Which of the following is the electronic configuration of the central…

The correct answer is option 3.\(t_{2g}^5e_g^2\).

The given complex is \([Co(H_2O)_6]^{2+}\)

Let the oxidation number of the central metal be \(x\)

so, \(x + 6(0) = +2\)

or, \(x = +2\)

The electronic configuration of the central metal atom is

\(_{27}Co = [_{18}Ar] 4s^2 3d^7\)

But the central metal is in \(+2\) oxidation state so the configuration will be

\(Co^{2+} = [_{18}Ar] 4s^0 3d^7\)

Here, \(H_2O\) is an weak field ligand so the filling of electron in the \(d\)-orbital will be \(t_{2g}^5e_g^2\).