d and f Block Elements - General introduction and electronic configuration

Write the electronic configuration of $Fe^{3+}$ ($Z$ for $Fe = 26$).

$[Ar] 3d^5$

The ground state configuration of $Fe$ is $[Ar] 3d^6 4s^2$. To form $Fe^{3+}$, three electrons are removed. Electrons are removed from the $4s$ orbital first, then from the $3d$ orbital: $[Ar] 3d^6 4s^2 \rightarrow [Ar] 3d^5$.

Why does Gadolinium ($Z=64$) have a configuration of $[Xe] 4f^7 5d^1 6s^2$ instead of $[Xe] 4f^8 6s^2$?

Due to the extra stability of the half-filled $f$-subshell ($4f^7$).

The $4f$ and $5d$ orbitals are very close in energy. By shifting one electron to the $5d$ orbital, the $4f$ subshell becomes exactly half-filled ($4f^7$), which provides extra exchange energy and symmetry, making the atom more stable.

Explain why $Sc^{3+}$ is colorless while $Ti^{3+}$ is colored in aqueous solution.

$Sc^{3+}$ has $3d^0$ configuration, while $Ti^{3+}$ has $3d^1$ configuration.

Color in transition metal ions usually arises from $d-d$ transitions. $Sc^{3+}$ ($[Ar] 3d^0$) has no electrons in the $d$-orbital to undergo transition. $Ti^{3+}$ ($[Ar] 3d^1$) has one unpaired electron which can be excited, resulting in the absorption of specific wavelengths of light.