The stability of an electronic configuration increases significantly when subshells are completely filled or half-filled. For f-orbitals, a half-filled configuration means having 7 electrons ($f^7$). - Europium (Eu, Z=63) has the electronic configuration $ [Xe] 4f^7 6s^2 $. Its $4f$ subshell is half- filled. - Gadolinium (Gd, Z=64) has the electronic configuration $ [Xe] 4f^7 5d^1 6s^2 $. Its $4f$ subshell is half-filled. The other elements given do not have half-filled f-orbitals in their ground state: - Samarium (Sm, Z=62): $ [Xe] 4f^6 6s^2 $ - Terbium (Tb, Z=65): $ [Xe] 4f^8 5d^1 6s^2 $ - Promethium (Pm, Z=61): $ [Xe] 4f^5 6s^2 $ Thus, Eu and Gd are the elements with half-filled f-orbitals.