The electronic configurations follow the Aufbau principle with exceptions driven by the stability of half-filled ($f^7$) and fully-filled ($f^{14}$) subshells.

1. Europium (Eu, Z=63): [Xe] $4f^7 6s^2$. The $4f$ orbital is exactly half-filled, providing extra stability.
2. Gadolinium (Gd, Z=64): [Xe] $4f^7 5d^1 6s^2$. To maintain the stable half-filled $4f^7$ configuration, the incoming electron enters the $5d$ orbital instead of pairing in the $4f$ orbital.
3. Terbium (Tb, Z=65): [Xe] $4f^9 6s^2$. The electron from the $5d$ orbital (seen in Gd) moves to the $4f$ orbital along with the new electron, resulting in $4f^9$.