Step 1: Concept
The Wilkinson's catalyst is a well-known organometallic compound used as a homogeneous catalyst for the hydrogenation of alkenes.
Step 2: Meaning
The chemical formula for Wilkinson's catalyst is $RhCl(PPh_{3})_{3}$, where $Rh$ is Rhodium, $Cl$ is Chlorine, and $PPh_{3}$ is Triphenylphosphine.
Step 3: Analysis
In the complex $RhCl(PPh_{3})_{3}$, the triphenylphosphine ($PPh_{3}$) ligands are neutral and the chloride ($Cl$) ligand has a $-1$ charge. To maintain electrical neutrality, the oxidation state of Rhodium must be $+1$.
Step 4: Conclusion
Therefore, the metal ion is $Rh^{+}$, the ligand is $Cl^{-}$, and the other ligand is $PPh_{3}$.
Final Answer: (B)