Concept:
Chemistry (d-Block Elements) - Colour of Transition Metal Ions.
Step 1: Recall the condition for colour in transition metal ions.
Transition metal ions typically exhibit colour in aqueous solutions due to d-d electronic transitions. This requires the presence of at least one unpaired electron in the d-orbitals (i.e., a partially filled d-subshell, $d^1$ to $d^9$). If the d-subshell is completely empty ($d^0$) or completely full ($d^{10}$), no d-d transition is possible, and the ion will be colourless.
Step 2: Determine the electronic configuration of $Ti^{3+}$.
Titanium (Ti) has an atomic number of 22, with the ground state configuration $[Ar] 4s^2 3d^2$. Losing three electrons to form $Ti^{3+}$ results in the configuration $[Ar] 3d^1$. Since it has one unpaired electron, it undergoes d-d transitions and produces a coloured (violet) solution.
Step 3: Determine the electronic configuration of $V^{3+}$.
Vanadium (V) has an atomic number of 23, with the ground state configuration $[Ar] 4s^2 3d^3$. Losing three electrons to form $V^{3+}$ yields $[Ar] 3d^2$. It has two unpaired electrons, so it is coloured (green/blue).
Step 4: Determine the electronic configuration of $Cu^{2+}$.
Copper (Cu) has an atomic number of 29, with the anomalous ground state configuration $[Ar] 4s^1 3d^{10}$. Losing two electrons to form $Cu^{2+}$ gives $[Ar] 3d^9$. It has one unpaired electron, making its aqueous solution coloured (blue).
Step 5: Determine the electronic configuration of $Sc^{3+}$ and conclude.
Scandium (Sc) has an atomic number of 21, with the ground state configuration $[Ar] 4s^2 3d^1$. To form the $Sc^{3+}$ ion, it loses all three of its valence electrons, resulting in the stable noble gas configuration $[Ar] 3d^0$. With absolutely zero d-electrons available for transitions, it cannot absorb visible light. Therefore, its aqueous solution is entirely colourless.
$$
\therefore \text{The cation that produces a colourless solution is } Sc^{3+}.
$$