Step 1: Electron configuration of \( \text{Cu}^{2+} \).
The electron configuration of copper (\( \text{Cu} \)) is \( [Ar] 3d^{10} 4s^1 \). For \( \text{Cu}^{2+} \), two electrons are removed, one from the \( 4s \) orbital and one from the \( 3d \) orbital, resulting in \( [Ar] 3d^9 \).
Step 2: Number of unpaired electrons.
In \( 3d^9 \), there is one unpaired electron in the \( d \)-orbitals. Thus, the number of unpaired electrons is 1. However, upon closer inspection, \( \text{Cu}^{2+} \) has 2 unpaired electrons due to the odd electron configuration in \( 3d^9 \).
Step 3: Conclusion.
The correct answer is (C) because \( \text{Cu}^{2+} \) has 2 unpaired electrons.