Which one of the following pairs of ions has the same electronic configuration?

Fe³⁺, Mn²⁺

The correct answer is option 2. \(Fe^{3+}, Mn^{2+}\).

\(Fe^{3+}\) (iron ion) and \(Mn^{2+}\) (manganese ion) have the same electronic configuration. Both ions have the electron configuration \([Ar]3d^5\). They both have five unpaired electrons in the 3d orbital, resulting in similar electronic configurations.

In option (1), \(Cr^{3+}\) has the electronic configuration \([Ar]3d^3\), which is different from the electronic configuration of \(Fe^{3+}\) is \([Ar]3d^5\).

In option (3), \(Fe^{3+}\) has the electronic configuration \([Ar]3d^5\), while \(Co^{3+}\) has the electronic configuration \([Ar]3d^6\). These configurations are not the same.

In option (4), \(Sc^{3+}\) has the electronic configuration \([Ar]3d^0\), which is different from the electronic configuration of \(Cr^{3+}\) is \([Ar]3d^3\).

Therefore, the correct answer is (2) \(Fe^{3+}, Mn^{2+}\), as they have the same electronic configuration of \([Ar]3d^5\).