Step 1: Understanding the Concept:
Colour in transition metal ions arises from d-d transitions, which require unpaired electrons or vacant d-orbitals.
Step 2: Detailed Explanation:
\begin{itemize}
\item Cu\(^{2+}\): d\(^9\) configuration, one unpaired electron, coloured (blue).
\item Cu\(^+\): d\(^{10}\) configuration, fully filled, no d-d transitions possible, colourless.
\item Ni\(^{2+}\): d\(^8\) configuration, two unpaired electrons, coloured (green).
\item Fe\(^{3+}\): d\(^5\) configuration, five unpaired electrons, coloured (yellow/brown).
\end{itemize}
Step 3: Final Answer:
Cu\(^+\) is colourless, option (B).