Step 1: Electron configuration and unpaired electrons.
To determine the number of unpaired electrons, we need to consider the electron configuration of each ion and identify the number of unpaired electrons.
Step 2: Analysis of options.
(A) \( \text{Mg}^{2+} \): The electron configuration of \( \text{Mg} \) is \( [Ne] \), and for \( \text{Mg}^{2+} \), it is \( [Ne] \), with no unpaired electrons.
(B) \( \text{Ti}^{3+} \): The electron configuration of \( \text{Ti} \) is \( [Ar] 3d^2 4s^2 \), and for \( \text{Ti}^{3+} \), it is \( [Ar] 3d^1 \), with 1 unpaired electron.
(C) \( \text{V}^{3+} \): The electron configuration of \( \text{V} \) is \( [Ar] 3d^3 4s^2 \), and for \( \text{V}^{3+} \), it is \( [Ar] 3d^2 \), with 2 unpaired electrons.
(D) \( \text{Fe}^{3+} \): The electron configuration of \( \text{Fe} \) is \( [Ar] 3d^6 4s^2 \), and for \( \text{Fe}^{3+} \), it is \( [Ar] 3d^5 \), with 5 unpaired electrons.
Step 3: Conclusion.
The correct answer is (C) because \( \text{V}^{3+} \) has 2 unpaired electrons.