$
• The outermost shell changes from the $n=3$ shell to the $n=2$ shell.
• Also, the number of electrons decreases while nuclear charge remains the same, so effective attraction per electron increases.
• Therefore, $\mathrm{Na^+}$ is smaller than metallic sodium.

Hence, Statement I is true.

Analyze Statement II

Statement II says: Ions are always smaller in size than the corresponding elements.

This is not always true.

• Cations are usually smaller than their parent atoms, e.g. $\mathrm{Na^+} < \mathrm{Na}$
• But anions are larger than their parent atoms, e.g. $\mathrm{Cl^-} > \mathrm{Cl}$

So the word always makes the statement false.

Hence, Statement II is false.

Choose the correct option

• Statement I: True
• Statement II: False

Therefore, the correct option is: $\boxed{\text{D}}$

Compare with stored correct answer

• Derived answer: $\boxed{\text{D}}$
• Stored correct answer: $\boxed{\text{D}}$

They match.