Key Idea Only those transition metal complexes are expected to absorb visible light, in which d-subshell is incomplete (ie, has unpaired electron) and excitation of electron from a lower energy arbital to higher energy orbital is possible.
(a) In $\left[\mathrm{Sc}\left(\mathrm{H}_2 \mathrm{O}\right)_3\left(\mathrm{NH}_3\right)_3\right]^{3+}, \mathrm{Sc}$ is present as $\mathrm{Sc}^{3+}$.
$\mathrm{Sc}^{3+}=[\mathrm{Ar}] 3 \mathrm{~d}^0, 4 \mathrm{~s}^0$
Since, in this complex excitation of electron is not possible, it will not absorb visible light.
(b) In $\left[\mathrm{Ti}(\mathrm{en})_2\left(\mathrm{NH}_3\right)_2\right]^{4+}, \mathrm{Ti}$ is present as $\mathrm{Ti}^{4+}$.
$\mathrm{Ti}^{4+}=[\mathrm{Ar}] 3 \mathrm{~d}^0, 4 \mathrm{~s}^0$
Hence, it will not absorb visible light.
(c) In $\left[\mathrm{Cr}\left(\mathrm{NH}_3\right)_6\right]^{3+}, \mathrm{Cr}$ is present as $\mathrm{Cr}^{3+}$.
$\mathrm{Cr}^{3+}=[\mathrm{Ar}] 3 \mathrm{~d}^3, 4 \mathrm{~s}^0$
Since, this complex has three unpaired electrons, excitation of electrons is possible and thus, it is expected that this complex will absorb visible light.
(d) In $\left[\mathrm{Zn}\left(\mathrm{NH}_3\right)_6\right]^{2+}, \mathrm{Zn}$ is present as $\mathrm{Zn}^{2+}$.
$\begin{gathered}
\mathrm{Zn}^{2+}=[\mathrm{Ar}] 3 \mathrm{~d}^{10}, 4 \mathrm{~s}^0 \\
{\left[\mathrm{Zn}\left(\mathrm{NH}_3\right)_6\right]^{2+}=[\mathrm{Ar}] 3 d^{10}}
\end{gathered}$
Hence, this complex will not absorb visible light.
Since, this complex has three unpaired electrons, excitation of electrons is possible and thus, it is expected that this complex will absorb visible light.
(d) In $\left[\mathrm{Zn}\left(\mathrm{NH}_3\right)_6\right]^{2+}, \mathrm{Zn}$ is present as $\mathrm{Zn}^{2+}$.
$\begin{gathered}
\mathrm{Zn}^{2+}=[\mathrm{Ar}] 3 \mathrm{~d}^{10}, 4 \mathrm{~s}^0 \\
{\left[\mathrm{Zn}\left(\mathrm{NH}_3\right)_6\right]^{2+}=[\mathrm{Ar}] 3 d^{10}}
\end{gathered}$
Hence, this complex will not absorb visible light.